# A Guide to Calculate Convection Coefficients for Thermal Problems Application Note

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

Download "A Guide to Calculate Convection Coefficients for Thermal Problems Application Note"

## Transcription

1 A Guide to Calculate Convection Coefficients for Thermal Problems Application Note Keywords: Thermal analysis, convection coefficients, computational fluid dynamics, free convection, forced convection. Abstract: The present application note is a guide that can be used to calculate thermal convection coefficients. As such it approaches the topic of computational fluid dynamics (CF) since the problem of calculating convection coefficients is situated at the intersection between CF and Thermal analysis. Some basic presentation of the theoretical bacground is also included for more clarity of the approach of the subject. A few eamples of the computational process are also included and deal with practical cases of free convection as well as forced convection.

2 1. Introduction Procedure to calculate convection coefficients As widely nown the specification of convection coefficients is a necessity in thermal applications when cooling of surfaces in contact with fluids (liquids and/or gases) occurs and a thermal convection mechanism taes place. At its core the problem is in fact one in which the thermal aspect is strongly coupled with the fluid flow aspect: temperature distribution influences the fluid flow characteristic quantities while the fluid flow parameters influence the temperature distribution. It can be said that in such a scenario convection coefficients if necessary at all- can be obtained as one of the results of a coupled Computational Fluid ynamics (CF) Thermal analysis. While the full analysis of the coupled problem is quite complicated, there are ways to simplify the computational tas and produce results for the convection coefficients that have acceptable accuracy. One of the most widely spread is the method using dimensionless parameters. This method is quite easy to use, however it has the disadvantage that it doesn t allow an understanding of underlying physics of this comple phenomenon. This is why in the following paragraphs we ll also discuss the basics of the physical mechanisms of heat convection since a minimal understanding on the physical bacground is necessary. Only after that we ll present the mechanics of calculating the convection coefficients based on formulas and numbers. When it comes to convection, two main cases need to be considered. The case of free (natural) convection and the case of forced convection. The essential components of heat transfer by convection mechanisms are given in Newton s law of cooling: Q w ( T ) h A T (1) where Q is the rate of heat (power) transferred between the eposed surface A of the wall and the fluid. T w is the temperature of the wall, T is the temperature of the free stream of fluid, h is the convection coefficient (also called film coefficient), the quantity we want to calculate. An observation is in order regarding (1): the equation should be seen more as a definition of the convection coefficient h rather than a law of heat transfer by convection. Indeed, equation (1) doesn t eplain anything about the convection mechanism, which is a rather complicated one. So the simplicity of (1) is misleading and in sharp contrast with what we now about the compleity of the convection phenomenon. All that compleity is revealed only when we investigate the ways to find the dependencies of h the convection coefficient- on many factors. We find that h is a complicated function of the fluid flow, thermal properties of the fluid, the geometry and orientation in space of the system that ehibits convection. Moreover, the convection coefficient is not uniform on the entire surface and it also depends on the location where the temperature of the fluid is

3 evaluated. In most cases it is therefore convenient and practical to use average values for the convection coefficients.. Quantities and numbers frequently used in convection coefficient calculations The occurrence of turbulent flow is usually correlated with Rayleigh number, which is simply the product of the Grashof and Prandtl numbers: Ra Gr Pr () Grashof number is given by the epression in (3) Gr 3 L g ρ β ( T µ w T ) 3 L g β ( T ν w T ) (3) where L [m] is the characteristic length, g [m / s ] is gravity, ρ [Kg /m 3 ] is the density of the fluid, β [1/K] is the thermal epansion coefficient, µ [Kg / m s] is the dynamic viscosity, ν [m / s] is the inematic viscosity. All fluid characteristics (such as density, viscosity, etc) are evaluated at film temperature, Tw + T T f For perfect (ideal) gases β 1 T f, while for liquids and non-ideal gases the epansion coefficient must be obtained from appropriate property tables. (4) Prandtl number is the ratio of two molecular transport properties, the inematic viscosity ν which affects the velocity profile and the thermal diffusivity α, which affects the temperature profile. α ρ c p µ ν ρ ν c p µ Pr α where [W/m K] is the fluid thermal conductivity, c p [J/Kg K] is the fluid specific heat.

4 Nusselt number is used directly to evaluate the convection coefficient according to (5): Nu h L (5) In equation (5) the bar above quantities signifies an average value. A few comments are necessary regarding the characteristic length. For a vertical wall the characteristic length is the height H of the wall (for free convection), for horizontal cylinder or for a sphere the characteristic length is the diameter. 3. The case of free convection Free convection occurs when an object is immersed in a fluid at a different temperature. It is considered that the fluid is in a quiescent state. In this situation there is an energy echange between the fluid and the object. From a physics perspective the heat echange is due to buoyancy forces caused by density gradients developed in the body of the fluid. As a result free convection currents are produced that facilitate the heat transfer between the object and the fluid. The body force responsible for the free convection currents is as a rule - of gravitational nature (occasionally it may be centrifugal in rotating machines). Because gravity plays an important role in the convection phenomenon, the orientation in space of the respective walls matters for the calculation process of the respective convection coefficients. Free convection originates from a thermal instability: warmer air moves upward while the cooler, heavier air moves downward. A different type of instabilities may also arise: hydrodynamic instabilities that relate to a transition between a laminar flow to a turbulent flow. The laminar or turbulent character of the fluid flow impact on the heat echange mechanism between object walls and fluids. Therefore we have to have a way to characterize the hydrodynamic character of the flow in order to choose the applicable formulas for the calculation of the convection coefficients. Since the mechanism of convection is strongly dependent on both the fluid flow pattern and on the temperature distribution in the vicinity of the wall we ll tae a loo at the respective profiles. Temperature profile T w Velocity profile T Fig. 1 Temperature and velocity boundary layers

5 ue to the viscosity of the fluid, a very thin layer (a few molecular mean free path thic) doesn t move relative to the wall. This maes the velocity to increase from zero at the wall to a maimum value and then decrease bac to zero where the uniform temperature of the fluid (air) is reached. The temperature decreases from the value at the wall T w to room temperature T in the same distance from the wall. It is now clear that the temperature and velocity distributions are strongly interrelated. Also the distance from the wall in which they are related is the same since due to the uniformity of the temperature (ambient room temperature) the differences in density cease to eist. As a direct consequence the buoyancy in the volume of the fluid disappears too. Another observation that can be made is that due to the motionless of the air in the immediate vicinity of the wall, the heat transfer through this layer is by thermal conduction only. The actual convection mechanism is only active away from the wall. So in what we usually call convection, both thermal conduction and convection are present and interdependent. Considering a constant temperature wall, there is a relatively small temperature increase as the air moves upward. The increase of temperature in this boundary layer near the wall causes the heat transfer rate to decrease in the upward direction. For a sufficiently high wall the flow pattern can change from a laminar flow to a turbulent flow. This is another reason why convection is such a complicated phenomenon and quite difficult to treat with very high accuracy. The calculation of an average convection heat transfer coefficient is an approimation but as a rule a satisfactory one in most practical applications where convection is present. For most engineering calculations the convection coefficient is obtained from a relation of the form: Nu h L C Ra n (6) where Ra is the Rayleigh number (), C and n are coefficients. Typically n 1/4 for laminar flow and n 1/3 for turbulent flow. For turbulent flow Ra > 10 9, for laminar flow Ra < Vertical walls Epressions of the form (6) are used for vertical isothermal walls and are plotted in Fig.. All applicable properties of the fluid are evaluated at film temperature T f. For Rayleigh numbers less than 10 4, the Nusselt number should be obtained directly from Fig. rather than using (6).

6 C 0.59 N 1/4 C 0.1 N 1/3 laminar turbulent Fig. Nusselt number for natural convection (vertical wall) Strictly speaing equations of form (6) are applicable for isothermal walls. There may be situations where the wall may ehibit a uniform heat flu over the surface. In this case, the temperature over the surface of the wall is not necessarily constant. The film temperature is to be calculated with the temperature of the wall measured at the midpoint of the wall. An alternative formula that can be used for the entire range of Rayleigh numbers is presented in (7a): N u Ra [1 + (0.49 / Pr) 1/ 6 ] 9 /16 8 / 7 (7a) For the case of laminar flow equation (7a) is applicable, however a slightly better accuracy is obtained from (7b): N u 1/ Ra Ra 10 9 /16 4 / 9 [1 + (0.49 / Pr) ] 9 (7b)

7 3. Inclined surfaces The mechanics of the heat transfer is now different from the case with vertical walls. For an inclined wall the buoyancy force has a component normal as well as parallel to the respective surface. Therefore there will be a reduction in fluid velocity in a direction parallel to the plate. This reduction however doesn t necessarily translate in a reduction of the convection coefficient. The other determining factor in the mechanism is the whether the surface being considered is the top surface or the bottom surface. For most frequently encountered situations and for walls inclined from vertical with an angle θ between 0 and 60 degrees, the only change in the calculation of the convection coefficient is to replace g with g cos θ in (3). It should be noted that this is only appropriate for top and bottom surfaces of cooled and heated plates respectively. 3.3 Horizontal surfaces For horizontal plates, the buoyancy forces are essentially normal to the plate. As for inclined surfaces the convection mechanism is influenced by whether the surface is cooled or heated and by whether the surface is facing upward or downward. For a cold surface facing downward and for a hot surface facing upward the convection is much more effective than in the opposite cases. In case of horizontal surfaces we define the characteristic length as the ratio between the area of the surface and the perimeter (8): L A P (8) The formulas for the Nusselt number are: Upper surface of heated plate or lower surface of cooled plate: Nu 0.54 Ra Nu 0.15 Ra 1/ 4 (10 ( Ra 10 Ra ) ) (9) Lower surface of heated plate or upper surface of cooled plate: N u Ra 1/ (10 Ra ) (10) 3.4 Long horizontal cylinder Equation (11) gives the formula valid for the isothermal long cylinder. The formula (11) is an average value valid for a large spectrum of Rayleigh numbers. N u 1/ Ra /16 8 / 7 Ra [1 + (0.559 / Pr) ] 1 (11)

8 In the calculation regarding the Rayleigh number in (11) as characteristic length is considered the diameter of the cylinder. 4. The case of forced convection The physics of the heat transfer in the case of forced convection is similar to the natural (free) convection case. The first step in the process of calculating the convection coefficient is to determine the character (laminar or turbulent) of the flow since the convection coefficient depends strongly on which of these conditions eist. Similarly to the situation encountered in the case of free convection, a velocity boundary layer is developed. The boundary layer is initially laminar but at some distance from the leading edge small disturbances appear, are amplified and after a transition region they develop into a completely turbulent flow region. Therefore we ll assume that at some distance (critical distance c ) from the leading edge the turbulent flow occurs. This location is determined by the Reynolds number, Re ρ u µ u ν (1) where u is the velocity of the free stream of fluid. The physical interpretation of the Reynolds number is that it represents the ratio between inertia forces and viscous forces. In any flow there are some disturbances that can be amplified to lead to a turbulent flow. A small value of the Reynolds number means that the viscous forces are relatively important and the amplification of the disturbances is prevented. Also the thicness of the velocity boundary layer is related to the Reynolds number: at low values of the number we epect the thicness of the layer to increase. The role of the Reynolds number in forced convection is similar to the role of the Grashof number in free convection. Note that the Grashof number is a measure of the ratio between buoyancy forces to viscous forces in the velocity boundary layer. The critical value of the Reynolds number for which the flow over a flat plate transitions from a laminar to a turbulent flow varies between 10 5 and , depending on the roughness of the surface and the turbulence in the free stream. It is usual to consider for calculations a representative value of With this value equation (1) can be used to determine the critical length where the transition begins. The location where the transition begins is more conventional than physical, in reality the transition between laminar flow and turbulent occurs in a buffer zone between the two. However the critical characteristic length (measured from the leading edge) can be used as an average value in calculations for the purpose of determining the appropriate convection coefficient. It is

9 possible in practical applications to encounter situations where on the same surface the fluid flow transitions from a laminar flow to a turbulent flow. As a consequence it may be necessary to adjust the calculation of the convection coefficient accordingly. There is another number which is important in forced convection. As in the case of free convection one has to consider the Prandtl number. The significance of the Prandtl number is that it represents the ratio between energy transport by diffusion in the velocity layer and the thermal layer. For gases the Prandtl number is close to 1, for liquid metals Pr << 1, for oils the opposite is true, Pr >> Laminar flow over flat plates The convection coefficient is in general a function of distance (from the leading edge) mainly due to the fact that the Reynolds number (1) depends on. Therefore we ll give both a local value and an average value for the Reynolds number. Equation (13) is used for the laminar flow over isothermal plates for the local value of the Nusselt number. Equation (14) yields the average value of the Nusselt number. If the flow is laminar over the entire surface the may be replaced by L and (14) can be used to predict average conditions over the entire surface. Nu h 1/ 0.33 Re Pr Pr 0.6 (13) N u h 1/ Re Pr Pr 0.6 (14) As for free convection all fluid properties are evaluated at film temperature using (4). Note that the average value given by (14) for a surface from the leading edge to a location is twice the local value at that point. For low Prandtl numbers (the case of liquid metals) equations (13) and (14) cannot be applied. In such cases (15) should be used: Nu Pe 1/ Pr 0.05, Pe 100 (15) where Pe Re Pr is the Peclet number A single equation that can be applied for all Prandtl numbers (laminar flow over an isothermal plate) is presented in (16). Nu Re [1 + ( / Pr) Pr 1/ Pe / 3 1/ 4 ] 100 (16)

10 While (16) can be used for local evaluations of the convection coefficient, the average Nusselt number can be calculated with Nu Nu as discussed above. 4. Turbulent flow over flat plates The local Nusselt number for turbulent flow over an isothermal plate is given by: Nu Re 4 / 5 Pr 0.6 Pr 60 (17) As for the calculation of an average value for a plate with turbulent flow over its entire surface, it is acceptable to consider as average value the local value at the midpoint of the plate. 4.3 Mied flow conditions over flat plates In the case where there is a transition from laminar to turbulent flow the change in the respective convection coefficient is so large that the use of wrong formulas will liely cause large inaccuracy in the result. In this case an average value of the convection coefficient that taes into account the dual nature of the flow is a must. This tas can be accomplished using an averaging equation (18): h L 1 c + hlam d L 0 L c h turb d (18) where c is the critical length where the transition occurs between laminar and turbulent flow. The result of the averaging operation is: N u 1/ 4 / 5 4 / [ Re, c (Re L Re, c )] Pr 0.6 Pr 60, 5 10 Re L 10 with a typical value of Re,c , (19) becomes: N u L 4 / 5 ( Re L 871) Pr In situations for which L>> c (Re L >>Re,c ), a reasonable approimation of (0) is (1): (19) (0) N u L 4 / Re L Pr (1)

11 4.4 Constant heat flu case (flat plate) Results in the previous paragraphs dealing with forced convection are only valid for the case of isothermal plate. If the plate is subject to a uniform heat flu, the temperature distribution over the plate is not uniform. For laminar flow the appropriate formula for local Nusselt number is (): Nu 1/ Re Pr Pr 0.6 () while for turbulent flow it is (3) Nu Re 4 / 5 Pr 0.6 Pr 60 (3) 4.5 Cylinder in cross flow First of all let us specify that the Reynolds number is defined as: Re u ν (4) The equation to use for the entire range of Re as well as a wide range of Pr (all Re Pr>0.) is (5): N u 1/ 4 / Re Pr Re 5 / ( ) / 3 1/ [1 + (0.4 / Pr) ] 8,000 (5) where all properties are evaluated at T. The technical literature mentions a great variety of empirical correlation formulas, which as a rule yield close values for the calculated quantities (such as convection coefficients). As an eample for the cylinder in close flow another correlation widely used is given by (6): 1/ 4 m n Pr N u C Re Pr Pr w 0.7 < Pr < 500; 1 < Re < 10 6, (6) where all properties are evaluated at T, ecept Pr w, which is evaluated at wall temperature T w. Values of coefficients C and m are listed below. If Pr < 10, n 0.37; if Pr > 10, n 0.36.

12 Re C m The relationship between the Nusselt number and the convection coefficient is similarly with the previous cases before, Nu h (7) 4.6 Steps for calculating the convection coefficient Follow these simple steps to calculate the convection coefficient: - determine the appropriate geometry (flow over plate, cylinder, etc); - estimate the film temperature and evaluate all fluid properties at that temperature; - calculate the Reynolds number, determine (for flat plate) if the flow is laminar or turbulent; - decide on the formula to use (local or average coefficient). 5. Combined natural (free) and forced convection To obtain an indication of the relationship between free convection and forced convection one can use the ratio between Grashof number and the square of Reynolds number. In other words the above mentioned ratio gives a qualitative indication of the influence of the buoyancy forces on forced convection. When the Grashof number is of the same order of magnitude or larger than the square of the Reynolds number, free convection effects cannot be ignored, compared with the effects of forced convection. Similarly, when the square of Reynolds number is of the same order of magnitude as the Grashof number forced convection has to be taen into account together with natural convection. There are three main cases corresponding to different combinations of free convection effects and forced convection effects. If the buoyancy-induced motion and forced motion have the same direction we have a case of assisting flow. If the two flows are in opposite directions we have a transversal flow. Nu Nu ± Nu n composite n Forced n Natural (8)

13 In (8) the + sign applies for assisting and transverse flow cases, the sign applies for the case of opposing flow. The forced and natural components are determined according to the respective procedures indicated in the previous chapters from the eisting formulas. For n the most used value is n 3, however for the case of transverse flow over plat plates and cylinders n3.5 may provide a better correlation of data. Note that (8) should be seen as a first approimation for the mied convection which is a rather complicated phenomenon. Finally we note that although buoyancy effects can significantly enhance heat transfer for laminar forced convection, enhancement is typically negligible if the forced flow is turbulent. 6. Conclusion There is one important aspect that needs to be highlighted. In all calculations of the fluid properties the film temperature has to be used. The film temperature depends however of the temperature of the solid (wall) that we want to calculate as part of the thermal problem. This means that prior to the calculation of the convection coefficient the temperature of the surface ehibiting convection has to be estimated. Then the film temperature and the convection coefficient can be calculated. Once the thermal problem is solved (using the convection coefficient estimated as above) another iteration may be initiated by re-calculating the film temperature, a new convection coefficient and doing another thermal simulation. Another remar is that the process of calculation of convection coefficients based on empirical formulas can cause deviations of 15-5 % or more. One should eep in mind that the convection process is a very comple one as described in its fundamental aspects in the present document. For accurate predictions the integration of boundary layer equations has to be included in the computational process. 7. Eamples We present a number of eamples of how to use some of the formulas presented in the previous chapters. The eamples include cases of free (natural) convection and cases of forced convection. 7.1 Convection between a warm wall and ambient We consider the wall with height of L 0.71 m, width W 1.0 m at uniform temperature T w 3 C. The air in the room is quiescent at 3 C.

14 convection Fig. 3 Free convection eample Air properties are evaluated at film temperature, T f 400 K. They are: W/mK, 6 ν m / s α m ν Pr 0.69 α 1 β K T f / s 1 With the above properties we can now calculate the convection coefficient. From () and (3) one obtains from the Rayleigh number: Ra , and from paragraph 3 it follows that transition to turbulent flow occurs on the wall. As a consequence equation (7a) will be used to yield: N u Ra [1 + (0.49 / Pr) 1/ 6 ] 9 /16 8 / From (6) one obtains: h Nu L W / m K 0.71m 7 W / m K Using Newton s law of cooling (1), the power (heat rate) transferred from the wall to the room air is q 7.0 ( )(3 3) 1, 060W 7. Free convection between an air duct and ambient Let us consider the situation presented in Fig. 4 where the airflow through a duct 0.75 m wide and 0.3 m high maintains the outer duct surface at 45 C. The ambient air is assumed quiescent at room temperature of 15 C.

15 H At T f 303 K the air properties are: 6 ν m / s α.9 10 m ν Pr 0.71 α 1 β K T f W / m / s 1 Fig. 4 Geometry of the duct This is a case where the convection is considered separately from the sides as well as the other two horizontal surfaces (top and bottom). As previously discussed different formulas are used as appropriate. With the above one obtains for the Rayleigh number Ra.6 L 3. For the two sides L H 0.3 m, which yields Ra , corresponding to a laminar flow in the boundary layer. Therefore (7b) is used to obtain: H ( ) Nu [1 + (0.49 / 0.71) 4.3 W / m 7 1/ 4 h side 9 /16 4 / 9 For the top and bottom surfaces with (8) one gets L ~ w/ m and therefore Ra Using the second equation (9) and equation (10) one obtains: 0.15 Ra w / h top 0.7 Ra w/ 5.47 W / m h 1/ 4 bottom.07 W / m K K ] w K

16 7.3 Forced convection of air over an isothermal flat plate Assume air at a pressure of 6 N/m and 300 C flows with a velocity of 10 m/s over a flat plate 0.5 m long and 7 C surface temperature. It is clear that the convection occurs to transfer heat to the plate and not from the plate. Air flow L Fig. 5 Forced air convection over a flat plate Gas properties are available from tables usually at p 1 atm (at varying temperatures). The majority of properties such as, Pr, µ are with a very good approimation independent of the pressure. However others such as ν depend on pressure. The inematic viscosity varies with pressure because the density varies with pressure. According to the ideal gas law: ρ p R T Since ν µ ρ It follows that at the same temperature but at different pressure one has: ν 1 ν p p 1 and therefore the inematic viscosity of air at 437 K and 6,000 N/m is: ν m / s With (1) the Reynolds number is Re 9,597 which corresponds to a case of laminar flow over the entire surface of the plate. From (14) the average Nusselt number is: N u Re 1/ Pr 57.4

17 h Nu L 4.18 W / m K 7.4 Cross flow forced convection of air over a cylinder Consider a cylinder 1.7 mm in diameter and 94 mm long placed in a wind tunnel. The air flow in the wind tunnel occurs at 10 m/s and the air temperature is 6. C. There is a power dissipation inside the cylinder due to an electric resistance. As a result, the average temperature the cylinder is 18.4 C. Air flow Fig. 6 Cross flow of air over heated cylinder For this application one has to get the air properties at three temperatures: the temperature of free stream of air, film temperature and wall temperature. At T 6.C( 300 K) : ν Pr At T f 350 K: ν Pr m / s W / m K 6 At T w 401 K Pr w 0.69 m / s W / m K The Reynolds number: u Re 6, ν

18 The Nusselt number is calculated with (5) with all properties evaluated at T f : N u 1/ 0.6 Re Pr / 3 [1 + (0.4 / Pr) ] 1/ 4 Re 1 + ( ) 8,000 5 / 8 4 / h Nu 96 W / m K When using (6) the values for the constants are C 0.6, m 0.6. Since Pr < 10, n With (6) one calculates: Nu h Nu 0.6 (799) W / m (0.707) K One can see the different value from the one obtained with (5). This is only shown here to mae clearer the point that some variation should be epected when calculating convection coefficients with different formulas. Also note that in the result above the wall temperature is involved due to T w.

### Natural Convection. Buoyancy force

Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

### Chapter 7. External Forced Convection. Multi Energy Transport (MET) Lab. 1 School of Mechanical Engineering

Chapter 7 Eternal Forced Convection 1 School of Mechanical Engineering Contents Chapter 7 7-1 rag and Heat Transfer in Eternal Flow 3 page 7-2 Parallel Flow Over Flat Plates 5 page 7-3 Flow Across Cylinders

### NATURAL/FREE CONVECTION

NATURA/FREE CONVECTION Prabal Talukdar Associate Professor Department of Mechanical Engineering IIT Delhi E-mail: prabal@mech.iitd.ac.in Natural/free convection P.Talukdar/Mech-IITD Natural Convection

### FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES

FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the

### What is convective heat transfer?

What is convective heat transfer? A Combustion File downloaded from the IFRF Online Combustion Handbook ISSN 1607-9116 Combustion File No: 276 Version No: 1 Date: 29-03-2004 Author(s): Source(s): Sub-editor:

### Review: Convection and Heat Exchangers. Reminders

CH EN 3453 Heat Transfer Review: Convection and Heat Exchangers Chapters 6, 7, 8, 9 and 11 Reminders Midterm #2 Wednesday at 8:15 AM Review tomorrow 3:30 PM in WEB L104 (I think) Project Results and Discussion

### Module 2 : Convection. Lecture 20a : Illustrative examples

Module 2 : Convection Lecture 20a : Illustrative examples Objectives In this class: Examples will be taken where the concepts discussed for heat transfer for tubular geometries in earlier classes will

### In Chapters 7 and 8, we considered heat transfer by forced convection,

cen58933_ch09.qxd 9/4/2002 2:25 PM Page 459 NATURAL CONVECTION CHAPTER 9 In Chapters 7 and 8, we considered heat transfer by forced convection, where a fluid was forced to move over a surface or in a tube

### Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

### ME 144: Heat Transfer Convection Relations for External Flows. J. M. Meyers

ME 144: Heat Transfer Convection Relations for External Flows Empirical Correlations Generally, convection correlations for external flows are determined experimentally using controlled lab conditions

### Heat Transfer From A Heated Vertical Plate

Heat Transfer From A Heated Vertical Plate Mechanical and Environmental Engineering Laboratory Department of Mechanical and Aerospace Engineering University of California at San Diego La Jolla, California

### Experimental Study of Free Convection Heat Transfer From Array Of Vertical Tubes At Different Inclinations

Experimental Study of Free Convection Heat Transfer From Array Of Vertical Tubes At Different Inclinations A.Satyanarayana.Reddy 1, Suresh Akella 2, AMK. Prasad 3 1 Associate professor, Mechanical Engineering

### Ravi Kumar Singh*, K. B. Sahu**, Thakur Debasis Mishra***

Ravi Kumar Singh, K. B. Sahu, Thakur Debasis Mishra / International Journal of Engineering Research and Applications (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue 3, May-Jun 3, pp.766-77 Analysis of

### 3 Numerical Methods for Convection

3 Numerical Methods for Convection The topic of computational fluid dynamics (CFD) could easily occupy an entire semester indeed, we have such courses in our catalog. The objective here is to eamine some

### Iterative calculation of the heat transfer coefficient

Iterative calculation of the heat transfer coefficient D.Roncati Progettazione Ottica Roncati, via Panfilio, 17 44121 Ferrara Aim The plate temperature of a cooling heat sink is an important parameter

### Entrance Conditions. Chapter 8. Islamic Azad University

Chapter 8 Convection: Internal Flow Islamic Azad University Karaj Branch Entrance Conditions Must distinguish between entrance and fully developed regions. Hydrodynamic Effects: Assume laminar flow with

### Chapter 8 Steady Incompressible Flow in Pressure Conduits

Chapter 8 Steady Incompressible Flow in Pressure Conduits Outline 8.1 Laminar Flow and turbulent flow Reynolds Experiment 8.2 Reynolds number 8.3 Hydraulic Radius 8.4 Friction Head Loss in Conduits of

### XI / PHYSICS FLUIDS IN MOTION 11/PA

Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

### 1. (Problem 8.23 in the Book)

1. (Problem 8.23 in the Book) SOLUTION Schematic An experimental nuclear core simulation apparatus consists of a long thin-walled metallic tube of diameter D and length L, which is electrically heated

### Internal Convection: Fully Developed Flow

Internal Convection: Fully Developed Flow Laminar Flow in Circular Tube: Analytical local Nusselt number is constant in fully develop region depends on surface thermal condition constant heat flux Nu D

### Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

### HANDLY & FREQUENTLY USED FORMULAS FOR THERMAL ENGINEERS

HANDLY & FREQUENTLY USED FORMULAS FOR THERMAL ENGINEERS GEOMETRY & MATH GEOMETRI & MATEMATIK Cylindrical (Tube) Volume V = p / 4 d 2 L [m 3 ] Cylindrical (Tube) Surface A = p d L [m 2 ] Rectangular Triangle

### Basic Equations, Boundary Conditions and Dimensionless Parameters

Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

### Chapter 1. Governing Equations of Fluid Flow and Heat Transfer

Chapter 1 Governing Equations of Fluid Flow and Heat Transfer Following fundamental laws can be used to derive governing differential equations that are solved in a Computational Fluid Dynamics (CFD) study

### Correlations for Convective Heat Transfer

In many cases it's convenient to have simple equations for estimation of heat transfer coefficients. Below is a collection of recommended correlations for single-phase convective flow in different geometries

### Heating In Agitated & Non-Agitated Vessels

Heating In Agitated & Non-Agitated Vessels IBD/BFBiMidland Section Engineering Symposium on Heat Transfer and Refrigeration Burton-on-Trent Jan 2014 Mark Phillips Briggs of Burton Contents Heat Energy

### HEAT TRANSFER IN BLOCK WALLS

HEAT TRANSFER IN BLOCK WALLS S. Hassid and E. Levinsky Environmental & Water Resources Engineering Department Technion - Israel Institute of Technology Haifa 32 - Israel ABSTRACT Combined conduction-convection-radiation

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 6. Flow of Fluid and Bernoulli s Equation 7.

### Effect of Aspect Ratio on Laminar Natural Convection in Partially Heated Enclosure

Universal Journal of Mechanical Engineering (1): 8-33, 014 DOI: 10.13189/ujme.014.00104 http://www.hrpub.org Effect of Aspect Ratio on Laminar Natural Convection in Partially Heated Enclosure Alireza Falahat

### THERMAL STRATIFICATION IN A HOT WATER TANK ESTABLISHED BY HEAT LOSS FROM THE TANK

THERMAL STRATIFICATION IN A HOT WATER TANK ESTABLISHED BY HEAT LOSS FROM THE TANK J. Fan and S. Furbo Abstract Department of Civil Engineering, Technical University of Denmark, Brovej, Building 118, DK-28

### ENSC 283 Introduction and Properties of Fluids

ENSC 283 Introduction and Properties of Fluids Spring 2009 Prepared by: M. Bahrami Mechatronics System Engineering, School of Engineering and Sciences, SFU 1 Pressure Pressure is the (compression) force

### Natural Convective Heat Transfer from Inclined Narrow Plates

Natural Convective Heat Transfer from Inclined Narrow Plates Mr. Gandu Sandeep M-Tech Student, Department of Mechanical Engineering, Malla Reddy College of Engineering, Maisammaguda, Secunderabad, R.R.Dist,

### Week 5. Convection Heat Transfer. See Website for material on convective heat transfer.

WK5TPCSWEB.TEX ECE 309 M.M. Yovanovich Week 5 Lecture 1 Convection Heat Tranfer. See Webite for material on convective heat tranfer. Overview of Convective Heat Tranfer Newton' Law of Cooling: _Q conv

### Chapter (1) Fluids and their Properties

Chapter (1) Fluids and their Properties Fluids (Liquids or gases) which a substance deforms continuously, or flows, when subjected to shearing forces. If a fluid is at rest, there are no shearing forces

### Numerical Investigation of Heat Transfer Characteristics in A Square Duct with Internal RIBS

merical Investigation of Heat Transfer Characteristics in A Square Duct with Internal RIBS Abhilash Kumar 1, R. SaravanaSathiyaPrabhahar 2 Mepco Schlenk Engineering College, Sivakasi, Tamilnadu India 1,

### Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

### CH-205: Fluid Dynamics

CH-05: Fluid Dynamics nd Year, B.Tech. & Integrated Dual Degree (Chemical Engineering) Solutions of Mid Semester Examination Data Given: Density of water, ρ = 1000 kg/m 3, gravitational acceleration, g

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### Heattransferina tankintank combi store

Søren Knudsen Heattransferina tankintank combi store DANMARKS TEKNISKE UNIVERSITET Rapport BYG DTU R-025 2002 ISSN 1601-2917 ISBN 87-7877-083-1 1 Contents Contents...1 Preface...2 Summary...3 1. Introduction...4

### Basic Principles in Microfluidics

Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces

### International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015

International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):2278-5299 EXPERIMENTAL STUDY

### Properties behind effective Transformer Oil Cooling. Hendrik Cosemans, General Manager Nynas Dubai S11

Hendrik Cosemans, General Manager Nynas Dubai As a Belgian national, where 3 official languages are part of the national structure, Hendrik is adding English and Spanish to his language portfolio. And

### CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### Effective parameters on second law analysis for semicircular ducts in laminar flow and constant wall heat flux B

International Communications in Heat and Mass Transfer 32 (2005) 266 274 www.elsevier.com/locate/ichmt Effective parameters on second law analysis for semicircular ducts in laminar flow and constant wall

### LAB #2: Forces in Fluids

Princeton University Physics 103/105 Lab Physics Department LAB #2: Forces in Fluids Please do NOT attempt to wash the graduated cylinders once they have oil in them. Don t pour the oil in the graduated

### Taylor Columns. Martha W. Buckley c May 24, 2004

Taylor Columns Martha W. Buckley c May 24, 2004 Abstract. In this experiment we explore the effects of rotation on the dynamics of fluids. Using a rapidly rotating tank we demonstrate that an attempt to

### Accurate Air Flow Measurement in Electronics Cooling

Accurate Air Flow Measurement in Electronics Cooling Joachim Preiss, Raouf Ismail Cambridge AccuSense, Inc. E-mail: info@degreec.com Air is the most commonly used medium to remove heat from electronics

### AA200 Chapter 9 - Viscous flow along a wall

AA200 Chapter 9 - Viscous flow along a wall 9.1 The no-slip condition 9.2 The equations of motion 9.3 Plane, Compressible Couette Flow (Review) 9.4 The viscous boundary layer on a wall 9.5 The laminar

### A COMPUTATIONAL FLUID DYNAMICS STUDY ON THE ACCURACY OF HEAT TRANSFER FROM A HORIZONTAL CYLINDER INTO QUIESCENT WATER

A COMPUTATIONAL FLUID DYNAMICS STUDY ON THE ACCURACY OF HEAT TRANSFER FROM A HORIZONTAL CYLINDER INTO QUIESCENT WATER William Logie and Elimar Frank Institut für Solartechnik SPF, 8640 Rapperswil (Switzerland)

### ENHANCEMENT OF NATURAL CONVECTION HEAT TRANSFER BY THE EFFECT OF HIGH VOLTAGE D.C. ELECTRIC FIELD

Int. J. Mech. Eng. & Rob. Res. 014 Amit Kumar and Ritesh Kumar, 014 Research Paper ISSN 78 0149 www.ijmerr.com Vol. 3, No. 1, January 014 014 IJMERR. All Rights Reserved ENHANCEMENT OF NATURAL CONVECTION

### Min-218 Fundamentals of Fluid Flow

Excerpt from "Chap 3: Principles of Airflow," Practical Mine Ventilation Engineerg to be Pubished by Intertec Micromedia Publishing Company, Chicago, IL in March 1999. 1. Definition of A Fluid A fluid

### HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS

HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS P.R.Hatwar 1, Bhojraj N. Kale 2 1, 2 Department of Mechanical Engineering Dr. Babasaheb Ambedkar College of Engineering & Research,

### NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

### THERMAL ANALYSIS OF WATER COOLED CHARGE AIR COOLER IN TURBO CHARGED DIESEL ENGINE

THERMAL ANALYSIS OF WATER COOLED CHARGE AIR COOLER IN TURBO CHARGED DIESEL ENGINE J.N. Devi Sankar 1, P.S.Kishore 2 1 M.E. (Heat transfer in Energy Systems) Student, Department of Mechanical Engineering,

### Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

### Physics 103 CQZ1 Solutions and Explanations. 1. All fluids are: A. gases. B. liquids. C. gases or liquids. D. non-metallic. E.

Physics 03 CQZ Solutions and Explanations. All fluids are: A. gases B. liquids C. gases or liquids D. non-metallic E. transparent Matter is classified as solid, liquid, gas, and plasma. Gases adjust volume

### 15. The Kinetic Theory of Gases

5. The Kinetic Theory of Gases Introduction and Summary Previously the ideal gas law was discussed from an experimental point of view. The relationship between pressure, density, and temperature was later

### E 490 Fundamentals of Engineering Review. Fluid Mechanics. M. A. Boles, PhD. Department of Mechanical & Aerospace Engineering

E 490 Fundamentals of Engineering Review Fluid Mechanics By M. A. Boles, PhD Department of Mechanical & Aerospace Engineering North Carolina State University Archimedes Principle and Buoyancy 1. A block

### CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER

International Journal of Advancements in Research & Technology, Volume 1, Issue2, July-2012 1 CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER ABSTRACT (1) Mr. Mainak Bhaumik M.E. (Thermal Engg.)

### Module 1 : Conduction. Lecture 5 : 1D conduction example problems. 2D conduction

Module 1 : Conduction Lecture 5 : 1D conduction example problems. 2D conduction Objectives In this class: An example of optimization for insulation thickness is solved. The 1D conduction is considered

### FREE CONVECTION FROM OPTIMUM SINUSOIDAL SURFACE EXPOSED TO VERTICAL VIBRATIONS

International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 214-224, Article ID: IJMET_07_01_022 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

### EffectofBuoyancyForceontheflowfieldinaTriangularCavity

Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 14 Issue 3 Version 1.0 Year 014 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global

### Free Convection Film Flows and Heat Transfer

Deyi Shang Free Convection Film Flows and Heat Transfer With 109 Figures and 69 Tables < J Springer Contents 1 Introduction 1 1.1 Scope 1 1.2 Application Backgrounds 1 1.3 Previous Developments 2 1.3.1

### Heat/Mass Transfer Analogy - Laminar Boundary Layer

Chapter 3. Heat/Mass Transfer Analogy - Laminar Boundary Layer As noted in the previous chapter, the analogous behaviors of heat and mass transfer have been long recognized. In the field of gas turbine

### Engine Heat Transfer. Engine Heat Transfer

Engine Heat Transfer 1. Impact of heat transfer on engine operation 2. Heat transfer environment 3. Energy flow in an engine 4. Engine heat transfer Fundamentals Spark-ignition engine heat transfer Diesel

### Turbulent Heat Transfer in a Horizontal Helically Coiled Tube

Heat Transfer Asian Research, 28 (5), 1999 Turbulent Heat Transfer in a Horizontal Helically Coiled Tube Bofeng Bai, Liejin Guo, Ziping Feng, and Xuejun Chen State Key Laboratory of Multiphase Flow in

### Tutorial 4. Buoyancy and floatation

Tutorial 4 uoyancy and floatation 1. A rectangular pontoon has a width of 6m, length of 10m and a draught of 2m in fresh water. Calculate (a) weight of pontoon, (b) its draught in seawater of density 1025

### Measuring flow velocity at elevated temperature with a hot wire anemometer calibrated in cold flow Benjamin, S.F. and Roberts, C.A.

Measuring flow velocity at elevated temperature with a hot wire anemometer calibrated in cold flow Benjamin, S.F. and Roberts, C.A. Author post-print (accepted) deposited in CURVE June 2013 Original citation

### Basic Fluid Mechanics. Prof. Young I Cho

Basic Fluid Mechanics MEM 220 Prof. Young I Cho Summer 2009 Chapter 1 Introduction What is fluid? Give some examples of fluids. Examples of gases: Examples of liquids: What is fluid mechanics? Mechanics

### Experiment: Viscosity Measurement B

Experiment: Viscosity Measurement B The Falling Ball Viscometer Purpose The purpose of this experiment is to measure the viscosity of an unknown polydimethylsiloxiane (PDMS) solution with a falling ball

### For one dimensional heat transfer by conduction in the x-direction only, the heat transfer rate is given by

Chapter.3-1 Modes of Heat Transfer Conduction For one dimensional heat transfer by conduction in the -direction only, the heat transfer rate is given by Q ka d (.3-4) In this epression, k is a property

### HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi

HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi 2 Rajesh Dudi 1 Scholar and 2 Assistant Professor,Department of Mechanical Engineering, OITM, Hisar (Haryana)

### du u U 0 U dy y b 0 b

BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

### Civil Engineering Hydraulics Mechanics of Fluids. Flow in Pipes

Civil Engineering Hydraulics Mechanics of Fluids Flow in Pipes 2 Now we will move from the purely theoretical discussion of nondimensional parameters to a topic with a bit more that you can see and feel

### (Refer Slide Time: 05:33)

Water and Wastewater Engineering Dr. Ligy Philip Department of Civil Engineering Indian Institute of Technology, Madras Sedimentation (Continued) Lecture # 9 Last class we were discussing about sedimentation.

### Laboratory exercise No. 4 Water vapor and liquid moisture transport

Laboratory exercise No. 4 Water vapor and liquid moisture transport Water vapor transport in porous materials Due to the thermal conductivity of water and other unfavourable properties and effects in porous

### Exergy Analysis of a Water Heat Storage Tank

Exergy Analysis of a Water Heat Storage Tank F. Dammel *1, J. Winterling 1, K.-J. Langeheinecke 3, and P. Stephan 1,2 1 Institute of Technical Thermodynamics, Technische Universität Darmstadt, 2 Center

### Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary

### Boundary Conditions in Fluid Mechanics

Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial

### Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli 620 015, Tamil Nadu, India

Experimental Thermal and Fluid Science 32 (2007) 92 97 www.elsevier.com/locate/etfs Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right

### Practice Problems on Viscosity. free surface. water. y x. Answer(s): base: free surface: 0

viscosity_01 Determine the magnitude and direction of the shear stress that the water applies: a. to the base b. to the free surface free surface U y x h u water u U y y 2 h h 2 2U base: yx y 0 h free

### Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity

1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood

### 1.4 Review. 1.5 Thermodynamic Properties. CEE 3310 Thermodynamic Properties, Aug. 26,

CEE 3310 Thermodynamic Properties, Aug. 26, 2011 11 1.4 Review A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container

### p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh

IVE1400: n Introduction to Fluid Mechanics Statics : Pressure : Statics r P Sleigh: P..Sleigh@leeds.ac.uk r J Noakes:.J.Noakes@leeds.ac.uk January 008 Module web site: www.efm.leeds.ac.uk/ive/fluidslevel1

### Heat transfer in Flow Through Conduits

Heat transfer in Flow Through Conduits R. Shankar Suramanian Department of Chemical and Biomolecular Engineering Clarkson University A common situation encountered y the chemical engineer is heat transfer

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Keywords: Heat transfer enhancement; staggered arrangement; Triangular Prism, Reynolds Number. 1. Introduction

Heat transfer augmentation in rectangular channel using four triangular prisms arrange in staggered manner Manoj Kumar 1, Sunil Dhingra 2, Gurjeet Singh 3 1 Student, 2,3 Assistant Professor 1.2 Department

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA. PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3 OUTCOME 1 - PHYSICAL PROPERTIES AND CHARACTERISTIC BEHAVIOUR OF FLUIDS TUTORIAL 1 - SURFACE TENSION

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Fundamentals of Heat and Mass Transfer

2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA

### NUCLEAR ENERGY RESEARCH INITIATIVE

NUCLEAR ENERGY RESEARCH INITIATIVE Experimental and CFD Analysis of Advanced Convective Cooling Systems PI: Victor M. Ugaz and Yassin A. Hassan, Texas Engineering Experiment Station Collaborators: None

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### Problem Statement In order to satisfy production and storage requirements, small and medium-scale industrial

Problem Statement In order to satisfy production and storage requirements, small and medium-scale industrial facilities commonly occupy spaces with ceilings ranging between twenty and thirty feet in height.

### 25.2. Applications of PDEs. Introduction. Prerequisites. Learning Outcomes

Applications of PDEs 25.2 Introduction In this Section we discuss briefly some of the most important PDEs that arise in various branches of science and engineering. We shall see that some equations can

### Correlation Equations of Heat Transfer in Nanofluid Al2O3- Water as Cooling Fluid in a Rectangular Sub Channel Based CFD Code

Correlation Equations of Heat Transfer in Nanofluid Al2O3- Water as Cooling Fluid in a Rectangular Sub Channel Based CFD Code Anwar Ilmar Ramadhan* 1, As Natio Lasman 2, Anggoro Septilarso 2 1 Mechanical

### When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs