Numerical investigation of heat transfer process form with constant heat flux in exothermic board by natural convection inside a closed cavity

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1 INTERNATIONAL JOURNAL OF MECANICS Numerical inestigation of heat transfer process form with constant heat flux in exothermic board by natural conection inside a closed caity Behnaz Arjoman Kermani,Islamic Azad uniersity, branch of Bardsir Abstract: Natural Conection process within a closed caity when heat source is on the ertical wall of it special importance.heat source generate constant heat flux. A common practical example of this case is electronic boards inside a computer or radiator in the room. One of the important parameters in designing electronic boards in the computer or another things is the maximum temperature of pieces; therefore we must examine the factors that affect this to hae a reduced the maximum temperature. Goerning equations on fluid flow mass, elocity and energy equations using the finite element method with power law, pr =.7, a non-uniform network is conerted to algebraic form. Because of buoyancy force the Momentum equation depended on temperature. Momentum equations and energy equation are soled simultaneously. Momentum equations that include unknown pressure sole with Simple algorithm. The elocities are obtained from Momentum equation must satisfy continuity equation. eat generation is constant. Wall s temperature is T (temperature of enironment). At first elocity of fluid is =. With these boundary conditions we check the effect of thermal springs placed inside the caity, caity dimensional, size of thermal springs (heat source) to reduce temperature. Conergence of the energy equation is -7. Conergence standard is temperature changes. Keywords closed caity, exothermic board, finite element, heat flux, natural conection I. INTRODUCTION eat transfer from the last few decades due to natural conection method considered high performance and many studies done and many papers are presented in this field. In natural conection of heat transfer inside a rectangular cube container walls that are part of it to produce heat in two-dimensional case reiew and to study the maximum in arious paid Rayleigh number (). In to study the flow field inside the rectangular container cube in the center of it a heat source is paid and stream lines in different pages has achieed. (). In 98 by moing into the chamber to the numerical method Bench mark to study and reiew the number of different Nu in Rayleigh number paid. (3). In 9 Symbolic calculation for free conection for porous material with constant heat flux in a circular caity (4). In 8 Modelling of the temperature change in ertical ground heat exchangers (5). In 7 experimental study of mixed conection laminar flow of water-alo3 nanofluid in horizontal tube with Uniform wall heat flux (6).This article examines the relationship between temperature changes with moing heat source and change its lengths, we hae heat source on a rectangular cube face is ertical. at first heat source with constant heat flux and a certain size on the ertical side in seen different positions to reiew and put it explains temperature changes.then the thermal springs located in a specific location and length of the side will change the temperature check which is the maximum temperature obtain. Finally, change dimensions of the chamber maximum temperature on the heat source obtains. II. Problem Formulation u w + + = x y z u u u u p µ = + t x y z ρ x ρ () u w u p µ = + t x y z ρ y ρ u w w w w w p µ = + β t x y z ρ z ρ u w w g T () (3) (4) T T T T T T T + u + + w = α + + t x y z x y z (5) A. Non dimensional equations u w + + = x y z (6) Issue, Volume 4,

2 INTERNATIONAL JOURNAL OF MECANICS u u u u p pr + u + + w = + u (7) t x y z x Ra = p pr + u + + w = + t x y z y Ra w w w w p pr + u + + w = + w t x y z z Ra (9) θ θ θ θ + u + + w = θ () t x y z pr Ra g=graitational T=temperature u,, w =elocity component β=coefficient of thermal expansion p=pressure N ρ = fluid density, m kg m s 3 m µ =dynamic iscosity, kg m. s Ra=Rayleigh number =reference elocity α=fluid thermal diffusiity Pr=prandtl number w q=heat flux 3 m L,w,h= caity dimensional L,W,=heat source dimensional =heat source height T = temperature of enironment x y z = = = x y z u w = = = u w t ν pr = α p = = t p ρ (8) k B. Boundary condition u(,y,z)=u( L,y,z)=u(x,,z)=u(x,,z)=u(x,y,)=u(x,y, W )= (,y,z)=( L,y,z)=(x,,z)=(x,,z)=(x,y,)=(x,y, W )= w(,y,z)=w( L,y,z)=w(x,,z)=w(x,,z)=w(x,y,)=w(x,y, W )= x= : θ =, x= l : θ = y= : θ =, y= h : θ = z= : θ =, z= w : θ = x=, : θ K = x q y=, : θ K = q y z=, : θ K = z q III. Problem Solution For this problem soling, we assume a caity of 4 4 cm and heat source dimensional 3 5 cm, pr=.7, Ra=3, the flow is Permanent, heat flux is constant. (fig) gβq = K T T θ = q K Ra= gβq Kνα 4 fig: cubic caity when one cubic heat source is on the ertical wall of caity Issue, Volume 4,

3 INTERNATIONAL JOURNAL OF MECANICS At first we should check if the problem is correct or not, then sole it because enough scientific and experimental studies are not aailable. We compare the results with preious qualitatie results which are aailable. For qualitatie study we draw fluid flow in the planes xz, xy with different alue for y and z when heat source is in the middle of ertical face symmetry completely. (Fig) maximum T distance heat source form caity ground Fig3: maximum heat source temperature changes in correlation with distance between heat source and caity ground in three heat fluxes figa In Fig4 the temperature function has shown on the heat source which is in the center of wall. We can see that the maximum temperature occurred in the center of area and decrease at the edge of area because edges of heat source interchange heating with enironment and then decrease temperature. fig (b) Fig: stream lines are shown on planes x-y (fig a), x-z (fig b) when one heat source is in the middle of caity s wall Now, we must sole the problem. At first a heat source is on the ertical face of caity (at y direction) and maximum temperature obtain with moing the heat source in seen location 5,, 5,, 5, 3 and 35cm from caity froth. We see in fig(3) when heat source is near the caity (5cm, cm, 3cm and 35cm), heat source temperature is the highest because the heat source is an obstacle in front of flow and the flow can t pass simply. eat source temperature increases at the cm distance from caity froth because heat source is far from the aboe and below walls and it can t lose heat.we change heat flux then we see the diagram is not changed; howeer the diagram is changed if the boundary condition is changed. Fig4. This diagram show temperature changes in the heat source s wall in three directions In fig5 temperature diagram at two different alues of y has shown therefore at the length of heat source (z) temperature increase and then decrease. Issue, Volume 4, 3

4 INTERNATIONAL JOURNAL OF MECANICS X= Fig5: heat source temperature ratio to the heat source s length with two different alue of y Fig6,fig7 and fig8 show stream-functions on the different planes of x, y, z when the heat source in the center of wall. We see that the most eddy occurred on the nearest pages to the heat source and eddy far from each other when the pages far from heat source. Fig 9 show stream function on the plane of x in the caity with three direction. X=5 Fig6: stream-function is shown with three different alues of x in the caity X=5 Fig7: stream-function is shown with three different alues of y in the caity Issue, Volume 4, 4

5 INTERNATIONAL JOURNAL OF MECANICS Fig, fig and fig show stream-function in three direction and we can see what place in the caity is hottest than another place. Fig: stream-function in three direction l when heat source in the center of ertical wall Fig8: stream-function is shown with three different alues of z in the caity Fig: : stream-function in three direction when heat source in the aboe of ertical wall Fig9: stream function on plane of x in three direction caity Issue, Volume 4, 5

6 INTERNATIONAL JOURNAL OF MECANICS Fig: stream-function in three direction when heat source in the below of ertical wall Fig 4: stream-function in three direction when heat source has maximum length and in the center of ertical wall In figure 3 we test another case. We put the heat source in the center of ertical wall and then change heat source dimension (change heat source length) therefore we examine arious heat source lengths of 3, 5,, 5,, 5, and 3cm (seen cases).we can see in fig (3) that the heat source temperature is decreased until 5cm and after that increased because the area for heat transfer is big. In this image we can see diagram with three alues for heat flux. All of them hae the similar diagram. In figure 4 we can see stream-function in three direction.it show places that has maximum temperature. In fig (5) we can show alues of temperature at the length of heat source.in this case the length of heat source is 4 cm. we see that temperature increase and then reduce but after that it increase suddenly and in 4cm it receied to temperature of enironment.we can see in this figure with two alue of y and I obtain the same result maximum T Fig5: eat source temperature to the heat source s length in two different y when heat source has minimum length and in the center of caity s wall Fig3: maximum temperature changes in correlation with heat source s length when heat source is in the center of caity s wall in three heat fluxes Issue, Volume 4, 6

7 INTERNATIONAL JOURNAL OF MECANICS At the end we are decreased the high of caity (we change h ) howeer olume caity is constant. With w increasing height, temperature decreases because conection takes place simply but increasing height is limited because when h is increased then w is decreased therefore circulation flow takes place hard (fig6).in fig7 we can see streamfunction in three direction when y/z=4.it show maximum temperature where happen maximum T Fig6: Maximum heat source temperature changes in correlation with caity dimension Fig7: stream-function in three direction when y/z=4 IV. Conclusion We result when we moe heat source on the ertical wall of caity minimum alue of temperature happened when the heat source far from center of wall and near to aboe and below walls reduce heat source temperature because it can heat transfer with enironment (wall s temperature is T ).howeer heat source can t more near to the walls because temperature increased. In this problem heat source has minimum temperature in 5cm from ground.with changing caity dimensional happen Minimum temperature when the heat source s length increased but it is limit. When y = or = z h w (caity dimensional) heat source temperature is minimum. Therefore if we increased h (heat source s high), decreased temperature. At the end we can result when length of heat source is 5cm, height of caity is 4cm and heat source distance from ground is 5cm, is the best case that happened. V. References [] Qi-ong Deng, Guang-Fa Tang, A combined temperature scale for analyzing natural conection in rectangular enclosure with discrete well heat source, International Journal of heat and mass transfer () Issue, Volume 4, 7

8 INTERNATIONAL JOURNAL OF MECANICS [] K.C.Karki, P.S.Sathymurthy, S.U.Patankar, Natural conection in a partition cubic enclosure, Department of mechanical engineering (99) [3] G.Deah, Natural conection of air in a square caity a bench mark numerical solution, Uniersity of new Soult Wales [4] kamyar mansour, Symbolic calculation for free conection for porous material of constant heat flux in a circular caity, Department Aerospace Engineering and New Technologies Research Center Amir Kabir Uniersity Technology Tehran(9) [5] Dr. LÁSZLÓ GARBAI, Prof, SZABOLCS MÉES, PhD STUDENT, Modelling of the temperature change in ertical ground heat exchangers with single U-tube installation, Department of Building Serices and Process Engineering Budapest Uniersity of Technology and Economics(8) [6] R. Ben MANSOUR, N. GALANIS*,, C. T. NGUYEN, C. AOUINA, Experimental Study of Mixed Conection Laminar Flow of Water-AlO3 Nanofluid in orizontal Tube with Uniform Wall eat Flux, Faculty of Engineering, Uniersité de Sherbrooke, Québec, CANADA JK R Faculty of Engineering, Uniersité de Moncton, Moncton, NB, CANADA EA 3E9(7) Issue, Volume 4, 8