HEAT AND MASS TRANSFER

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1 MEL242 HEAT AND MASS TRANSFER Prabal Talukdar Associate Professor Department of Mechanical Engineering g IIT Delhi MECH/IITD

2 Course Coordinator: Dr. Prabal Talukdar Room No: III, Course webpage: Pre-requisite: Fluid Mechanics (AML 160) Lectures: Tue, Wed, Fri: a.m. (Room No: IV LT1) Tut: p.m. (Tentative Room no: III352 MEL 242: Heat and Mass Transfer (3-1-0) Syllabus (for total 42 lectures) Introduction and basics of to heat transfer: Modes of heat transfer, Fourier s law, conductivity, diffusivity. Heat conduction equation: 1D Heat conduction, General heat conduction equation, Boundary and initial conditions, Heat generation. Steady heat conduction: Heat conduction in plane wall, cylinder, sphere, network analysis, critical radius of insulation, heat transfer from fins. Transient heat conduction: Lumped system analysis, transient heat conduction in large plane walls, long cylinders and spheres with spatial effect, Hil Heisler and Grober charts Numerical methods of heat conduction: Finite difference formulation, numerical methods for 1D and 2D steady state heat conduction. ( 10 lectures) Introduction to convection: Fundamentals, Velocity and thermal boundary layer, laminar, turbulent flows, conservation equations for mass, momentum and energy, solution of boundary layer equations, Analogy between heat and momentum transfer, Non-dimensional numbers External heat transfer: Drag and heat transfer, parallel flow over flat plates, flow across cylinders and spheres Internal heat transfer: Mean velocity and mean temperature, entrance region, constant heat flux and temperature condition in pipe flow, Hagen Poiseuille flow, Turbulent flow and heat transfer Natural/free convection: Equation of motion of Grashof number, natural convection over surfaces and inside enclosures ( 13 lectures)

3 Boiling and condensation: Boiling heat transfer, pool boiling, flow boiling, condensation heat transfer, film condensation, heat transfer correlations. ( 4 lectures) Heat Exchangers: Types of heat exchangers, overall heat transfer coefficient, analysis of heat exchangers, the log mean temperature method, ε-ntu method. ( 4 lectures) Introduction to radiation: Fundamentals, radiative properties of opaque surfaces, Intensity, emissive power, radiosity, i Planck s law, Wien s displacement law, Black and Gray surfaces, Emissivity, i i absorptivity, i Spectral and directional variations, Stephan Boltzmann law, Kirchhoff s law View factors: Definitions and relations, radiation heat transfer between two black surfaces, between diffuse gray surfaces, network method above two surfaces, re-radiating surface, radiation shield, radiation effects on temperature measurements. ( 7 lectures) Mass Transfer: Introduction, analogy between heat and mass transfer, mass diffusion, Fick s Law, boundary conditions, steady mass diffusion through a wall, cylinder and sphere, water vapour migration in buildings, transient mass diffusion, mass transfer in a moving medium, diffusion of vapor through a stationary gas: Stefan Flow ( 4 lectures) Evaluation: Tuts and Quiz (2 nos): 20% (Closed note, book) Quiz Quiz 1 Quiz 2 Minor Test I: 20% (Open note, closed book) Tentative Date August 27 November 5 Minor Test II: 25% (Open note, closed book) Major Test: 35% (Open note, closed book) Total: 100% Textbook: Fundamental of Heat and Mass Transfer: F. P. Incropera and D. P.Dewitt Heat Transfer: Yunus A. Cengel Heat Transfer: J.P. Holmann

4 Heat Transfer as a Course Has a reputation for being one of the most challenging, fundamental, conceptual courses in ME. It is the heart of thermal engineering i Why?? Physically diverse: thermodynamics, material science, diffusion theory, fluid mechanics, radiation theory Higher-level math: vector calculus, ODEs, PDEs, numerical methods Physically elusive: heat is invisible; developing intuition takes time Appropriate assumptions: required to simplify and solve most problems However, Heat Transfer is interesting, fun, and readily applicable to the real world

5 Heat Transfer Applications Heat transfer is commonly encountered in engineering systems and other aspects of life, and one does not need to go very far to see some application areas of heat transfer.

6 Human body

7 Heat Transfer - Thermodynamics Thermodynamics is concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another, and it gives no indication about how long the process will take. A thermodynamic analysis simply tells us how much heat must be transferred to realize a specified change of state to satisfy the conservation of energy principle. We are normally interested in how long it takes for the hot coffee in a thermos to cool to a certain temperature, which cannot be determined from a thermodynamic analysis alone. Determining the rates of heat transfer to or from a system and thus the times of cooling or heating, as well as the variation of the temperature, is the subject of heat transfer

8 Definition Heat transfer is energy transfer due to a temperature difference in a medium or between two or more media Different types of heat transfer processes are called different modes of heat transfer Conduction heat transfer is due to a temperature gradient in a stationary medium or media Convection heat transfer occurs between a surface and a moving fluid at different temperatures Radiation heat transfer occurs due to emission of energy in the form of electromagnetic eti waves by all bodies above absolute zero temperature Net radiation heat transfer occurs when there exists a temperature difference between two or more surfaces emitting radiation energy

9 Conduction Conduction heat transfer is due to random molecular and atomic vibrational, rotational and translational motions High temperature and more energetic molecules vibrate more and transfer energy to less energetic particles as a result of molecular collisions or interactions Q & Q x The heat flux (a vector) (W / m 2 ) is characterized by a transport property know as the Thermal Conductivity, k (W / m K) W = watts m = Meters K = temperature in Kelvin

10 Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons The rate of heat conduction through a medium depends on the geometry of the medium, its thickness, and the material of the medium, as well as the temperature difference across the medium

11 Q& cond Fourier s Law = ka T 2 T1 ΔT = ka Δxx Δxx (W) In the limiting case of x 0, the equation above reduces to the differential form Q& cond = ka dt dx (W) The negative sign ensures that heat transfer in the positive x direction is a positive quantity Fourier s law of heat conduction after J. Fourier, who expressed it first in his heat transfer text in 1822 T 1 = T 2 =

12 Thermal Conductivity Specific heat C p is a measure of a material s ability to store thermal energy. For example, C p = 4.18 kj/kg C for water and C p = 0.45 kj/kg C for iron at room temperature, which indicates that water can store almost 10 times the energy that iron can per unit mass. Likewise, the thermal conductivity k is a measure of a material s ability to conduct heat. For example, k = W/m C for water and k = 80.2 W/m C for iron at room temperature, which indicates that iron conducts cts heat more than 100 times faster than water can. Thus water is a poor heat conductor relative to iron, although water is an excellent medium to store thermal energy

13 Range of Thermal Conductivity The thermal conductivities of gases such as air vary by a factor of 10 4 from those of pure metals such as copper. Note that pure crystals and metals have the highest thermal conductivities, and gases and insulating materials the lowest.

14 A simple experimental setup to determine the thermal conductivity of a material.

15 The range of thermal conductivity of various materials at room temperature

16 The thermal conductivity of a substance is normally highest in the solid phase and lowest in the gas phase. Unlike gases, the thermal conductivities of most liquids id decrease with increasing i temperature, with water being a notable exception. In solids, heat conduction is due to two effects: the lattice vibrational waves induced by the vibrational a motions o of the molecules es positioned at relatively fixed positions in a periodic manner called a lattice, and the energy transported via the free flow of electrons in the solid. The thermal conductivity of a solid is obtained by adding the lattice and electronic components. The relatively high thermal conductivities of pure metals are primarily due to the electronic component.

17 The lattice component of thermal conductivity strongly depends on the way the molecules are arranged Unlike metals, which are good electrical and heat conductors, crystalline solids such as diamond d and semiconductors such as silicon are good heat conductors but poor electrical conductors. As a result, such materials find widespread use in the electronics industry. For example, diamond, which is a highly ordered crystalline solid, has the highest known thermal conductivity at room temperature. Even small amounts in a pure metal of foreign molecules that are good conductors themselves seriously disrupt the flow of heat in that tmetal. For example, the thermal conductivity of steel containing just 1 percent of chrome is 62 W/m C, while the thermal conductivities of iron and chromium are 83 and 95 W/m C,

18 The variation of the thermal conductivity of various solids, liquids, and gases with temperature (from White)

19 Thermal Diffusivity The product ρc p, which is frequently encountered in heat transfer analysis, is called the heat capacity of a material. Both the specific heat C p and the heat capacity ρc p represent the heat storage capability of a material. But C p expresses it per unit mass whereas ρc p expresses it per unit volume, as can be noticed from their units J/kg C and J/m 3 C, respectively. Another material property that appears in the transient heat conduction analysis is the thermal diffusivity, which represents how fast heat diffuses through a material and is defined as The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat will be conducted further

20 Note that the thermal diffusivity ranges from 0.14 x 10-6 m 2 /s for water to 174 x 10-6 m 2 /s for silver, which is a difference of more than a thousand times. Also note that the thermal diffusivities of beef and water are the same. This is not surprising, since meat as well as fresh vegetables and fruits are mostly water, and thus they possess the thermal properties of water.

21 Forced Convection Natural Convection Boiling Condensation

22 Convection Convection heat transfer involves both energy transfer due to random molecular motions and by bulk motion of the fluid Convection heat transfer includes both forced convection and natural convection In convection heat transfer, the transfer of heat is between a surface and a moving fluid (liquid or gas), when they are at different temperatures. The rate of transfer is given by Newton s Law of Cooling. q '' = h(t s T ) T q Moving fluid T s T s > T

23 Typical values of convection heat transfer coefficient i Process h (W / m 2 K) Free Convection Gases 2-25 Liquids Forced Convection Gases Liquids 50-20,000 with Phase Change Boiling or Condensation ,000

24 Radiation All surfaces of finite temperature emit energy in the form of electromagnetic waves In the absence of an intervening medium, there is a heat transfer by radiation between two surfaces at different temperatures The maximum flux, E (W / m 2 ), at which radiation may be emitted from a blackbody surface is given by: Stefan Boltzmann Law E = σ 4 b T s E b where T s E b or E = Surface emissive power (W / m 2 ) T = absolute temperature (K) σ = Stefan-Boltzmann constant = 5.67 x 10-8 (W / m 2 K 4)

25 For a real surface: E = εσt s 4 For a surface with absorptivity α,, the incident radiation (G, W/m 2 ) that is absorbed by the surface is given by: G abs = α G G where G = incident radiation (W / m 2 ) G abs T = absolute temperature (K) ε = surface emissivity (0 ε 1) α = surface absorptivity (0 α 1)

26 For a gray surface α = ε When radiant energy is incident on a transparent surface, it can be absorbed, reflected, or transmitted through the material. Hence, G = G absorbed + G transmitted + G reflected = ( α + τ + ρ)g α + τ + ρ = 1 where ρ = materials surface reflectivity τ = materials transmissivity

27 Consider a small gray surface at temperature T s that is completely enclosed by the surroundings at temperature T sur. The net rate of radiation heat transfer from the surface is: q sur q s T sur '' 4 q 4 rad = Es αgsur = εσts ασtsur T s q '' rad q = A = εσ T 4 s ασ T 4 sur = h r ( T T ) s sur Where h r is the radiation heat transfer coefficient, W / m 2 K r 2 2 = ( )( ) ε σ T + T T T h + s sur s sur

28 Conduction example

29 Calculate the heat flux from your hand when it is exposed to moving air and water, assuming the surface temperature of your hand is 30 C. Convection example

30 Radiation ex. An instrumentation package has a spherical outer surface of diameter D = 100 mm and emissivity ε = The package is placed in a large space simulation chamber whose walls are maintained at 77 K. If the operation of the electronic components is restricted to the temperature range of 40 T 85 C, what is the range of acceptable power dissipation for the package?

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