Chapter3

# Chapter3 - Chapter 1 Recap Heat transfer(or heat is energy...

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Copyright 2001 John Baldwin 1 ChEn 323 – Chapter 3 – Slide 1 Chapter 1 Recap Heat transfer (or heat) is energy in transit due to a temperature difference. Modes of heat transfer: § Conduction: Transfer of energy from more energetic to less energetic particles of a substance due to interactions between the particles. § Convection: Transfer of energy due to the bulk movement of materials (may be forced or natural, and/or may be single phase or changing phase). § Radiation: Energy emitted by matter at a finite temperature. Heat transfer is concerned with the rate of heat exchange. Conservation of energy restatement: Problem solving methodology. dt dE E E E st out g in = - + ChEn 323 – Chapter 3 – Slide 2 Chapter 2 Recap General form of Fourier’s Equation for flux: Properties for conduction: § Thermal conductivity § Thermal diffusivity The heat diffusion equation § General form § Cylindrical form § Spherical form + + - = - = x T x T x T k T k q k j i t T C q dz dT k z dy dT k y dx dT k x p = + + + r t T C q z T k z T k r r T kr r r p = + + + r f f 2 1 1 t T C q T sin k sin r T k sin r r T kr r r p = + + + r q q q q f f q 2 2 2 2 2 1 1 1

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2 ChEn 323 – Chapter 3 – Slide 3 Chapter 3: 1-D Steady State Conduction Objectives Understand how one-dimensional, steady-state heat transfer problems are treated Comfortably apply equivalent thermal circuits with pertinent expressions for conduction resistances Familiar with how the heat equation and Fourier’s law may be used to obtain temperature distributions and fluxes Appreciation of the role extended surfaces can play in the design of thermal systems and be able to design them Note: we will use 2 class periods to cover this material ChEn 323 – Chapter 3 – Slide 4 Plane Wall From the last chapter the diffusion equation in rectangular coordinates is: 0 = dx dT k dx d t T C q dz dT k z dy dT k y dx dT k x p = + + + r For one dimension at steady state with no source or sink in the wall this becomes: = dx dT k q x Now, flux which is Will be constant with no source or sink, so the general solution is ( 29 1 , 2 , 1 , 1 , 2 , 1 , 1 , 2 , 1 , 1 2 1 2 , 2 1 , 2 , 1 , 2 1 , ) ( , ; ) ( ) 0 ( ) ( s s s s s x s s s s s s s s T T L kA T x L T T dx d kA q So T x L T T x T Then T LC C L C T C T so T L x T T x T with C x C x T - = + -
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## This note was uploaded on 03/26/2008 for the course CHEN 323 taught by Professor Johnbaldwin during the Fall '03 term at Texas A&M.

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Chapter3 - Chapter 1 Recap Heat transfer(or heat is energy...

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