Chapter 2 Heat Conduction Equation2-30 Consider a thin disk element of thickness Δzand diameter D in a long cylinder (Fig. P2-30). The density of the cylinder is ρ, the specific heat is C, and the area of the cylinder normal to the direction of heat transfer is , which is constant. An energy balanceon this thin element of thickness Δzduring a small time interval Δt can be expressed as AD=π24/⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛+⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛Δ−⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛elementtheofcontent energy theofchangeofRateelementtheinsidegenerationheat ofRate+at surfaceat theconductionheatofRateat surfacetheat conductionheat ofRatezzzor, &&&QQGEtzzz−+=+ΔΔΔelementelementBut the change in the energy content of the element and the rate of heat generation within the element can be expressed as ΔΔΔΔEEEmCTTCAzTttttt telement=−=ΔT−=−+++()ρand &GgVgAelementelement==zΔSubstituting,
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.