Thermodynamics HW Solutions 89

Thermodynamics HW Solutions 89 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-30 Consider a thin disk element of thickness Δ z and 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 balance on this thin element of thickness Δ z during a small time interval Δ t can be expressed as AD = π 2 4 / = + Δ element the of content energy the of change of Rate element the inside generation heat of Rate + at surface at the conduction heat of Rate at surface the at conduction heat of Rate z z z or, && & QQ G E t zz z −+ = Δ Δ element element But the change in the energy content of the element and the rate of heat generation within the element can be expressed as Δ Δ ΔΔ EE E m C T T C A z T tt t tt t element =− = Δ T = ++ + () ρ and & Gg Vg A element element == z Δ Substituting,
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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.

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