Thermodynamics HW Solutions 138

Thermodynamics HW Solutions 138 - determined to be K W/m 24...

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Chapter 2 Heat Conduction Equation 2-102 A plate with variable conductivity is subjected to specified temperatures on both sides. The rate of heat transfer through the plate is to be determined. Assumptions 1 Heat transfer is given to be steady and one-dimensional. 2 Thermal conductivity varies linearly. 3 There is no heat generation. T 2 k ( T ) T 1 L Properties The thermal conductivity is given to be kT k T () ( ) = + 0 1 β . Analysis The average thermal conductivity of the medium in this case is simply the conductivity value at the average temperature since the thermal conductivity varies linearly with temperature, and is
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Unformatted text preview: determined to be K W/m 24 . 34 2 K 350) + (500 ) K 10 (8.7 + 1 K) W/m 25 ( 2 1 ) ( 1-4-1 2 ave ave ⋅ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × ⋅ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + β + = = T T k T k k Then the rate of heat conduction through the plate becomes W 30,820 = − × ⋅ = − = m 15 . 0)K 35 (500 m) 0.6 m K)(1.5 W/m 24 . 34 ( 2 1 ave L T T A k Q & Discussion We would obtain the same result if we substituted the given k ( T ) relation into the second part of Eq, 2-76, and performed the indicated integration. 2-61...
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