problem4-80 - PROBLEM 4.80 KNOWN Plane composite wall with...

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PROBLEM 4.80 KNOWN: Plane composite wall with exposed surfaces maintained at fixed temperatures. Material A as temperature-dependent thermal conductivity. h FIND: Heat flux through the wall (a) assuming a uniform thermal conductivity in material A evaluated at the average temperature of the section, and considering the temperature-dependent thermal conductivity of material A using (b) a finite-difference method of solution in IHT with a space ncrement of 1 mm and (c) the finite-element method of FEHT. i SCHEMATIC: ASSUMPTIONS: (1) Steady-state, one-dimensional conduction, (2) No thermal contact resistance etween the materials, and (3) No internal generation. b A NALYSIS: (a) From the thermal circuit in the above schematic, the heat flux is 1 2 AB 2 x A B B T T T T q R R R ′′ = = ′′ ′′ ′′ + (1, 2) a nd the thermal resistances of the two sections are (3, 4) A A A B B R L / k R L / k ′′ ′′ = B = T he thermal conductivity of material A is evaluated at the average temperature of the section ( ) { } A o 1 AB o k k 1 T T / 2 T α = + + (5) S ubstituting numerical values and solving the system of equations simultaneously in IHT, find < 2 AB x T 563.2 K q 52.64 kW / m ′′ = =
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