Question
Asked Sep 10, 2019
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Consider a large plane wall of thickness L = 0.3 m, thermal conductivity k = 2.5 W/m·K, and surface area A = 12 m2. The left side of the wall at x = 0 is subjected to a net heat flux of , while the temperature at that surface is measured to be T1 = 80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperature of the right surface of the wall at x = L.

Gо
Ti
х
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Gо Ti х

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Expert Answer

Step 1

(a)

 

Write the differential equation for one dimensional heat transfer through conduction for a slab.

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d'T 1dT dx2 k a dt

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Step 2

For steady state heat transfer without heat generation the differential equation will be reduced to.

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d2T -0 (1)

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Step 3

Boundary conditions ar...

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dT(0 700 W/m2 -k T(0)-80 °C

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Engineering

Mechanical Engineering

Heat Transfer

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