To determine the effect of the temperature dependence of the thermal conductivity on the temperature distribution in a solid, consider a material for which this dependence may be represented by: k = k0 + a T, where “k0“ is a positive constant and “a” is a coefficient that may be positive or negative. Starting with a steady-state energy balance, derive a relationship for temperature (T) as a function of distance (x) from the lower temperature wall. You may assume that there is no heat generation within the wall.
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