Question

If heat is transferred across a solid slab with constant density and heat capacity at steady state and no heat generation with temperature dependent thermal conductivity will the heat flux be the same at both ends?

Answer 1

Now consider the basic sketch given below

Where K is the thermal conductivity of the block Hi is the convective heat transfer coefficient of the left side fluid in contact with the block and Ho is the convective heat transfer coefficient of the right side fluid in contact with the block.

Now K is temperature dependent. Now the Temperature at both ends will be different in general case. When this is the case, the value of thermal conductivity will also be different and hence the heat flux will also very as K value is different.

Hence the heat flux will be different at both ends.