Does the thermal boundary conditions have an effect on the thermal conductivity of the material? I have attached a basic problem to understand the calculation of effective thermal conductivity of a material.
I think thermal boundary also the factors for themal conductivity.
In the problems described by you, 'effective' thermal conductivity does not arise. When the interior material reaches 500 C, further heat transfer will cease. The entire process is in unsteady state, tending towards thermal equilibrium. The thermal diffusivity will come into reckoning, but even there, there is no effective value for it.
If you have a porous material through which both conduction and radiation occur, then you can think of an 'equivalent' (you might also call it 'effective') thermal conductivity that will depend on the temperature of the radiating surface. Note that, as the material heats up, the equivalent value will change.
The 'equivalent' thermal conductivity will also arise if natural convection is occurring in the pores of the insulation.
Going back to your question (Does the thermal boundary conditions have an effect on the thermal conductivity of the material?), thermal conductivity is always a function of temperature. For most common materials, this dependence on temperature is available readily. You can ignore variation of thermal conductivity if you are working in a narrow temperature range.
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