Coefficient of Thermal conductivity

[imselva]

TL;DR Summary

K depends on temperature. K varies with temperature. For all the materials we have a tabular data of K for different temperatures.
While calculating Q for which temperature K value has to be taken?
Which K value is valid?

We know that,

Conduction Heat Transfer Q = KA(t2-t1)/thickness

K is the coefficient of thermal conductivity. If T2 = 1020°C and T1= 22°C also consider we know A and thickness value.

K depends on temperature. K varies with temperature. For all the materials we have a tabular data of K for different temperatures.
While calculating Q for which temperature K value has to be taken?
Which K value is valid?

 

[Lord Jestocost]

The equation Q = KA(t2-t1)/thickness is only valid in case the coefficient of thermal conductivity can be assumed to be about constant in the given temperature range.

 

[imselva]

If it is not constant, how to calculate it analytically?
Is there any other relation to calculate Q

 

[Lord Jestocost]

Heat conduction problems with temperature dependent material properties are preferentially solved using numerical methods.

 

[Chestermiller]

$$Q=-kA\frac{dT}{dx}$$so $$Q\Delta x=-A\int_{T_1}^{T_2}{kdT}$$