From my observation of certain experimental data it is predicting that - increase in thermal conductivity will result in increase in thermal stress. Correct me if I am wrong KINDLY.
You are wrong. Basically it is exactly the other way around: when parts with higher thermal conductivity are heated / cooled, lower temporary stresses arise in these parts than in the same parts with lower thermal conductivity. But the thermal conductivity is not the only property of the material that influences the temporary stresses. No less important are two other properties: the coefficient of thermal expansion and the modulus of elasticity. Only the combination of these three properties says how the stresses in the material develop with temperature changes. By the way, the slight differences in thermal conductivity hardly play a role for your superalloys. The differences in the modulus of elasticity of nickel and titanium-based alloys have a much greater effect on the stresses.
As I know increasing heat on a surface of material will increase both thermal stresses and material expansion.
Thermal stress =( Youngs modulus)X(Thermal strain). We know that thermal strain is produced when temperature changes. Therefore, we can say that thermal stress is a function of both Youngs modulus and thermal strain of the material.
As said, thermal conductivity and elastic modulus are the two parameters of vital importance in determining thermal stress.
Thermal conductivity is a parameter defines the ability of the matter to transfer heat. But the thermal stress is the function of Young modulus and thermal strain, which by itself based on the change in the temperature for the same domain.
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