Question

What happens to the thermal conductivity of a wall of its thickness is doubled

Answer 1

Thermal conductivity across material is also known as Heat Induction. 

There is not a direct linear relationship between material thickness and heat conducted. But as the thickness of the material increases, heat conductivity reduces. 

Heat induction or thermal conductivity is measured in Watts per meter-kalvin as (W/m.k)

Attached is the sample graph image of thickness vs heat conducted through material. It clearly shows that it is not a direct linear relation. 

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Answer 2

The thermal conductivity is doubled if the thickness of wall is doubled because the larger the area of a solid the larger will be the number of molecules and electrons on each layer so the greater will be rate of flow of heat through solid.