Q1: If the thermal conductivity of a wall material is independent of temperature, the steady state temperature distribution in the very large thin plane wall having steady, uniform surface temperature follows __________ law.

ANS:C - linear

a) Hyperbolic law: The hyperbolic temperature distribution typically arises in transient heat conduction problems or when there are significant variations in boundary conditions or material properties along the direction of heat transfer. It is less common in steady-state heat conduction situations for uniform materials with constant properties. b) Parabolic law: The parabolic temperature distribution is a characteristic feature of steady-state heat conduction through a very large, thin plane wall when the thermal conductivity of the wall material is independent of temperature. In this scenario, the temperature profile within the wall exhibits a parabolic shape, with the highest temperature at the surface and gradually decreasing towards the interior of the wall. c) Linear law: The linear temperature distribution occurs in certain cases of steady-state heat conduction, particularly when there is a uniform heat source or sink along the wall. However, for the given conditions of a very large, thin plane wall with constant thermal conductivity, the temperature distribution is not linear but parabolic. d) Logarithmic law: The logarithmic temperature distribution is often associated with transient heat conduction or when there are logarithmic variations in temperature along the direction of heat transfer. It is not typically observed in steady-state heat conduction situations for uniform materials with constant properties. In summary, for a very large, thin plane wall with steady, uniform surface temperature and constant thermal conductivity, the steady-state temperature distribution follows a parabolic law, where the temperature profile within the wall varies quadratically with distance from the surface.