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 tempeature follows __________ law.

ANS:A - parabolic

A parabolic temperature distribution refers to a temperature profile across a medium where the temperature variation follows a parabolic shape. In the context of heat conduction, a parabolic temperature distribution typically occurs under certain conditions, particularly when there is a steady-state heat transfer through a medium with uniform boundary conditions. Explanation:

1. Steady-State Heat Conduction: In steady-state heat conduction, the temperature within a medium remains constant with time. This typically occurs when the thermal properties and boundary conditions of the medium do not change over time.
2. Uniform Boundary Conditions: A parabolic temperature distribution often arises when the boundaries of the medium are maintained at constant temperatures. For example, if one side of a slab is held at a higher temperature and the other side is held at a lower temperature, and heat is allowed to flow through the slab, the temperature distribution within the slab will follow a parabolic shape.
3. Heat Conduction Equation: The parabolic temperature distribution can be derived from the heat conduction equation, which relates the rate of heat transfer to the temperature gradient within the medium. The exact form of the temperature profile depends on the geometry of the medium, boundary conditions, and material properties such as thermal conductivity.
4. Symmetry: The parabolic temperature distribution is often symmetric about the midpoint of the medium. This means that the temperature gradient is steeper near the boundaries where heat enters or leaves the medium and becomes more gradual toward the center.
5. Example: A common example of a parabolic temperature distribution is the steady-state heat conduction through a long, uniform rod with one end held at a higher temperature and the other end held at a lower temperature. The temperature along the length of the rod will vary parabolically from the higher temperature at one end to the lower temperature at the other end.