The diameter of a conical section fabricated from pure Alumi

The diameter of a conical section fabricated from pure Aluminum is given as D= ax^1/4 where a is a constant number. The temperatures at the two ends located at x₁ and x₂ are T₁ and T₂. The lateral surface is well insulated. Derive an expression for the temperature distribution and calculate heat transfer rate.

Solution

Derive an expression for the temperature distribution T(x) in symbolic form, assuming 1-D conditions. Sketch the temperature distrubution. Then calculate the heat rat qx.