A hollow tube possesses a length l , inner radius R₁ , and outer radius R₂ . The material has a thermal conductivity K . Determine the heat flowing through the walls of the tube if the flat ends are maintained at temperatures T₁ and T₂ ( T₂ > T₁ ).

Step-by-step solution

The heat flows longitudinally along the length of the tube because the temperature difference is maintained across its flat ends. The cross-sectional area of the hollow tube through which heat flows is the area of the annular region, given by A = R₂^2 - R₁^2 = (R₂^2 - R₁^2) . The length of the tube is l and the temperature difference is T = T₂ - T₁ . According to the law of thermal conduction, the rate of heat flow is H = KA T l . Substituting the values, we get H = K (R₂^2 - R₁^2)(T₂ - T₁) l .