Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along t

Question

Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as q̇ = cos(2πx/L). The steady state temperature at the mid-location of the rod is given as TA. What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h?

Accepted Answer

TA. The temperature at the mid-location of the rod remains unchanged at TA because the increase in the convective heat transfer coefficient does not affect the steady-state temperature distribution established by the internal heat generation and the boundary conditions. The insulated end prevents any heat loss, and the steady state is defined by the balance of internal generation and heat loss at the exposed end.

Solution

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