A rod of length `L` with sides fully insulated is made of a material whose thermal conductivity `K` varies with temperature as `K=(alpha)/(T)` where `alpha` is constant. The ends of rod are at temperature `T_(1)` and `T_(2)(T_(2)gtT_(1))` Find the rate of heat flow per unit area of rod .

Explanation

`(dQ)/(dt) =q = - KA(dT)/(dx)`
Heat transfer across each differential element is same
`q = - ((alpha)/(T))A (dT)/(dx)`
`underset(0)overset(L)intqdx= -alphaAunderset(T_(1))overset(T_(2))int(dT)/(T)rArrq =-(alphaA)/(L)ln((T_(2))/(T_(1)))`
` q=(alphaA)/(L)ln((T_(2))/(T_(1)))` .