The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x respectively. Temperatures on the opposite faces of composite slab are `T_(1) and T_(2)` where `T_(2)gtT_(1)`, as shown in fig. what is the rate of flow of heat through the slab in a steady state?

Explanation

Let T be the temperature of the common face of the composite slab of two materails. In the steady state, the rates of flow of heat through the two slabs will be same i.e.,
`(Delta Q)/(Delta t) =(KA(T_(2)-T))/(x) =( 2KA(T-T_(1)))/(4x0`
or `T_(2) -T =(T-T_(1))/(2) or T = (2T_(2)+T_(1))/(3)`
`:. (Delta Q)/(Delta t) = (KA)/(x) [T_(2)-(2T_(2)+T_(1))/(3)] = (KA)/(3x) [T_(2)-T_(1)]`.