A composite slab consists of two rectangular slabs of different materials, having coefficients of conductivity 2K and K. The two ends of the slabs are at temperatures `T_1` and `T_2` (where ` T_1 gt T_2` ). How will the rate of heat flow depend on a where 3a and a are the lengths of two slabs? Consider that the two slabs have equal thickness.

Explanation

Let the temperature of interface of two slabs be T. At steady state, rate of heat flow through the two slabs will be equal
` therefore (2KA (T_1 - T) )/(3a) = (KA(T- T_2) )/(a)`
` rArr 3/2 (T_1 - T) = T - T_2`
`2/3 T_1+T_2 = 2/3 T + T = (5T)/(3)`
` rArr (5T)/(3) = (2T_1 3T_2)/(3) `
` rArr T = (2T_1 + 3t_2)/(5)`
` therefore ` Rate of heat flow through slab of thickness 3a and coefficient of thermal conductivity 2K is
`Q_1 = (2KA)/(3a) [ T_2 - ((2T_1 - 3T_2))/(5) ]`
` = (4KA)/(3a) (T_2 - T_1)`
` therefore Q_1 prop 1/a `
The rate of heat flow varies inversely as a.