Find the temperature distribution in a substance palced between two parallel plates kept at temperatures `T_1` and `T_2`. The plate separation is equal to `l`, the heat conductivity coefficient of the substance `x overline prop V overline T`.

Explanation

`Q = k(del T)/(del x) = -A sqrt(T) (del T)/(del x)`
=`-(2)/(3) A (del T^(3//2))/dx, (A = constant)`
=`(2)/(3) A((T_1^(3//2) - T_2^(3//2)))/(l)`
Thus `T^(3//2) = constant - (x)/(l) (T_1^(3//2) - T_2^(3//2))`
or using `T = T_1` at `x = 0`
`T^(3//2) T_1^(3//2)+(x)/(l) (T_2^(3//2) - T_1^(3//2))` or `((T)/(T_1))^(3//2) = 1 + (x)/(l) (((T_2)/(T))^(3//2) - 1)`
`T = T_1 [1 + (x)/(l) {((T_2)/(T_1))^(3//2) - 1}]^(2//3)`.