InterviewSolution
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InterviewSolution
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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`. |
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Answer» `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)`. |
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