All Problems

Transport Phenomena

Problem 2.251

Find the temperature distribution in a substance placed between two parallel plates kept at temperatures T1T_{1} and T2T_{2}. The plate separation is equal to l,l, the heat conductivity coefficient of the substance x∝ˉTx \bar{\propto} \sqrt{T}.

Reveal Answer
T=T1{1+(x/l)[(T2/T1)3/2−1]}2/3, where x is the distance from the plate maintained at the temperatureT1T=T_{1}\left\{1+(x / l)\left[\left(T_{2} / T_{1}\right)^{3 / 2}-1\right]\right\}^{2 / 3}, \text { where } x \text { is the distance from the plate maintained at the temperature} T_{1}
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