# A plane wall of length L units and Cross-section area A units was initially maintained at a temperature of T units. It is subjected to an ambient temperature of T∞ units at one surface. If the heat transfer coefficient at the surface of the wall is assumed to be h units, then what is the temperature gradient developed at the surface?

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A plane wall of length L units and Cross-section area A units was initially maintained at a temperature of T units. It is subjected to an ambient temperature of T∞ units at one surface. If the heat transfer coefficient at the surface of the wall is assumed to be h units, then what is the temperature gradient developed at the surface?

(a) (T∞-T)$\frac{h}{k}$

(b) (T∞-T)$\frac{1}{L}$

(c) T∞-T

(d) T-T∞

The question was posed to me in an online interview.

My doubt is from Eigen Value and Time Dependent Problems topic in chapter Single Variable Problems of Finite Element Method

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The correct option is (a) (T∞-T)$\frac{h}{k}$

For explanation: Let Tx be temperature gradient developed at the surface. If the heat transfer coefficient at the surfaces of a wall is assumed to be h units, then the heat interaction at the surfaces of the wall is evaluated by Equating the conduction heat transfer to the convection heat transfer, i.e.,

kATx = hA(T-T∞)

Tx=(T∞-T)$\frac{h}{k}$.

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