Question

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

Answer 1

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)\(\frac{h}{k}\).