Question

A plane wall was maintained initially at a temperature of 35°C. It is subjected to an ambient temperature of 45°C at one surface. If the heat transfer coefficient at the surfaces of the wall is assumed to be infinite, then what is the new temperature at the wall surface?

(a) 35°C

(b) 45°C

(c) 40°C

(d) 50°C

This question was addressed to me in my homework.

I'd like to ask this question from Eigen Value and Time Dependent Problems in chapter Single Variable Problems of Finite Element Method

Answer 1

The correct answer is (b) 45°C

To explain: Let X be the unknown new temperature at the wall surface. If the heat transfer coefficient at the surfaces of a wall is assumed to be h, 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(X-T∞)

\(\frac{-kT_x}{h}\)=X-T∞

Given h = ∞

\(\frac{-kT_x}{\infty}\)=X-T∞

0=X-T∞

X=T∞, given T∞=45°C

X=45°C.