# A plane wall was maintained initially 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 surfaces of the wall is assumed to be infinite, then what is the new temperature at the wall?

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A plane wall was maintained initially 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 surfaces of the wall is assumed to be infinite, then what is the new temperature at the wall?

(a) T

(b) T∞

(c) T∞-T

(d) T-T∞

This question was posed to me in exam.

This is a very interesting question from Eigen Value and Time Dependent Problems topic in section Single Variable Problems of Finite Element Method

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Correct option is (b) T∞

The explanation is: 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∞.

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