A plane slab of thickness L and thermal conductivity {k} is heated with a fluid on one side ( P ), and the other side (Q) is maintained at a constant temperature, T_{Q} of 25^{\circ} C, as shown in the figure. The fluid is at 45^{\circ} {C} and the surface heat transfer coefficient, {h}, is 10 {W} \/ {m}^{2} {K}. The steady state temperature. TP (in { }^{\circ} {C} ) of the side which is exposed to the fluid is ___________(correct to two decimal places).

GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 59 of 65

Marks: +1, -0

A plane slab of thickness L and thermal conductivity

{k}

is heated with a fluid on one side (

P

), and the other side

(Q)

is maintained at a constant temperature,

T_{Q}

25^{∘} C

, as shown in the figure. The fluid is at

45^{∘} {C}

and the surface heat transfer coefficient,

{h}

, is

10 {W} \/ {m}^{2} {K}

. The steady state temperature. TP (in

{ }^{∘} {C}

) of the side which is exposed to the fluid is ___________(correct to two decimal places).

Solution:

Assuming steady state conditions
Thermal circuit

Assuming steady state, heat transferred from fluid will be equal to heat transferred from wall.

q=

Rate of heat transfer

=\;{45-T_{p}}/{1 {/} h A}=\;{T_{p}-25}/{L {/} k A}

⇒ \;\; \;{45-T_{p}}/{(\;{1}/{10})}=\;{T_{p}-25}/{{0.2}/{2.5}}

T_{P}=33.889^{∘} {C}

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