Question

A plane wall of thickness 0.1 mm and thermal conductivity 25 W/m K having uniform volumetric heat generation of 0.3 MW/m3 is insulated on one side, while the other side is exposed to a fluid at 92 oC. The convection heat transfer coefficient between the wall and the fluid is 500 W/m2 K. Determine the maximum temperature in the wall.

Answer 1

Answer:

The maximum temperature is 90.06° C

Explanation:

Given that

t= 0.1 mm

Heat generation

$q_g=0.3\ MW/m^3$

Heat transfer coefficient

$h=500\ W/m^2K$

Here one side(left side) of the wall is insulated so the all heat will goes in to right side .

The maximum temperature will at the left side.

Lets take maximum temperature is T

Total heat flux ,q

$q=q_g\times t$

$q=0.3\times 1000000\times 0.1 \times 10^{-3}\ W/m^2$

$q=30\ W/m^2$

So the total thermal resistance per unit area

$R=\dfrac{t}{K}+\dfrac{1}{h}$

$R=\dfrac{0.1\times 10^{-3}}{25}+\dfrac{1}{500}$

R=0.002 K/W

We know that

q=ΔT/R

30=(T-90)/0.002

T=90.06° C

The maximum temperature is 90.06° C