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

The maximum temperature is 90.06° C

Step-by-step 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* t`

`q=0.3* 1000000* 0.1 * 10^(-3)\ W/m^2`

`q=30\ W/m^2`

So the total thermal resistance per unit area

`R=(t)/(K)+(1)/(h)`

`R=(0.1* 10^(-3))/(25)+(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