Question

A plane wall of thickness 0.1 m 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 32°C. 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 212 °C.

Step-by-step explanation:

Heat generation ,q

`q=0.3\ MW/m^3`

Heat flux

`q`

`q`

`q`

We know that total heat = heat flux x area

Q= 30 KW A

The maximum temperature will be at the insulated surface because fro insulated surface does not allow to flow the heat.

The total thermal resistance

`R=(L)/(KA)+(1)/(hA)`

`R=(0.1)/(25A)+(1)/(500A)`

`R=(0.006)/(A)`

Heat transfer Q

Q=ΔT/R

Lets take temperature at insulated side is T

`30* 1000 A=(T-32)/((0.006)/(A))`

`30* 1000 =(T-32)/(0.006)`

T= 180 + 32

T=212 °C.

So the maximum temperature is 212 °C.