Question

plane wall, 7.5 cm thick, generates heat internally at the rate of 105W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 120°C. The convection heat transfer coefficient between the wall and the environment is 750 W/m2K. If the thermal conductivity of the wall is 20 W/m K, calculate the maximum temperature in the wall.

Answer 1

T=120.04°C

Step-by-step explanation:

Given that

L= 7.5 cm

q = 105 W/m³

T∞=120°C

h=750 W/m²K

K=20 W/mK

Here given that one side of the wall is insulated that is why the maximum temperature will be at the insulated surface.

The total heat transfer from the wall

Q= q A L

Q= 150 x 0.075 A

Q=7.875 A W

A=Area of wall

Now the total thermal resistance R

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

`R=(0.075)/(20A)+(1)/(750A)`

`R=(0.00508)/(A)`

We also know that

`Q=(\Delta T)/(R)`

Temperature at insulated side = T

`7.875 A=(T-120)/((0.00508)/(A))`

`7.875 =(T-120)/(0.00508)`

T=120.04°C