Question

A 6cm OD, 2cm thick copper hollow sphere [k=386W/m.C] is uniformly heated at the inner surface at a rate of 150W/m2. The outside surface is cooled with air at 20C with a heat transfer coefficient of 10W/m2.oC. Calculate the temperature of the outer surface

Answer 1

The outside surface temperature=21.66 C.

Step-by-step explanation:

Given that

Outer diameter=6 cm

Inner diameter=2 cm

`Heat\ flux\ at\ inner\ surface\q=150(W)/(m^2)`

Outside temperature=20 C

`Outside\ heat\ transfer\ coefficient=10(W)/(m^2-K)`

To find the outside temperature

Heat out from sphere=Heat absorb by surrounding

`q* A_i=hA_o\Delta T`

`q* d_i^2=hd_o^2(T_o-20)`

Now by putting the values

`150* 2_i^2=10* 6_o^2(T_o-20)`

`So\ T_o=21.66C`

So the outside surface temperature=21.66 C.