Question

A long, circular aluminum rod is attached at one end to a heated wall and transfers heat by convection to a cold fluid.

(a) If the diameter of the rod is tripled, by how much would the rate of heat removal change?
(b) If a copper rod of the same diameter is used in place of the aluminum, by how much would the rate of heat removal change?

Answer 1

a. Heat removal rate will increase

b. Heat removal rate will decrease

Step-by-step explanation:

Given that

One end of rod is connected to the furnace and rod is long.So this rod can be treated as infinite long fin.

We know that heat transfer in fin given as follows

`Q_(fin)=√(hPKA)\ \Delta T`

We know that area

`A=(\pi)/(4)d^2`

Now when diameter will triples then :

`A_f=(\pi)/(4){\left (3d \right )}^2`

`A_f=9A`

`Q'_(fin)=√(9hPKA)\ \Delta T`

`Q'_(fin)=3√(hPKA)\ \Delta T`

`Q'_(fin)=3Q`

So the new heat transfer will increase by 3 times.

Now when copper rod will replace by aluminium rod :

As we know that thermal conductivity(K) of Aluminium is low as compare to Copper .It means that heat transfer will decreases.