Question

One end of a metallic rod of area $A$ and length $L$ is kept in stream as shown in figure below. A steady state is reached after sometime in which the amount of heat passing through any cross section of the rod per sec is $Q$. $Q$ will increase if

• A. $L$ is increased
• B. $A$ is increased
• C. the room temperature is increased.
• D. all of the above.

Answer 1

Answer: (B)

$A$ is increased

The heat transferring through a rod is given by:
$\dot{Q}=KA\frac{dT}{dx}$
As we can see it is directly proportional to $A$ and inversely proportional to length($L$).
Hence if $A$ is increased the heat transfer also increases. On increasing temperature of surroundings, the temperature gradient remains unaffected. On increasing the length, the heat transfer reduces.
Hence option B is correct