Question

Consider laminar forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?

Short answer

Based on the analysis and solution provided, the short answer is: The heat flux will be higher near the inlet of a circular tube under laminar forced convection conditions, due to the higher temperature gradient between the wall and the fluid at the inlet as compared to the exit.

Step-by-step solution

Understand laminar forced convection in a circular tube

In a laminar forced convection flow, the fluid moves in parallel layers, and the heat is transferred primarily through the conduction mechanism. When a fluid flows through a circular tube, the flow near the walls is slowed down due to viscous effects, resulting in a velocity profile that is parabolic in nature.

Recognize the importance of temperature gradient

Heat flux is directly proportional to the temperature gradient, which is the difference in temperature across the fluid layer. Higher temperature gradient means higher heat transfer rate. Therefore, we need to analyze how the temperature gradient varies along the length of the circular tube.

Analyze the temperature gradient near the inlet and the exit of the tube

When the fluid enters the tube, it has a uniform temperature distribution. As it flows through the tube and gets heated, the temperature near the wall increases. Since the velocity of the fluid near the wall is lower than the velocity at the center of the tube, the temperature gradient near the wall is higher compared to the center of the tube. Hence, we can expect a higher heat flux near the inlet. As the fluid moves along the length of the tube towards its exit, the overall temperature of the fluid increases, and the temperature gradient between the wall and the fluid reduces. The velocity profile remains parabolic, but the temperature difference along the flow length decreases. This results in a lower heat flux near the exit.

Conclude the answer

The heat flux will be higher near the inlet of the circular tube compared to the exit. This is because, near the inlet, the temperature gradient between the wall and the fluid is higher, and as the fluid flows towards the exit, the temperature gradient decreases due to the increase in the overall fluid temperature. Thus, the heat transfer rate is higher at the inlet than at the exit.