Question

Consider turbulent 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

Explain your reasoning. Answer: The heat flux will be higher near the inlet of the circular tube. This is because the thermal boundary layer, which is responsible for much of the heat transfer, is thinner at the inlet, leading to a steeper temperature gradient and a higher heat transfer rate. As the fluid moves along the tube, the boundary layer thickness increases, causing a decrease in the temperature gradient and a lower heat flux near the exit.

Step-by-step solution

Understanding turbulent forced convection

Turbulent forced convection is a heat transfer process in which a fluid moves through a conduit (like a circular tube in this exercise) and exchanges heat with the walls of the conduit. In this case, the fluid flow is turbulent, which indicates that the fluid particles move in an irregular and chaotic manner, leading to a higher mixing rate and, consequently, a higher heat transfer rate.

Factors affecting heat flux

Heat flux is the rate at which heat is transferred per unit area along the direction of heat transfer. There are several factors influencing the heat flux in the case of turbulent forced convection in a circular tube, including fluid properties, tube geometry, flow conditions, and temperature difference between the fluid and tube wall. Some of these factors, like flow velocity and fluid properties, change along the length of the tube, impacting the heat flux variation from the inlet to the exit.

The effect of thermal boundary layer on heat flux:

As the fluid flows through the circular tube, a thermal boundary layer develops near the tube wall. In this layer, the temperature gradient is steep, and much of the heat transfer occurs. The thickness of the boundary layer increases with distance along the flow direction, leading to a decrease in the temperature gradient and, consequently, a lower heat flux.

Conclusion

Considering the development of the thermal boundary layer and the decreasing temperature gradient along the flow direction, we can conclude that the heat flux will be higher near the inlet of the circular tube than near the exit. The reason for this is that the thermal boundary layer is thinner at the inlet, resulting in a steeper temperature gradient and, therefore, a higher heat transfer rate.