Question

Consider laminar natural convection from a vertical hot plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?

Short answer

Answer: The heat flux will be higher at the bottom of the vertical heated plate in laminar natural convection. This is due to the steeper temperature gradient at the bottom of the plate, as the fluid in contact with the plate is continuously getting heated and rising upwards, promoting a more efficient heat transfer.

Step-by-step solution

Understanding Laminar Natural Convection

Laminar natural convection occurs when a fluid flows around a heated or cooled surface due to the difference in fluid density caused by the temperature differences. As fluid gets heated, it becomes less dense and rises up, while colder fluid nearby moves in to replace the rising heated fluid. This circulation creates a convection current that transfers heat from the surface to the surrounding fluid.

Analyzing the Vertical Heated Plate

In the case of a vertical heated plate, the fluid immediately in contact with the plate will get heated and become less dense, prompting it to rise upwards. As the heated fluid rises, it moves away from the plate, allowing colder fluid to move in and take its place near the plate. The fluid close to the bottom of the plate will have a higher temperature gradient compared to the fluid close to the top of the plate since the fluid at the bottom has not yet had time to rise up along the plate and transfer its heat.

Determining the Heat Flux Distribution

Heat flux is the amount of heat transferred per unit area within a respective direction. The heat flux will be higher where the temperature gradient is steeper. As mentioned previously, the temperature gradient near the bottom of the plate will be steeper compared to that near the top of the plate. This is due to the fact that the fluid near the bottom is getting continuously heated and is rising, whereas the fluid near the top has already transferred some of its heat and has had time to cool slightly as it moves upwards along the plate.

Conclusion

Based on the temperature gradient and fluid motion around the vertical heated plate, it can be concluded that the heat flux will be higher at the bottom of the plate compared to the top. This is because the temperature gradient is steeper near the bottom of the plate, and the fluid there is continuously getting heated and rising upwards in the laminar natural convection process.