Question

For laminar flow of a fluid along a flat plate, one would expect the largest local convection heat transfer coefficient for the same Reynolds and Prandl numbers when (a) The same temperature is maintained on the surface (b) The same heat flux is maintained on the surface (c) The plate has an unheated section (d) The plate surface is polished (e) None of the above

Short answer

a) The same temperature is maintained on the surface b) The same heat flux is maintained on the surface c) The plate has an unheated section d) The plate surface is polished e) None of the above Answer: (b) The same heat flux is maintained on the surface.

Step-by-step solution

Option (a): The same temperature is maintained on the surface

If the temperature is kept constant on the surface, the heat transfer by convection will be relatively stable. However, since the temperature difference between the fluid and the surface is not specified, we cannot determine if this will result in the largest local convection heat transfer coefficient.

Option (b): The same heat flux is maintained on the surface

Maintaining the same heat flux on the surface means that the heat transfer rate per unit area is constant. This would usually lead to a larger temperature difference between the fluid and the surface, resulting in a higher convection heat transfer coefficient compared to a scenario with a constant temperature on the surface. Therefore, this option has more potential to provide the largest local convection heat transfer coefficient.

Option (c): The plate has an unheated section

An unheated section means that there is no heat transfer happening in that part of the plate. This does not contribute to the increase of the convection heat transfer coefficient. Thus, this option cannot result in the largest local convection heat transfer coefficient.

Option (d): The plate surface is polished

A polished surface can reduce the fluid friction and might allow the fluid to flow more smoothly along the surface. However, this doesn't necessarily increase the local convection heat transfer coefficient, as it depends on other factors such as temperature difference and heat flux. This option alone doesn't guarantee the largest local convection heat transfer coefficient.

Option (e): None of the above

This option suggests that none of the previous options would result in the largest local convection heat transfer coefficient. However, as we analyzed, option (b) has the potential to provide this, so selecting this option would be incorrect. Based on the analysis, the correct answer is:

Concluding Answer:

(b) The same heat flux is maintained on the surface.