Solve the following problem:
Q: The average free convection coefficient for the exterior surfaces of a long, horizontal rectangular duct exposed to a quiescent fluid can be estimated from the Hahn-Didion (H-D) correlation where the characteristic length is the half-perimeter
p = (w + H), and wand H are the horizontal width and vertical height, respectively of the duct. The thermo physical properties are evaluated at the film temperature.
(a) Consider a horizontal 0.15-m-square duct with a surface temperature of 35°C in ambient air at 15°C. Calculate the average convection coefficient and the heat rate per unit length using the H-D correlation.
(b) Calculate the average convection coefficient and the heat rate per unit length considering the duct as formed by vertical plates (sides) and horizontal plate (top and bottom). Do you expect this estimate to be lower or higher than that obtained with the H-D correlation? Explain the difference, if any.
c) Using an appropriate correlation calculate the average convection coefficient and the heat rate per unit length for a duct of circular cross section having a perimeter equal to the wetted perimeter of the rectangular duct of part (a). Do you expect this estimate to be lower or higher than that obtained with the H-D correlation? Explain the difference, if any.