91Ó°ÊÓ

For both cases: Diameter of the tube, \(D = 5 \mathrm{~cm} = 0.05 \mathrm{~m}\) (converted from centimeters to meters) Air velocity, \(V = 25 \mathrm{~m/s}\) For case (a) - air flowing inside the tube: Bulk mean temperature, \(T_{a,\text{bulk}} = 50^{\circ} \mathrm{C}\) For case (b) - air flowing across the outer surface of the tube: Film temperature, \(T_{b,\text{film}} = 50^{\circ} \mathrm{C}\)

For both cases, we need more information to calculate the heat transfer rate. Since this information is not provided in the problem statement, we will assume that the heat transfer rates are the same for both cases. This assumption will allow us to compare the convection heat transfer coefficients between the two cases. Let the heat transfer rate be \(Q\).

For case (a) - air flowing inside the tube: The area of the inside surface of the tube, \(A = \pi D_l\) where \(D_l\) is the inner diameter of the tube. Since the tube has a thin wall, we can assume that \(D_l \approx\) 0.05 m. Thus, \(A_{a} = \pi \times (0.05\mathrm{~m})\) For case (b) - air flowing across the outer surface of the tube: The area of the outer surface of the tube, \(A = \pi D_o\) where \(D_o\) is the outer diameter of the tube. Since the tube has a thin wall, we can assume that \(D_o \approx\) 0.05 m. Thus, \(A_{b} = \pi \times (0.05\mathrm{~m})\)

For both cases, we will use the formula \(h = \frac{Q}{A \cdot \Delta T}\). \(\Delta T = T_\text{surface} - T_\text{bulk/film}\) is the temperature difference between the tube surface and the bulk/film temperature of the air. We are not given the surface temperature, and may not be able to determine the temperature difference. Therefore, an accurate numeric answer for the convection heat transfer coefficients cannot be provided for either case. However, it is possible to make a qualitative comparison between the heat transfer in both cases. For case (a), the convection heat transfer is generally more effective when air flows inside the tube, as there is a more uniform and smoother flow profile, which increases the movement of heat away from the tube surface. For case (b), the flow of air on the outer surface of the tube may have disturbances and turbulence which can result in local hotspots or uneven heat transfer. Without the surface temperature and heat transfer rates required to compute the convection heat transfer coefficients for each case, we can conclude that case (a) generally has a higher convection heat transfer coefficient compared to case (b).