Airstream at 1 atm flows, with a velocity of \(15 \mathrm{~m} / \mathrm{s}\), in parallel over a 3-m-long flat plate where there is an unheated starting length of \(1 \mathrm{~m}\). The airstream has a temperature of \(20^{\circ} \mathrm{C}\) and the heated section of the flat plate is maintained at a constant temperature of \(80^{\circ} \mathrm{C}\). Determine \((a)\) the local convection heat transfer coefficient at the trailing edge and (b) the average convection heat transfer coefficient for the heated section.

Question: Calculate (a) the local convection heat transfer coefficient at the trailing edge and (b) the average convection heat transfer coefficient for the heated section of a flat plate given the following information: Flow velocity = 10 m/s, Length of the flat plate = 3 m, Unheated starting length = 0.5 m, Airstream temperature = 20°C, Heated section temperature = 60°C. Use the Blasius correlation for laminar flow over a flat plate. Answer: (a) The local convection heat transfer coefficient at the trailing edge can be calculated as follows: 1. Calculate the mean temperature: \(T_m = \frac{20 + 60}{2} = 40\)°C 2. Determine the air properties at 40°C: \(\rho\), \(\mu\), \(k\), \(C_p\), and \(\nu\) (refer to air property tables or an online calculator) 3. Calculate the Reynolds number at the trailing edge: \(Re_x = \frac{U_\infty x}{\nu}\) 4. Determine the Nusselt number at the trailing edge using the Blasius correlation: \(Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}\) 5. Calculate the local convection heat transfer coefficient at the trailing edge: \(h_x = \frac{k}{x}Nu_x\) (b) The average convection heat transfer coefficient for the heated section can be calculated as follows: 1. Calculate the average Nusselt number for the heated section using the Petukhov correlation: \(Nu_L = C Re_L^m Pr^n \frac{1}{\left[1 + L_0 / L\right]^{0.75}}\) 2. Calculate the average convection heat transfer coefficient for the heated section: \(h_L = \frac{k}{L}Nu_L\) Remember to use consistent units and the appropriate air properties when performing the calculations.