1. Convection heat transfer for laminar flow along a flat plate can be described by Nu = 0.332 Re³ Pr0333 where Re = хир μ and the range of application is Re, <5 x 10', 0.6 < Pr<10. Oil (with physical properties p = 868 kg/m³, = 0.0065 Pa s, 2 = 1.6 W/m°C, c, = 2000 J/kg°C) flows past a flat plate at a velocity far from the plate of 1.25 m/s. Calculate the Prandtl number, and check the validity of the correlation. Calculate the Reynolds number and the local heat transfer coefficient at the following distances along the plate: x 0.1, 0.5, 1, and 2 metres. At what distance along the plate is the correlation no longer valid? 2. From Question 1 above, clearly the local heat transfer coefficient varies along the plate. The average heat transfer coefficient over a length L of the plate is found by integrating the expression for h(x) over a distance L along the plate, as follows: h. = h(x) dx Write the expression for h(x) in terms of Re and Pr. Integrate this expression, and find a correlation for the average Nusselt number, Num, over a distance L, of the form Nu == const x Re Pr where Nu => h_ L 2 What is the relationship between h, and h(L)? Calculate the average heat transfer coefficient for the system described in Question 1 over the following distances: L=0.1, 0.5, 1, and 2 metres. 3. Calculate the Reynolds and Prandtl numbers describing the turbulent flow of water at 30°C and a flowrate of 15 m³/hour down a smooth pipe of 5 cm i.d., and hence calculate the heat transfer coefficient using the Colburn equation: Nu = 0.023 Re Pr333 Find the thermophysical properties of water at 30°C from steam tables.