Question

2. (25 pts) Engine oil flows with a velocity of 6 m/s over a flat plate having 1m length and 1 m width. The oil has a free stream temperature To= 80 °C and the plate surface temperature is maintained at Ts = 0 °C. a. Determine whether the flow over the plate transitions to turbulent regime. b. Calculate the average friction factor and the average heat transfer coefficient for the plate by using the appropriate correlations. c. Calculate the drag force acting on the plate and the overall heat transfer rate. Hint: Engine oil properties at the film temperature of 40 C: density p =876 kg/m3, specific heat cp= 1964 J/kgk, dynamic viscosity u=0.2177 kg/m*s, thermal conductivity k=0.1444 W/mK, and Pr = 2962

Answer 1

Oil Properties at meaty film temp. 40°c) $= 876 Kglio?, Cp = 1964 g/kyk, M = 0.2177 Kojimas K = 0.1444 w/mk, pr = 2962 To=8803 u=6 m/ Is = oc b=1m = 0.2177 Klaim (a) Re = JUL 876 X 6 X 1 = 2414331 M -- ReL < Ree, where Ree - critical Reynold's number For flow over flat plate Ree = 5*105 Hence the flow is Laminar. And there is no transition from Lamsnow to turbulent. co) The average value of heat transfer co-efficient for Laminar flow over flat pate is given by 0,5 2.333 ño x 0.664 x (RPL) 0.144470.664 x(24143-31)00%x (2962) = 213.388 W/mmoc The average foretron factor co-efficient According to Blasius exact solution is given by ! 1.328 0.00854 12414313) х | Լ 0.33 1 CE 1.328 Then s

c) The Local fachon co-effcrents 0.664 Care (fu 7472) Cfx Rese efni Ju² 2 at y=h 0.664 0.00427 124143,31 The shearing stress due to friction, Zo= cft -> Zo 0.00427 x 876 x 36 x 0.5 Nm? = 67. 171 W/m2 4. The total drag force on the plate, fo's Area of the plate 67.171 x 1 x 1 67.171 M Fo= Tox overall heat transfer rate, Q = ħ xas x (Too-Ts heating of plate = 213.388 X 1X1 X (80-0) 1707 1.04 watt 17.071 kW