at V = 2 m/s, T = 45°C, and atmospheric pressur over an isothermal plate at T, = 20°C. In the first case, Re, = 5 x 10°, while in the second case the flow is tripped to a turbulent state at x=0 m. At what x-location are the thermal boundary layer thicknesses of the two %3D ual2 Wbot ore th locel hoot Auves ot this loco
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- Consider two cases involving parallel flow of dry air at V=V= 2.5 m/s, T∞=45°C, and atmospheric pressure over an isothermal plate at Ts=20°C. In the first case, Rex,c=Rex,c=5 × 105, while in the second case the flow is tripped to a turbulent state at x=0 m. a. At what x‐location, in m, are the thermal boundary layer thicknesses of the two cases equal? in m b. what is the q'' lam at W / m^2 c. what is the q'' turb at W / m^2QuestionNo.3 An approximated velocity profile for a laminar boundary layer is given as u(y) × Usin| 28 where U is the stream velocity far from the wall and 8 is the boundary layer thickness, as shown in Fig 2. If the fluid is helium (µ = 1.94 × 10-5N.s/m²) at 20°C and 1 atm, and if U = 10.8 m/s and ô= 3 cm, %3D use the formula to (a) Estimate the wall shear stress Tw in N/m2, and (b) Find the position in the boundary layer where t is one-half of Tw 2/2 U y = 8 u(y) Figure 2Consider parallel flow over a flat plate for air at 300 K and engine oil at 380 K. The free stream velocity is u temperature difference between the surface and the free stream is the same in both cases, with Ts > T (a) Determine the location, in m, where transition to turbulence occurs, xc, for both fluids. 8 X (b) For laminar flow over a flat plate, the velocity boundary layer thickness is given by = layer thickness 6, in m, for x = 1 for each fluid. Part A Determine the location, in m, where transition to turbulence occurs, xc, for both fluids. (c) Determine the thermal boundary layer thickness 6₁, in m, for x = 1 for each fluid. At an x-location where both fluids experience laminar flow conditions, which fluid has the largest temperature gradient at the plate surface, — dT/ dy|y_o? Which fluid is associated with the largest local Nusselt number Nu? Which fluid is associated with the largest local heat transfer coefficient h? y=0 Xc,air = Xc,eo = i m 5 Rex m = 1.6 m/s. The Determine…
- Problem-2 For the turbulent incompressible boundary layer, the velocity profile is given as u/Ue, y = y/8, Ue and d are boundary-layer edge velocity where, u = and boundary layer thickness, respectively. Using momentum integral equation, prove that: 8/x = 0.383/Re,/5 8% /x = 0.0479/Re/5 and 0/x = 0.0372/Re/5In the laminar flow of air (Pr = 0.7) over a heated plate, if & and 8, denote, respectively, the hydrodynamic and thermal boundary layer thicknesses, then (a) 8 = 8, (c) 8 8- (d) 8 = 0 but 8,# 0Consider two cases involving parallel flow of dry air at V = 3.5 m/s, T, = 45°C, and atmospheric pressure over an isothermal plate at T, = 20°C. In the first case, Ree = 5× 105, while in the second case the flow is tripped to a turbulent state at.x = 0m. At what x -location, in m, are the thermal boundary layer thicknesses of the two cases equal? What are the local heat fluxes, in W/m?, at this location for the two cases? X = m d'am W/m2 i urb W/m? i
- Cooling water for a power plant is stored in a pond 900 m in length and 400 m wide. A dry wind at 300 K blows in a horizontal direction parallel to the 900 m side of the pond at a velocity of 2 m/s. The cooling water is at 300 K. Known the air dynamic viscosity v= 1.67 x10m?/s.; the Re transition from laminar flow to turbulent flow is 500,000; and the saturated water vapor pressure at 300 K is 3580 Pa; gas constant R= 8.3144 J/mole.K. 1.) At what position across the pond is the air flow no longer laminar? Would it reasonable to assume that the mean gas-film mass transfer coefficient for water vapor in air is dominated by turbulent flow mass transfer? 2.) As part of an engineering analysis to predict the evaporation rate of water from the pond, determine the mean gas film mass transfer co-efficient. 3.) Calculate the rate of water evaporation from the pond.5. Water flows over a L=0.3 m long plate at 1.2 m/s velocity and 3°C temperature. There is a correlation between the water temperature and the plate surface temperature as Ts(x) -T=Cx0.75 across the plate (C = 54.27 °C/m0.75). The surface temperature varies throughout the plate. Find the average heat transfer coefficient for this case.A thin metal sheet serving the purpose of an an anemometer has a length of 2.5 cm with a width of 8 mm. Wind with a temperature T, and velocity Uz blows parallel to the longest side of the sheet. The metal sheet is heated through a solar powered system giving our heat both sides at Q Watts. The anemometer is used in air with T,= 20C, C, = 1.005KJ/Kg K, v = 1.522 X 105 m2/s, p = 1.19 Kg/m³ and Pr = 0.72. The surface temperature, T, of the metal sheet was measured at the rear end however, it can be assumed to be constant. You are required to calculate an estimate of the wind speed when T = 32 °C and Q = 0.5 W.
- Consider laminar flow entering a tube. Before the fluid enters, the velocity profile is constant and equal to to. The tube diameter is D and radius R. You are interested in estimating how much distance the fluid must travel into the tube before the classic Poiseuille parabolic velocity profile is established - this distance is called the "entrance length" or Zent- Using boundary layer theory, which of the following would be a reasonable estimate? (Hint: assume as flow enters the tube, you can model the growing viscous boundary layer as laminar flow over a flat plate, and note that the De where v = Reynolds number for a tube is Rep %3D Zent = (Rep) Zent = D 2 (Rep) Zent = 2. Rep - Rep O Zent R-Rep %3D O None of the above.Q.3 Air (density 1.2 kg/m3 and kinematic viscosity 15 centistokes) flows over a flat plate, at zero angle of incidence, at a velocity of 20 m/s. If Reynolds number at transition is taken as 2.5 × 105, maximum distance, from leading edge up to which the boundary layer remains laminar isConsider two cases involving parallel flow of dry air at V = 4m/s, T, = 45°C, and atmospheric pressure over an isothermal plate at T, = 20°C. In the first case, Re = 5 x 105, while in the second case the flow is tripped to a turbulent state at x = 0m. At what x -location, in m, are the thermal boundary layer thicknesses of the two cases equal? What are the local heat fluxes, in W/m?, at this location for the two cases? X = i W/m? urb W/m? i