Consider the velocity boundary layer profile for flow over a flat plate to be of the form
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Fundamentals of Heat and Mass Transfer
- A stirrer mixes liquid chemicals in a large tank. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Discuss the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, ?, z) and velocity components (ur, u?, uz) at all surfaces, including the blades and the free surface? What pressure boundary conditions are appropriate for this flow field? Write mathematical equations for each boundary condition and discuss.arrow_forwardConsider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid body. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Present the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, 0, z) and velocity components (ur, uo, U:) at all surfaces, including the tank walls and the free surface? What pressure boundary conditions are appropriate for this flow field? Explain. Free surface Ps Paa Liquidarrow_forwardThe answer is handwritten and step by steparrow_forward
- (b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = ở. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. C5 Table 2: Equation of Velocity Profile Setting Equation wU = 2y/8 - (y/S² 1arrow_forwardQ4-Q6: A device is used to cool hot copper spheres of diameter 5 mm from an average temperature of 200C to 50C by letting them fall in air at 25°C and latm. Use drag coefficient C, = 0.4 and Whitaker correlation in your calculations. Assume the spheres fall at their terminal velocities during the process. Q4 improve the accuracy? Iteration is not required. ) Determine the terminal velocity of a sphere. Is the use of C, = 0.4 appropriate? If not, how toarrow_forwardAn approximation for the boundary-layer shape in is the formula u(y) - U sin 0 sys d where U is the stream velocity far from the wall and d is the boundary layer thickness, as in Fig. If the fluid is helium at 20°C and 1 atm, and if U = 10.8 m/s and 8= 3 cm, use the formula to (a) estimate the wall shear stress Tw in Pa, and (b) find the position in the boundary layer where t is one-half of Tw. -- y = 6 u(y)arrow_forward
- Consider the laminar boundary layer flow of an isothermal fluid ( U ∞ , T ∞ ) over a flat isothermal wall ( T 0 ). At a certain distance x from the leading edge, the local skin friction coefficient is C f , x = 0.0066. What is the value of the local Nusselt number at the same location if the Prandtl number is Pr = 7?arrow_forwardThis is a practice question, not graded assignment. Understand that to find the answer to below question, we need to solve Navier-Stokes and energy equation for this flow to derive the velocity profile and temperature profile. Please show step-by-step equations including step-by-step integration. Please also provide explanation. An incompressible fluid flows through a rectangular cross section duct, with width much larger than height of the cross section. The duct surface is heated at a uniform rate along its length. If the centreline of the flow is along the centre of the duct where y = 0, the distance from the centreline to the surface of the duct is b = 25 mm, and the thermal conductivity of the fluid is 0.6 W/mK, what is the local heat transfer coefficient in the developed region of the flow? Give your answer in W/m^2K to 1 decimal place.arrow_forwardWe are testing a flat plate of length L = 1.125 m and width W = 0.225 m in a stream of air flowing with a velocity of 20 m/s. In test case 1, the air is flowing parallel to L and in test case 2 air is flowing parallel to W. Find: What portion of the boundary layer flow is laminar in each case? What is the highest laminar boundary layer thickness in each case? Assuming the flow is entirely turbulent over the plate, calculate the drag force in both test cases Take air density as 1.2 kg/m3 and its viscosity as μ=18×10−6μ=18×10−6 N.s/m2.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning