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1. Consider a flat plate with variable wall temperature, Tu-T(), and neglect viscous dissipation ...
For flow over a flat plate with non-uniform wall temperature ??(?) = ?∞ + ??^? where...
For flow over a flat plate with non-uniform wall temperature ??(?) = ?∞ + ??^? where ? and ? being constants, by still using the following dimensionless temperature ?(?) =( ?? − ?)/ (?? − ?∞) show that the energy equation in the boundary layer reduces to: ?"+ ??? ∙ ?′(1− ?) + (?? /2) ?′? = 0 while the boundary conditions can be written as ? = 0: ? = 0 ? → 1: ? = 1 where ?...
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms...
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms of Reynolds and Prandtl numbers) for laminar flow of a fluid over a surface with a free stream velocity of U. (which is a constant). Assume the fluid velocity in the momentum boundary layer is the same as the free stream velocity and (T-Tw)/(To-Tw)=(y/St), where T is the fluid temperature field in the thermal boundary layer, To is the free stream temperature, Twis the...
Consider laminar flow of an incompressible fluid past a flat plate. The boundary layer velocity profile...
Consider laminar flow of an incompressible fluid past a flat plate. The boundary layer velocity profile is given as u = U sin () a. Determine the boundary layer thicknesses 8, 8, as a function of x. Express in terms of Reynolds number. b. Using momentum integral theory, determine the wall shear stress tw, as a func. of x. Express in terms of Reynolds number. C. Determine the friction drag coefficient, Cof-
Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the...
Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the flat plate. A boundary layer thickness δ is formed close to the plate surface. Using the control volume analysis of the boundary layer (the von Karman equation) determine relationships of the a. boundary layer displacement thickness, δ* b. momentum thickness, θ c. shear stress on the flat plate surface, Tu as a function of the velocity deficit 1- Then use the approximation that the...
Use the integral method for boundary layer flow and convective heat transfer over a flat plate he...
Use the integral method for boundary layer flow and convective heat transfer over a flat plate heated by maintaining a constant heat flux q"w, for the case of very low Prandtl number, Pr0. Assume that the free stream velocity of the fluid, U, and free stream temperature, T-do not vary with x. Using the integral form of energy equation, show that under these conditions: (a) the temperature profile, (T- T) is given by, 41 2 CT-T oa (b) the wall...
Consider air flows with velocity of U?=U= 10 m/s over a semi-finite smooth flat plate with...
Consider air flows with velocity of U?=U= 10 m/s over a
semi-finite smooth flat plate with L=97 cm long. Calculate the
followings by assuming ? = 1.568 x 10-5 m2/s and ?=1.177
kg/m3.
Figure 1 : Boundary layer over a flat plate
Consider air flows with velocity of U?=U=10 m/s over a
semi-finite smooth flat plate with L=97 cm long. Calculate the
followings by assuming ? = 1.568 x 10-5 m2/s and ?=1.177
kg/m3.
b) Under some flow and boundary...
14.12 Consider the laminar boundary layer that develops on a flat plate aligned with the freestream...
14.12 Consider the laminar boundary layer that develops on a flat plate aligned with the freestream flow direction. The flow is incompressible, the freestream flow speed is U and the pressure is constant in the flow direction, i.e., op/az = 0. The vertical velocity component is constant and equal to-t Determine the horizontal velocity component, u(x, v). Is there any restriction on the value of u? Uoo 0
3). Standard air flows over a flat plate as shown. Laminar Find: boundary layer forms on...
3). Standard air flows over a flat plate as shown. Laminar Find: boundary layer forms on the surface. Assume the boundary (a). Wall shear stress, Fj)! layer bas a cubic velocity profile: (b). Boundary layer thickness, x)! (c). Shape factor (H-8t/0) Momentum integral equation on a flat plate is ax) Ud(u/U) Ху 1m The displacement thickncss and the momentum thickness are Freestream velocity is 1.0 m/s. The fluid viscosity and density are 1.55 x 10 m'ls and 1.23 kg/m, respectively...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x component of velocity in the in- compressible laminar boundary layer is a sinusoidal variation from u-0 at the surface (y-0) to the freestream velocity, U, at the boundary-layer edge (y-5). The equation for the profile is u-Usin( %), where cVx and c is a constant. The boundary layer is 9 mm thick 1 m from the edge of the plate. (a) Predict the boundary-layer...
Please make the hand writing legible. Thanks Consider the situation depicted below, in which an incompressible...
Please make the hand writing legible. Thanks
Consider the situation depicted below, in which an incompressible fluid flows over a flat surface of solid. Upstream of the surface, the fluid has velocity U and uniform temperature To. As the fluid is viscous, both a momentum boundary layer, and a thermal boundary layer form, and heat is transferred to the solid surface. A convective coefficient h can be used to describe the dimensional heat transfer rate to the solid, and is...
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms of Reynolds and Prandtl numbers) for laminar flow of a fluid over a surface with a free stream velocity of U. (which is a constant). Assume the fluid velocity in the momentum boundary layer is the same as the free stream velocity and (T-Tw)/(To-Tw)=(y/St), where T is the fluid temperature field in the thermal boundary layer, To is the free stream temperature, Twis the...
Consider laminar flow of an incompressible fluid past a flat plate. The boundary layer velocity profile is given as u = U sin () a. Determine the boundary layer thicknesses 8, 8, as a function of x. Express in terms of Reynolds number. b. Using momentum integral theory, determine the wall shear stress tw, as a func. of x. Express in terms of Reynolds number. C. Determine the friction drag coefficient, Cof-
Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the flat plate. A boundary layer thickness δ is formed close to the plate surface. Using the control volume analysis of the boundary layer (the von Karman equation) determine relationships of the a. boundary layer displacement thickness, δ* b. momentum thickness, θ c. shear stress on the flat plate surface, Tu as a function of the velocity deficit 1- Then use the approximation that the...
Use the integral method for boundary layer flow and convective heat transfer over a flat plate heated by maintaining a constant heat flux q"w, for the case of very low Prandtl number, Pr0. Assume that the free stream velocity of the fluid, U, and free stream temperature, T-do not vary with x. Using the integral form of energy equation, show that under these conditions: (a) the temperature profile, (T- T) is given by, 41 2 CT-T oa (b) the wall...
14.12 Consider the laminar boundary layer that develops on a flat plate aligned with the freestream flow direction. The flow is incompressible, the freestream flow speed is U and the pressure is constant in the flow direction, i.e., op/az = 0. The vertical velocity component is constant and equal to-t Determine the horizontal velocity component, u(x, v). Is there any restriction on the value of u? Uoo 0
3). Standard air flows over a flat plate as shown. Laminar Find: boundary layer forms on the surface. Assume the boundary (a). Wall shear stress, Fj)! layer bas a cubic velocity profile: (b). Boundary layer thickness, x)! (c). Shape factor (H-8t/0) Momentum integral equation on a flat plate is ax) Ud(u/U) Ху 1m The displacement thickncss and the momentum thickness are Freestream velocity is 1.0 m/s. The fluid viscosity and density are 1.55 x 10 m'ls and 1.23 kg/m, respectively...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x component of velocity in the in- compressible laminar boundary layer is a sinusoidal variation from u-0 at the surface (y-0) to the freestream velocity, U, at the boundary-layer edge (y-5). The equation for the profile is u-Usin( %), where cVx and c is a constant. The boundary layer is 9 mm thick 1 m from the edge of the plate. (a) Predict the boundary-layer...
Please make the hand writing legible. Thanks
Consider the situation depicted below, in which an incompressible fluid flows over a flat surface of solid. Upstream of the surface, the fluid has velocity U and uniform temperature To. As the fluid is viscous, both a momentum boundary layer, and a thermal boundary layer form, and heat is transferred to the solid surface. A convective coefficient h can be used to describe the dimensional heat transfer rate to the solid, and is...
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