Solve the incompressible boundary layer equations for laminarflow over a flat plate, assuming that viscous dissipation isactive.
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Solve the incompressible boundary layer equations for laminarflow over a flat plate, assuming that viscous dissipation isactive. The boundary layer equations
are given below:
Transcribed Image Text:
Continuity equation: x-momentum equation: Energy equation: น U ƏT ƏT əx ду +v ди Əv + əx əy du ????u +v əx ду = α =0 a²T eq. (1) ²u = (5) 3,72424 eq. (2) ¹ Jy² + ( ²7 ) (34) ² eq. (3) The boundary conditions for equations (1), (2), and (3) are given below: At x = 0: u(0, y) = U, v(0,y) = 0, T(0, y) = Too At y = 0: u(x,0) = 0, v(x,0) = 0, T(x,0) = Tw At y → ∞o: u(x, ∞0) = U∞, v(x,∞) = 0, T(x, ∞0) = T∞o You are being assigned to analyze the boundary layer for flow over a flat plate. Laminar flow of oil over a flat plate. U∞ = 10 m, T∞ = 37°C, Tw= 17°C (wall temperature) sec The energy equation (3) has a term for viscous dissipation. Properties of the oil are given in the table below (evaluated at 27 °C). These properties may be assumed to be constant throughout the computational domain. Density Specific heat Dynamic viscosity 884 kg/m³ 1.91 kJ/kg-K 0.486 N-sec/m² Thermal conductivity 0.145 W/m-K Prandtl No. 6400 The boundary layer (BL) equations are parabolic in the x (stream wise) coordinate. What this means is that the dependent variables at a given x location do not depend on downstream values, i.e. they only depend on upstream values. It turns out that this simplifies the solution process as will be discussed below. Continuity equation: x-momentum equation: Energy equation: น U ƏT ƏT əx ду +v ди Əv + əx əy du ????u +v əx ду = α =0 a²T eq. (1) ²u = (5) 3,72424 eq. (2) ¹ Jy² + ( ²7 ) (34) ² eq. (3) The boundary conditions for equations (1), (2), and (3) are given below: At x = 0: u(0, y) = U, v(0,y) = 0, T(0, y) = Too At y = 0: u(x,0) = 0, v(x,0) = 0, T(x,0) = Tw At y → ∞o: u(x, ∞0) = U∞, v(x,∞) = 0, T(x, ∞0) = T∞o You are being assigned to analyze the boundary layer for flow over a flat plate. Laminar flow of oil over a flat plate. U∞ = 10 m, T∞ = 37°C, Tw= 17°C (wall temperature) sec The energy equation (3) has a term for viscous dissipation. Properties of the oil are given in the table below (evaluated at 27 °C). These properties may be assumed to be constant throughout the computational domain. Density Specific heat Dynamic viscosity 884 kg/m³ 1.91 kJ/kg-K 0.486 N-sec/m² Thermal conductivity 0.145 W/m-K Prandtl No. 6400 The boundary layer (BL) equations are parabolic in the x (stream wise) coordinate. What this means is that the dependent variables at a given x location do not depend on downstream values, i.e. they only depend on upstream values. It turns out that this simplifies the solution process as will be discussed below.
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Lets tackle the solution by writing a MATLAB program that calculates the velocity u v and temperature T profiles using the given finite difference method and then uses these profiles to plot the veloc... View the full answer
Related Book For
Principles of heat transfer
ISBN: 978-0495667704
7th Edition
Authors: Frank Kreith, Raj M. Manglik, Mark S. Bohn
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