Consider The Situation Depicted Below In Which An Incompressible Fluid Flows Over A Flat Surface Of Solid Upstream Of 1 (120.37 KiB) Viewed 53 times
Consider The Situation Depicted Below In Which An Incompressible Fluid Flows Over A Flat Surface Of Solid Upstream Of 2 (26.5 KiB) Viewed 53 times
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 U₁ 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 a function of L, the location along the surface. a.) If the flow in the boundary layer is steady and laminar, write out the appropriate dimensional equations for the conservation of mass (of the fluid), momentum, and energy for this situation. Also write out the equation for the convection coefficient. You may assume that the entire situation is two- dimensional and that d'u/dx², the second derivative of the x-direction velocity with respect to x (the direction along the plate) is equal to zero. *HINT: See the equations in the textbook provided for mass and momentum equations for laminar boundary layer. b.) Non-dimensionalize the governing equations in part a.) with the parameters provided in the diagram below used as normalization constants. Be sure to define all dimensionless variables used. What is the dimensionless number parameterizing the convection coefficient (h) and what dimensionless ratios does it depend upon?
Convection Coefficient, h determined from fluid flow profile and fluid properties Incoming Velocity Uo, Temperature T.. Pressure P... L Boundary Layer Fluid Properties: Dynamic Viscosity, μ Density, p Specific Heat, Cp Thermal Conductivity, k Surface is at temperature, T
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