This course is intended as a one semester course for first year graduate students on convection heat transfer. Topics to be covered include basic concepts in heat transfer, differential formulation of the continuity, momentum and energy equations, exact solution of one-dimensional flow problems, boundary layer flow, approximate solutions using the integral method, heat transfer in channel flow, correlation equations in forced and free convection, flow through porous media, convection in microchannels.
Convection heat transfer. The continuum and thermodynamic equilibrium concepts. Fourier's law of conduction.
Conservation of mass, momentum and energy equations in Cartesian, cylindrical and spherical coordinates. The Boussinesq approximation. Non-dimensional form of the governing equations. Boundary conditions. Nusselt number. Scale analysis.
Couette flow. Poiseuille flow. Rotating flows.
Boundary layer concept, the governing equations, simplification of momentum and energy equations. Solutions of external flow: flow over a flat plate with constant temperature and constant heat flux conditions. Blausius solution, Pohlhausen's solution. Laminar boundary layer flow over semi-infinite flat plate: variable surface temperature. Laminar boundary layer flow over a wedge: uniform surface temperature.
Integral method approximation. Integral formulation of mass, momentum and energy equations. Integral solutions of flow and temperature field over a semi-infinite flat plate for uniform temperature and heat flux conditions.
Hydrodynamic and thermal entry regions; analytic and numerical solutions. Fully developed region; uniform surface flux and uniform surface temperature cases. Thermal entrance region for laminar flow through tubes; Graetz solution.
Laminar free convection over a vertical plate with uniform temperature; similarity transformation. Laminar free convection over a vertical plate with uniform surface heat flux. Inclined plates. Integral solution of momentum and energy equations.
Examples of turbulent flows. Eddies and vorticity. Scales of turbulence. Characteristics of turbulence. Conservation equations for turbulent flow. Turbulent boundary layer equations. Reynolds stress and heat flux. The closure problem of turbulence.Eddy diffusivity. Momentum transfer in external turbulent flow: Modeling eddy diffusivity: Prandtl's mixing length theory, universal turbulent velocity profile. Approximate solution for momentum transfer: momentum integral method. Energy transfer in external turbulent flow; Momentum and heat transfer analogies, universal turbulent temperature profile, algebraic and integral methods for heat transfer coefficient. Effect of surface roughness on turbulence.
Entry length. Governing equations; conservation equations, apparent shear stress and heat transfer, mean velocity and temperature. Universal velocity profile; results from flat plate flow, development in cylindrical coordinates, velocity profile for the entire pipe. Momentum-heat transfer analogies; Reynolds analogy for pipe flow, adapting flat plate analogies to pipe flow. Algebraic method using universal temperature profile. Other correlations for smooth pipe. Heat transfer in rough pipes.
External forced convection correlations; flow over a flat plate, cylinder and sphere. Internal forced convection correlations for entrance and fully developed regions. Flow in non-circular channels. Free convection correlations.
Continuum, surface forces, mean free path, macro and micro channels. General features; Transition to turbulent flow, Nusselt number. Governing equations; compressibility, axial conduction, dissipation. Velocity slip. Analytic solutions; Slip flow, Couette flow with viscous dissipation. Poiseuille channel flow. Fully developed Poiseuille flow in microtubes.
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