Flow and Thermal Considerations When a moving fluid comes into contact with a surface at some temperature difference (e.g. heated surface, cold fluid) the fluid will transfer heat to/from the surface in a process analogous to conduction (random motion of the fluid) advect heat away from the point of contact by its motion (bulk motion of the fluid) The combined effect of these two phenomena is called convection, which is described by Newton’s Law of Cooling fluid temperature [K] heat flux [W/m2] heat transfer coefficient [W/m2-K] surface temperature [K] Implications: the “direction” of heat flux can be considered normal to the surface the heat transfer coefficient is related of the nature of the fluid flow in order to study convection heat transfer we must also study fluid dynamics

Convection Coefficients There are local and average heat transfer coefficients because flow conditions vary along a surface both the local heat flux (q”) and local heat transfer coefficient (h or hx) vary along the surface The local heat transfer coefficient is defined as The average heat transfer coefficient is defined as

Fluid Dynamics: Boundary Layers Velocity Boundary Layer (External Flow) consequence of viscous effects associated with relative motion between a fluid and a surface region of the flow characterized by shear stresses and velocity gradients region between the surface and free stream whose thickness δ increases in the flow direction manifested by a surface shear stress τs that generates a drag force FD. spherical approximate boundary layer thickness shear stress for Newtonian fluids drag force over surface area μ is the dynamic viscosity of the fluid

Fluid Dynamics: Boundary Layers Thermal Boundary Layer (External Flow) consequence of heat transfer between the surface and fluid region of the flow characterized by heat fluxes and temperature gradients region between the surface and free stream whose thickness δt increases in the flow direction manifested by a surface heat flux, q”s that provides a convection heat transfer coefficient, h. spherical approximate boundary layer thickness heat flux at the surface heat transfer coefficient kf is the thermal conductivity of the fluid

Fluid Dynamics: Boundary Layers Boundary Layer Equations 2D, steady, incompressible flow negligible body forces constant & uniform fluid properties (μ,C,k) Apply conservation of mass, momentum, and energy to differential control volume (dxdy)