1. 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

2. 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

3. 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

4. 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

5. 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)