Thermodynamics- Convection and External Flow Flashcards
What is velocity boundary layer thickness (δ) defined by?
Distance from surface that the flow velocity is 99% of the free stream velocity.
Where is thermal boundary layer thickness defined to be?
The distance from the surface where
Ts-T)=0.99(Ts-Tinf
Are the velocity and thermal boundary layer thicknesses the same?
No
Formula for critical Reynolds number
ρ uinf xc/μ
Where xc is distance along surface to where transition to turbulence begins (start of transition region)
How does δ vary as you go further along the surface?
Starts at 0. Up like root x curve. At start of transition region root x style curve is steeper upwards.
How does heat transfer coefficient vary as you go further along the surface?
Starts high near x=0. Curves down quite steep like exponential decay to start of transition region. Steep straight line up to highest point at end of transition region. Curves down exponentially very slowly in turbulent region due to the thermal resistance of the fluid.
Formula for heat transfer coefficient, h
h=(-kdT/dy)/(Ts-Tinf)
ds are curly and derivative is at y=0
Formula for h bar over a uniform surface temperature
h bar=(1/A)ShdA
Where integral is between 0 and whole area
Formula for h bar for flat plate in parallel flow
h bar=(1/L)ShdL
Integral is between 0 and L
Approximations for velocity boundary layer
Sending partial derivative of u with respect to x is much less than that with respect to y.
dp/dx is about dpinf/dx
Think p is pressure
Approximation for thermal boundary layer
Second partial derivative of T with respect to x is much less than that with respect to y
Governing equations for conservation of mass, momentum, energy for boundary layers
See slide 10 of intro to convection
Formula for Prandtl number
Pr=Cpμ/k=ν/α
Formula for Nusselt number
Nu=hL/kf
External flow
Fluid not surrounded by surface, eg over flat plate
