Thermodynamics- Internal Flow Flashcards
What does inviscid mean?
No viscosity
Describe the velocity in the regions of internal flow from entrance
The velocity distribution is uniform at the entrance. Boundary layers form and increase in thickness along the hydrodynamic entrance region. The velocity profile is not uniform due to velocity boundary layer thicknesses increasing and the inviscid region decreases. Once these boundary layers meet at the centreline, the velocity profile becomes parabolic in the fully developed region and no longer changes with distance along the flow. The flow is assumed to be axisymmetric.
Describe the thermal conditions in the regions of internal flow from the entrance
You can assume either that there is a constant heat flux or a constant wall temperature. Temperature distribution uniform at entrance. Thermal boundary layer forms and thickens in the thermal entrance region. For Ts>Tinlet the temperature is greater in the boundary layers and closer to walls. When thermal boundary layers merge at centreline, temperature profile still varies along the fully developed region but the dimension form of the temperature profile doesn’t (see p526).
What velocity and temperature is used for mass flow rate and thermal energy transport calculations?
Mean velocity defined so that when multiplied by CSA and density gives mass flow rate (see p520).
Mean temperature defined so that when multiplied by mass and Cp gives true rate of thermal energy advection integrated over the cross-section (see p525).
Formula for calculation of local heat flux in internal flow
q”s=h(Ts-Tm)
s subscript is at surface
Formula for hydraulic diameter
Dh=4xCSA/Perimeter
Relations for hydrodynamic entry length in laminar and turbulent flow
Laminar: xfd,h/Dh is about 0.05Re
Turbulent: xfd,h/Dh is between 10 and 60
xfd,h is hydrodynamic entry length
Relations for thermal entry length in laminar and turbulent flow
Laminar: xfd,t/Dh is about 0.05RePr
Turbulent: xfd,t/Dh is between 10 and 60
xfd,t is thermal entry length
How does convection heat transfer coefficient, h, vary along internal flow
Starts very high but decreases steeply (exponential decay) until xfd,t where it remains constant along the fully developed region as hfd.
Is constant surface heat flux is assumed what is formula for mean temperature from entrance onwards?
Tm(x)=Tm,i + (q”sP/mCp)x
So it varies linearly with x along the tube.
When assuming constant surface heat flux, why must Ts increase with Tm?
Because q”s is a function of temperature difference between them so for it to stay constant in the fully developed region, this difference must remain constant. h is also independent of x.
When assuming uniform surface temperature, what is formula for log-mean temperature?
ΔTlm=(ΔTo-ΔTi)/ln(ΔTo/ΔTi)
Where ΔTi is difference between Tm and Ts at the inlet
Where ΔTo is this difference at the outlet (or second point)
Formula for heat transfer when contant temperature outer flow over inner flow
q=UbarAsΔTlm=ΔTlm/Rt
U bar is mean overall heat transfer coefficient
Local Nu for laminar flow in circular tube for both assumptions (fully developed flow)
Uniform surface heat flux: Nu=4.36
Uniform surface temperature: Nu=3.66
Local Nu for turbulent flow in a circular tube (fully developed flow) for smooth surfaces and Re>10,000
Nu=0.023Re^(4/5)Pr^n
n is 0.4 when fluid is being heated
n is 0.3 when fluid is being cooled
