Thermodynamcis- Free Convection Flashcards
What does free convection refer to?
Fluid motion induced by buoyancy forces
How do buoyancy forces arise?
Due to density gradients and a body force. In heat, these are due to temperature gradients and gravity.
Describe what happens when a fluid is between two plates and the bottom one is hotter
There is unstable fluid circulation. The temperature of the fluid is greater at the bottom so is less dense and it rises above colder fluid. This colder fluid sinks due to gravity but then is heated so goes in a cycle.
What are two types of free boundary flows?
Plumes and buoyant jets
Describe plumes
Initial velocity of fluid is zero. Fluid rises from a submerged heated object, e.g a wire. Width of plume increases with distance from the object to form a parabolic shape. Velocity of rising fluid is greatest at centre of plume and follows sort of normal distribution curve outwards to zero at its width.
Describe buoyant jets
Heated fluid starts with some horizontal velocity and rises up in a curve due to the buoyancy force. It’s width increases with distance from point of discharge and also increases faster further away (not parabolic). Normal distribution of velocity about centre line of jet going to zero at its width.
Formula for Grashof number, Gr
GrL=gβ(Ts-Tinf)L^3/ν^2
Which is buoyancy force over viscous force
L is characteristic length of surface (sphere would be diameter)
β is thermal expansion coefficient
L in Gr is subscript
g is 9.81
Formula for Rayleigh number, Ra
RaL=GrLxPr=gβ(Ts-Tinf)L^3/να
Pr is prandtl number
α is in tables
Formula for thermal expansion coefficient, β
β=-(1/ρ)(δρ/δT)P
All deltas are curly ds
P is subscript for constant pressure
How to use Gr and Re to see if convection is forced or free
Find Gr/Re^2
If around 1 then forced and free are comparable
If much greater than 1 then free convection
If much less than 1 then forced convection
Both subscript L
Another term for free convection
Natural convection
Nusselt number for mixed convection
Nu^n is about NuFC^n+/-NuNC^n FC and NC are forced and natural convection and are subscript \+ for assisting and transverse flows - for opposing flows n is often around 3
Describe free convection boundary layer development on a vertical hot plate
The fluid ascends near the plate and the boundary layer thickens as you go up like a parabola. Maximum velocity is in the boundary layer and zero velocity at the outer adage and the surface of the plate. Temperature decreases exponentially away from plate until is constant at Tinf.
Formula for Nu for free convection up a vertical hot plate
Nux=(Grx/4)^1/4 x g(Pr)
x is subscript
g(Pr) means function of Pr given on page 9
Formula for mean Nu for free convection up a hot plate
NuL bar=4/3xNuL
Also in terms of Ra and Pr for laminar and all conditions on p10
Condition for transition to turbulence for free convection up a hot plate
Rayleigh number, Ra, reaches 10^9
Describe free convection from horizontal plates
Hot surface facing up: fluid circulates and rises once heated
Cold surface facing down: fluid circulates and falls once cooled.
Formulae for average Nu for horizontal plates and free convection
See p11 and 12 and p610 of textbook for how they apply
Describe boundary layer development on heated horizontal cylinder
Looking at circular cross-section. From bottom starts thinnest and gradually increases round towards the top of the circle from both sides and meets in a plume.
Describe local Nu distribution on heated horizontal cylinder
If the angle on the circular cross-section is defined as being measured around the circle from the bottom, Nu decreases in a curve down so it is very steep approaching π radians. Only gradual decrease for small angles.
Formulae for average Nu for heated spheres and horizontal cylinders
Long see page 2
Is free convection more or less efficient than forced?
Less efficient
What does τ mean when dealing with enclosed rectangular cavities?
The angle from the longest side of the cavity to the horizontal plane. It is 0 or 180 degrees for horizontal cavity and is 90 for vertical cavity.
For heating below a horizontal cavity, what can be said about the fluid below the critical Ra?
This is 1708 and below. The fluid layer is thermally stable and the mean Nu is 1.
For heating below a horizontal cavity, what can be said about the fluid at 3x10^5
Buoyancy driven flow is turbulent and the average Nu is calculated using the formula on page 4
For heating from above a horizontal cavity, what can be said about the fluid?
The fluid layer is unconditionally stable and the average Nu is 1
For heating one side of a vertical cavity, what can be said about the fluid for Ra<10^3?
There is recirculating (cellular) flow where the fluid ascends along the hot wall and descends along the cold wall. In this case the buoyancy driven flow is weak and heat transfer is primarily through conduction and the Nu is 1.
For heating one side of a vertical cavity, what can be said about the fluid for Ra>10^3?
Same recirculating pattern but cellular flow intensified and becomes more concentrated in thin boundary layers adjoining the sidewalls. The core becomes nearly stagnant. See page 623 of textbook for Nu formulae.
Describe the flow in an annular cavity between two concentric cylinders where the inner cylinder is hotter
Fluid rises up from top of inner cylinder to outer cylinder where it follows the circumference down to bottom of it. At the centre of the bottom cylinder, the fluid is forced up to bottom of inner cylinder and rises up around it toe start again. Flow pattern reversed is inner cylinder is colder.
Formula for heat transfer rate between two concentric cylinders
q=(2πkeff/ln(ro/ri))(Ti-To)
keff is effective thermal conductivity
o and i are subscript for outer and inner
Formula for effective thermal conductivity
keff/k=0.386(Pr/(0.861+Pr)^1/4 x Ra^1/4
Or if this is less than 1, keff/k=1
Ra has a special characteristic length given on p7
