Thermodynamcis- Free Convection

Question 1

What does free convection refer to?

Answer 1

Fluid motion induced by buoyancy forces

Question 2

How do buoyancy forces arise?

Answer 2

Due to density gradients and a body force. In heat, these are due to temperature gradients and gravity.

Question 3

Describe what happens when a fluid is between two plates and the bottom one is hotter

Answer 3

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.

Question 4

What are two types of free boundary flows?

Answer 4

Plumes and buoyant jets

Question 5

Describe plumes

Answer 5

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.

Question 6

Describe buoyant jets

Answer 6

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.

Question 7

Formula for Grashof number, Gr

Answer 7

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

Question 8

Formula for Rayleigh number, Ra

Answer 8

RaL=GrLxPr=gβ(Ts-Tinf)L^3/να
Pr is prandtl number
α is in tables

Question 9

Formula for thermal expansion coefficient, β

Answer 9

β=-(1/ρ)(δρ/δT)P
All deltas are curly ds
P is subscript for constant pressure

Question 10

How to use Gr and Re to see if convection is forced or free

Answer 10

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

Question 11

Another term for free convection

Answer 11

Natural convection

Question 12

Nusselt number for mixed convection

Answer 12

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

Question 13

Describe free convection boundary layer development on a vertical hot plate

Answer 13

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.

Question 14

Formula for Nu for free convection up a vertical hot plate

Answer 14

Nux=(Grx/4)^1/4 x g(Pr)
x is subscript
g(Pr) means function of Pr given on page 9

Question 15

Formula for mean Nu for free convection up a hot plate

Answer 15

NuL bar=4/3xNuL

Also in terms of Ra and Pr for laminar and all conditions on p10

Question 16

Condition for transition to turbulence for free convection up a hot plate

Answer 16

Rayleigh number, Ra, reaches 10^9

Question 17

Describe free convection from horizontal plates

Answer 17

Hot surface facing up: fluid circulates and rises once heated
Cold surface facing down: fluid circulates and falls once cooled.

Question 18

Formulae for average Nu for horizontal plates and free convection

Answer 18

See p11 and 12 and p610 of textbook for how they apply

Question 19

Describe boundary layer development on heated horizontal cylinder

Answer 19

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.

Question 20

Describe local Nu distribution on heated horizontal cylinder

Answer 20

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.

Question 21

Formulae for average Nu for heated spheres and horizontal cylinders

Answer 21

Long see page 2

Question 22

Is free convection more or less efficient than forced?

Answer 22

Less efficient

Question 23

What does τ mean when dealing with enclosed rectangular cavities?

Answer 23

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.

Question 24

For heating below a horizontal cavity, what can be said about the fluid below the critical Ra?

Answer 24

This is 1708 and below. The fluid layer is thermally stable and the mean Nu is 1.

Question 25

For heating below a horizontal cavity, what can be said about the fluid at 3x10^5

Answer 25

Buoyancy driven flow is turbulent and the average Nu is calculated using the formula on page 4

Question 26

For heating from above a horizontal cavity, what can be said about the fluid?

Answer 26

The fluid layer is unconditionally stable and the average Nu is 1

Question 27

For heating one side of a vertical cavity, what can be said about the fluid for Ra<10^3?

Answer 27

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.

Question 28

For heating one side of a vertical cavity, what can be said about the fluid for Ra>10^3?

Answer 28

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.

Question 29

Describe the flow in an annular cavity between two concentric cylinders where the inner cylinder is hotter

Answer 29

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.

Question 30

Formula for heat transfer rate between two concentric cylinders

Answer 30

q=(2πkeff/ln(ro/ri))(Ti-To)
keff is effective thermal conductivity
o and i are subscript for outer and inner

Question 31

Formula for effective thermal conductivity

Answer 31

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