Natural Convection in Enclosed Spaces

Two vertical plates separated by a distance. Each plate at a different temperature.

Ends are insulated.

Convective heat transfer occurs in the fluid within the space.

3 21 2

, 2

,

1 2

Gr

Nu

g T TN

hN

kq

h T TA

Natural Convection in Enclosed Spaces

3, , Pr

1/ 4

, Pr 3 5, , Pr1/ 9

1/ 3

, Pr 5 7, , Pr1/ 9

For gases enclosed between vertical plates,

1.0 for 2 10

0.20 for 6 10 2 10/

0.0073 for 2 10 2 10/

For liqui

Nu Gr

Gr

Nu Gr

Gr

Nu Gr

hN N N

k

N NN N N

L

N NN N N

L

3, , Pr

1/ 4

, Pr 3 7, , Pr1/ 4

ds enclosed between vertical plates,

1.0 for 1 10

0.28 for 1 10 1 10/

Nu Gr

Gr

Nu Gr

hN N N

k

N NN N N

L

Natural Convection in Enclosed Spaces

1/ 4 3 5, , Pr , Pr

1/ 3 5, , Pr , Pr

For gases enclosed between horizontal plates,

with lower plate hotter than upper

0.20 for 7 10 3 10

0.061 for 3 10

For liquids enclosed between ve

Nu Gr Gr

Nu Gr Gr

N N N N N

N N N N N

1/ 3 0.074 5 9, , Pr Pr , Pr

rtical plates,

with lower plate hotter

0.069 for 1.5 10 1 10Nu Gr GrN N N N N N

Boiling

A: Free convection; B: Nucleate boiling; C: Transition Boiling;

D: Film boiling

Boiling

Type Excess Temperature (deg. C)

Free Convection: < 5

Nucleate Boiling: 5 – 25

Transition Boiling: 25 – 120

Film Boiling: > 120

The excess temperature is the surface temperature above the boiling point of the liquid.

Nucleate Boiling

Bubbles form at surface and separate, mixing the fluid. As temperature increases, the bubbles join to form bubble columns or jets. These eventually merge to form slugs. This type of boiling is the most desirable for a chemical process due to the high heat rates.

Transition Boiling

Film begins to form at surface. Surface changes from nucleate to film boiling.

Film Boiling

Surface completely covered with film blanket.

Nucleate Boiling Correlations

o o

2 o 2

1/ 3 1/3

3 3

or

For horizontal surfaces:

English ( : BTU/hr-ft - F) Metric ( : kW/m )

151 / 5000 1043 / 16

0.168 / 5000 5.56 / 16

w satT T T K F

h h

h T q A h T q A

h T q A h T q A

2 o 2

1/ 7 1/7

/ 75,000 / 240

For vertical surfaces:

English ( : BTU/hr-ft - F) Metric ( : kW/m )

87 / 1000 537 / 3

q A q A

h h

h T q A h T q A

h

3 30.240 / 1000 7.95 / 3

/ 20,000 / 63

T q A h T q A

q A q A

0.4

Pressure Correction: multiply by

where is in atm.P P

3 / 225 o 2 o

3 /1551 2

For forced convection inside tubes,

English: 0.077 : F; : BTU/hr-ft - F : psia

Metric: 2.55 : K; : W/m : kPa

P

P

h T e T h P

h T e T h K P

Nucleate Boiling Correlations

Film Boiling Correlations

1/ 43( )

( )

where 0.62 for horizontal cylinders

0.67 for spheres

is the density

is the enthalpy change from liq. to vapor

l v fgNu

v v v s sat

fg

g h DhDN C

k v k T T

C

C

h

is the diameter of the pipe

is the specific volume

is the thermal conductivity

is the surface temperature

is the boiling point temperature s

sat

D

v

k

T

T of the liquid

Subscript refers to the vapor

Subscript refers to the liquid.

v

l

Film boiling not desirable! Better to have nucleate!

Condensation

Film Condensation: Liquid film covers surface and flows continuously from the surface. Characteristic of clean, uncontaminated surfaces.

The presence of the liquid film reduces the heat transfer.

Condensation

Droplet Condensation: drops form in cracks, pits and cavities on the surface and may grow and coalesce thru condensation. More than 90% of the surface is covered by drops, ranging from a few micrometers in diameter to agglomerations visable to the naked eye. The droplets flow from the surface due to gravity.

Heat transfer for droplet condensation is higher than film. To be conservative, most design calculations assume film.

Condensation

Droplet Film

Condensation

Homogeneous condensation or fog formation resulting from increased pressure due to expansion.

Condensation

Direct contact condensation.

Condensation

1/ 43

Re

For vertical surfaces in laminar flow:

( )1.13 1800

where the subscripts refers to the liquid and refers to the vapor.

is th

L L v fgNu

L L L

fg

gh LhLN N

k k T

L v

h

Re

e latent heat of vaporization for the liquid.

All properties, except , are evaluated at the film temperature.

The Reynolds number is defined by

4 for a vertical tube of

sat w

fg

L

T T T

h

mN

D

Re

v

diameter,

4 for a vertical plate of width,

Frequently, and can be neglected.L

L

D

mN W

W

Condensation

Re

1/ 32 30.4

Re2

For turbulent flow, 1800,

0.0077

The solution is by trial and error since the

Reynolds number must be known.

LNu

L L

N

g LhLN N

k

Condensation

For tubes, the liquid thickens as the condensate flows down the tube.

For banks of tubes, the liquid may flow as a film to the lower tube, or it may drip to the lower tubes.

Condensation

1/ 43

For a vertical tier of horizontal tubes placed one below the other,

the average convective coefficient over the tubes is given by,

0.725

This equation works al

L L v fgNu

L L L

N

N

gh DhDN

k N k T

so for 1.N