Heat Transfer to Solids in a Flowing Fluid The heat transfer is dependent on: 1.Geometry of the body. 2.The position or orientation of the body (parallel,

Heat Transfer to Solids in a Flowing Fluid

The heat transfer is dependent on:

1. Geometry of the body.

2. The position or orientation of the body (parallel, perpendicular to flow).

3. Proximity of other bodies.

The heat transfer coefficient varies across the surface of the object. But the average heat transfer coefficient can be determined from an equation of the form:

1/ 3Re Pr

Re

Pr

where: is the Nusselt number,

, are constants

is the Reynolds number

is the Prandtl number

mNu

Nu

N CN N

hDN

kC m

N

N

Flow Parallel to a Flat Plate

L

0.5 1/ 3 5Re, Pr Re, Pr

Re

For heat transfer along the entire length of the surface, ,

for laminar flow:

0.664 3 10 0.7

where the Reynolds number is computed from

For turbulent

Nu L L

L

N N N N N

LvN

5Re, Pr

0.8 1/ 3Re, Pr

flow, 3 10 0.7

0.0366

L

Nu L

N N

N N N

Use fluid properties at average film temperature = (Ave. temp. of Wall + Ave. temp. of fluid)/2

Flow Perpendicular to a Single Cylinder

D

Re

1/ 3Re Prm

Nu

DvN

N CN N

Use properties at the film temperature. Velocity is free field velocity of fluid.

Flow Past a Single Sphere

Re

0.5 1/ 3Re Pr

Re Pr

2.0 0.60

1 70,000 0.6 400Nu

DvN

N N N

N N

Use properties at film temperature.

Flow Thru Tube BanksVery important for heat exchanger design!

Flow around the first bank is essentially the same as for a single tube. For subsequent rows, flow depends on the tube bank arrangement. The convection coefficient of a row increases with increasing row number until about the 5th row, after which there is little change. For aligned tubes, the front row shields the back rows, particularly for short distances between tubes. In general, heat transfer is encouraged by the staggered arrangement.

Flow Thru Tube Banks

In-Line Tubes Staggered Tubes

'

Tube spacing parallel to flow.

Tube spacing normal to flow.

Diagonal tube spacing for staggered rows.

P

n

P

S

S

S


max

maxRe

1/ 3Re Pr

ratio of minimum flow area to total front area, between tubes

maximum velocity in tube banks.

n

n

n

n

mNu

S

S D

vSv

S D

DvN

N CN N

Only for more than ten rows. Tables are available for non-equal ratios.


Correction factors for banks of less than ten tubes.


Procedure for solving tube bank problems:

Given: tube geometry, inlet temperature, tube surface temp., fluid velocity.

1. Assume an outlet temperature.

2. Determine properties of the fluid at the average temperature.

3. Calculate max. velocity based on geometry.

4. Calculate Reynolds number based on max. velocity.

5. Determine average heat transfer coefficent.

6. Determine overall q from total area of all tubes using temperature difference between tube wall and average fluid temperature.

7. Determine mass flow rate from:

8. Use to determine temperature drop.

9. Continue until guessed = calculated.

open areat tm vA A

Pq mC T

Heat Transfer for Flow in Packed Beds

2 / 3

' 0.35Re Re

'

2.876 0.3023

where: is the void fraction

is the superficial velocity based on the cross section

of the empty container in m/s

PH

fP

ChJ

k NC v N

v

'

Re

' '

is called the Colburn J factor

where the subscript means the property is evaluated at the

film temperature. All other properties are at the bulk flow temp.

H

P

f

J

D GN

G v

f

Convective Heat Transfer

Natural convection occurs when a quiescent fluid is exposed to a hot or cold surface.

If the surface is hot, the fluid next to the surface will be heated, its temperature will increase and its density will decrease. Due to the decreased density of the fluid next to the surface, it will rise due to buoyancy.

If the surface is cold, then the temperature of the fluid will be colder than the bulk fluid, its density will decrease and will fall due to buoyancy.



Typical chemical engineering problems involving convective heat transfer:

1. If a hot fluid is transported thru a pipe from process A to process B, how much will its temperature drop?

2. If a hot fluid is stored in a storage vessel, how much will the temperature drop each day?

3. What are the convective heat losses from my process unit, i.e., distillation column?

4. If a hot solid is cooled in the open, how long will it take to cool the solid to room temperature?


Natural convection heat transfer involves an additional dimensionless parameter called the Grashof number. The Grashof number represents the buoyancy force.

3 2

r 2

where: is the characteristic length, i.e. length of a heated plate

is the density of the fluid, at the film temperature.

is the coefficient of volumetri

fG

f

L g TN

L

c expansion.

is the temperature difference between surface and bulk fluid

is the fluid viscosity, evaluated at the film temperature

Remember:

2wall bulk

film

T

T TT


The volumetric expansion coefficient is defined as:

-1

1

where: is the volume

is the temperature

is the volumetric expansion coefficient, (deg)

dV

V dT

V

T

Ethyl alcohol: 112 x 10-5 /deg. C

Methyl alcohol: 120 “

Benzene: 124 “

Glycerin: 51 “

Air: 3 “


2

For ideal gases

1

1 1But and

and it follows that

1

For an ideal gas, and it follows that

1

g

dV

V dT

dV d

d

dT

P

R T

T

Ideal gas only

True for any material

Convective Heat TransferMost natural convection geometries are represented by the equation:

Pr

m

Nu GrN a N N

The physical properties are evaluated at the film temperature.

For vertical and horizontal plates and cylinders use Table 4.7.1 (handout).

For horizontal plates the length, L, is used.

For cylinders L is replaced by D.

For horizontal rectangles the average of the two dimensions is used.

For a horizontal circular disk, the diameter is multiplied by 0.9.

Simplified equations for various types of surfaces are provided in Table 4.7-2 (handout).


For natural convection at pressures other than 1 atm, the heat transfer coefficients are multiplied by a correction factor:

4 9 1/ 2Pr

9 2 / 3Pr

For from 10 to 10 multiply by

For > 10 multiply by

where is in atmospheres.

Gr

Gr

N N P

N N P

P

4 9Pr

3 3 3 o

The correlations in the tables apply mostly for

10 10

This generally holds for

4.7 m or 300 ft F

GrN N

L T K

Example - Convective Heat Transfer

4.7-2. A vertical cylinder 76.2 mm in diameter and 121.9 mm high is maintained at 397.1 K at its surface. It loses heat by natural convection to air at 294.2 K. Heat is lost from the sides and top – the bottom is insulated. Calculate the total heat loses neglecting radiation.






Heat Transfer to Solids in a Flowing Fluid The heat transfer is dependent on: 1.Geometry of the body. 2.The position or orientation of the body (parallel,

Documents

heat transfer coefficients

total heat

material slide

fluid2 slide

convective heat losses

average fluid temperature

average temperature

tube surface