Convection Part1

1
Convection Part1

• External Flow

2
Introduction
Recall Convention is the heat transfer mode
between a fluid and a solid or a 2 fluids of
different phases In order to simplify the
process we used Newtons correlation Where h is
the convective heat transfer coefficient also
called the film coefficient. h is a function
of Fluid flow Fluid properties Geometry of
the solid
3
There are four means to evaluate the heat
transfer coefficient 1) Dimensional
analysis 2) Exact analysis of boundary
layer 3) Approximate integral analysis of the
boundary layer 4) Analogy between energy and
momentum transfer Significant Parameters Nussel
t Number Nu
y
x
4
The heat transfer rate between the surface and
the fluid is At the surface itself Where k is
the thermal conductivity of the fluid. Therefore
5
Prandtl Number Pr
Momentum Diffusivity Thermal
Diffusivity The ratio of the momentum
diffusivity over the thermal diffusivity is a
combination of fluid properties and is also
thougth of as a property (Named Prandtl Number
Pr). Dependent on fluid and temperature
6
Dimensional Analysis of Convective Heat
Transfer Forced Convection movement dictated by v
Variable Symbol Dimensions
Tube Diameter D L
Fluid density ? M L-3
Fluid viscosity µ M L-1 t-1
Fluid heat capacity Cp Q M 1 T 1
Fluid thermal conductivity k Q t 1 L 1 T 1
Velocity v L t 1
Heat transfer coefficient h Q t 1 L 2 T 1
7
Using the Buckingham method we group the
variables in dimensionless number This
dimensional analysis for a forced convection in a
circular conduit indicates the possibility of
correlating the variables as Similarly we could
have developed the Stanton number instead of the
Nusselt
8
Free Convection movement dictated by
buoyancy Given the coefficient of thermal
expansion ß
Variable Symbol Dimensions
Significant length D L
Fluid density ? M L-3
Fluid viscosity µ M L-1 t-1
Fluid heat capacity Cp Q M 1 T 1
Fluid thermal conductivity k Q t 1 L 1 T 1
Fluid Coef. Therm. Exp. ß T 1
Gravitational acceleration G L t 2
Temperature difference ?T T
Heat transfer coefficient h Q t 1 L 2 T 1
9
Using the Buckingham method we group the
variables in dimensionless number Define
the Grashof number as This dimensional
analysis for a forced convection in a circular
conduit indicates the possibility of correlating
the variables as
10
(No Transcript)
11
(No Transcript)
12
Selected Dimensionless Groups
Group Symbol Definition Interpretation
Grashof Number Gr Ratio buoyancy to viscous forces
Colburn Factor jH Dimensionless heat transfer coefficient
Nusselt Number Nu Dimensionless surface temperature gradient
Prandtl Number Pr Ratio momentum to thermal diffusivity
Reynolds Re Ratio inertia to viscous forces
Stanton Number St Modified Nusselt number
Peclet Number Pe RePr Independent heat transfer parameter

13
Flat Plate in Parallel Flow
Turbulent Flow
Transition Region
Laminar Flow
d(x)
x
L
Properties of fluid evaluated at the film
temperature Tf
14
Forced Convection Flat Plate in Parallel
Flow Laminar flow Relt2 x 105 Prandtl number
gt0.6 The local Nusselt number is The average
Nusselt number All Prandtl number and Pe
gt100 The local Nusselt number is The average
Nusselt number
x
L
15
Forced Convection Flat Plate in Parallel
Flow Transition flow Rec5 x 105 60gtPrandtl
number gt0.6 3 x 106 gtRe gt 2 x 105 The average
Nusselt number
L
16
Forced Convection Flat Plate in Parallel
Flow Turbulent flow Regt3x106 60gtPrandtl number
gt0.6 107 gtRe gt3 x 106 The average Nusselt
number The local Nusselt number
17
Cylinder in a Cross Flow
Transition
Laminar
Turbulent
v
D
Separation
Properties of fluid evaluated at the film
temperature Tf
v
D
Separation
18
Forced Convection Cylinder in a Cross Flow The
average Nusselt number If
ReDPrgt0.2
ReD C m
0.4-4 0.989 0.330
4-40 0.911 0.385
40-4000 0.683 0.466
4000-40,000 0.193 0.618
40,000-400,000 0.027 0.805
19
Forced Convection Various Object in a Cross
Flow The average Nusselt number
Geometry ReD C m
Square 5x103-105 0.246 0.588
Square 5x103-105 0.102 0.675
Hexagon 5x103-1.95x104 1.95x104 -105 0.160 0.0385 0.638 0.782
Hexagon 5x103-105 0.153 0.638
Vertical Plate 4x103-1.5x104 0.228 0.731
20
Sphere in a Cross Flow
All properties of fluid evaluated at temperature
, except µs at Ts
Restrictions 0.71 lt Pr lt 380 3.5 lt ReD lt
7.6x104
21
Bank of Tubes in a Cross Flow
V
Fluid in cross flow over tube bank
22
Aligned Bank of Tubes in a Cross Flow
SL
D
ST
A1
Properties of fluid evaluated at the film
temperature Tf
23
Staggered Bank of Tubes in a Cross Flow
SL
D
A1
ST
Properties of fluid evaluated at the film
temperature Tf If else
24
Number of row (NL) greater or equal to 10 2000
lt ReD,max lt 40000 Pr gt 0.7 C1 in table
7.5 If number of row is smaller than
10 C2 in table 7.6
25
Number of row (NL) greater or equal to 20 1000
lt ReD,max lt 2x106 500 gt Pr gt 0.7 C in
table 7.7 If number of row is smaller than
10 C2 in table 7.8
All properties of fluid evaluated at the average
temperature except Prs at Ts
26
In this case the temperature difference in the
convective heat transfer equation is defined as
the log-mean temperature difference
?Tlm Where Ti is the temperature of the
fluid entering the bank To is the temperature
of the fluid leaving the bank And the outlet
temperature can be estimated using Where N is
the total number of tube and NT the transverse
number of tube. Finally the heat transfer rate
per unit length is
27
Packed Bed
Properties of fluid evaluated at the the average
temperature e is the porosity or void fraction
of the bed (0.3 to 0.5) Valid for gas flow
28
Ap,T is the total area of the particles and Ab,c
is the bed cross sectional area