Heat Transfer:
Convection Heat Transfer
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Section 6 – Thermal Analysis
Objectives
Module 3: Convection Heat Transfer
Page 2
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Understand the basics of convection heat transfer.
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Compare natural convection with forced convection.
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Learn how to model density variation.
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Identify dimensionless parameters.
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Study two examples:
 Heat transfer from a heat sink assembly
 Flow inside double-paned window cavities
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Section 6 – Thermal Analysis
Understanding Convection
Module 3: Convection Heat Transfer
Page 3
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Classified in two main categories: free and forced convection.
Convection can be further classified by the nature of flow, for
example: laminar or turbulent.
Heat transfer rates are higher in turbulent compared to laminar flow.
The heat transfer coefficient, denoted by “h”, is the main parameter
that needs to be estimated for any kind of convection heat transfer.
Units are Watts per meter squared−Kelvin (W/m2K). The value of “h”
is highly dependent on the boundary layer.
“h” is generally found by evaluating the Nusselt number (Nu) using
regressions available for common cases of convective flow.
hx
Nu 
k
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Where “x” is the length and “k” is the thermal
conductivity of a fluid.
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Section 6 – Thermal Analysis
Natural / Free Convection
Module 3: Convection Heat Transfer
Page 4
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Responsible for most natural heat transfer phenomenon and shapes
weather systems.
Can be used to advantage for passive
cooling or heating.
Should be abated where undesirable
by creating flow obstacles.
When modeling natural convection,
density variation cannot be ignored.
Rayleigh number provides the strength
of natural convection.
gTd
Ra 
k
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3
Where,
g = acceleration due to gravity
α = thermal expansion coefficient
ν = kinematic viscosity
d= characteristic length/diameter
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Section 6 – Thermal Analysis
Natural / Free Convection
Module 3: Convection Heat Transfer
Page 5
Convection from a horizontal cylinder is one of the
most common examples of natural convection.
Examples such as heat loss from hot pipes occur
frequently.
Churchill and Chu, 1975, established the following
regression

0.387 Ra D
Nu D  0.60 

1  (0.559 / Pr) 9 /16
103  Ra D  1013
1/ 6

Nu D  0.36 
0.518 Ra D

8 / 27 


1/ 4
1  (0.559 / Pr) 
9 / 16 4 / 9
2
Where,
Nu = Nusselt Number
Ra = Rayleigh Number
Pr = Prandtl Number
Hot air plume rising
after becoming heated
by a hot cylinder.
10 6  Ra D  109
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Picture courtesy of
H. Junaidi et al
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Modeling Density Variation
Section 6 – Thermal Analysis
Module 3: Convection Heat Transfer
Page 6
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Density variation must be taken into account, as natural convection
depends upon the temperature gradient and the variation of density
due to that temperature change.
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The Boussinesq density approximation model simplifies the
estimation of density variation.
   1   (T  T )

Where α is the coefficient of volume expansion. For liquids, α ranges
between 10-3 to 10-4
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ρo is the known value of density at temperature To
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Section 6 – Thermal Analysis
Forced Convection
Module 3: Convection Heat Transfer
Page 7
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Forced convection can be several times more efficient than natural
convection.
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Both natural and forced convection can be used in conjunction for
efficient designs.
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In order to compare the strength of forced and natural convection
when both are present, the Peclet number gives us a measure of
their relative strengths.
Pe 
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UL

Where:
U is the velocity
L is the characteristic length
α is the thermal diffusivity
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Section 6 – Thermal Analysis
Forced vs. Natural Convection
Module 3: Convection Heat Transfer
Page 8
PROCESS
Fluid Type
h (W/m2K)
Free convection
Gas
Liquid
Gas
2 – 25
50 – 1000
2.5 – 250
Liquid
50 – 20,000
Forced convection
Table: Typical ranges of values for the surface convection heat transfer
coefficient. (ref: Heat Transfer a problem solving approach; Tariq Muneer, Jorge
Kubie and Thomas Grassie)
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Section 6 – Thermal Analysis
Additional Dimensionless Parameters
Module 3: Convection Heat Transfer
Page 9
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Dimensionless parameters are frequently used both in fluid
mechanics and heat transfer. Their origins lie in prototype testing –
in order to simulate similar conditions on a scaled model,
dimensionless parameters or ratios of flow / heat transfer entities
would be matched.
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To study convection in more detail, the following dimensionless
numbers should be looked at :
 Grashof number
 Prandtl number
 Archimedes number
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Section 6 – Thermal Analysis
Example: Heat Sink Assembly
Module 3: Convection Heat Transfer
Page 10
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A heat sink assembly is a common
design element in electronics such
as desktop computers, laptops
and audio systems.
A video presentation for this
module is available for setting up
and solving a heat sink assembly
design that ties with this example.
20°
B C
Fins
(Aluminium)
Heat Spreader
(Copper)
Microprocessor
(Silicon)
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40
Watts
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Section 6 – Thermal Analysis
Additional Example: Flow Inside
Double-Paned Window Cavities
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Module 3: Convection Heat Transfer
Page 11
Convective flow inside window cavities has been studied in
great detail.
Many studies have looked at convection between two
parallel plates even at different angles.
A convective loop forms provided that the distance between
the two walls of the cavity is sufficient for the air to move.
MacGregor and Emery [1] proposed the following
relationship for cavities with a large aspect ratio (H/L):
NuL  0.42 Ra L
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1/ 4
Pr
0.012
( H / L)
0.3
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Where:
H = cavity height
L = cavity width
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Section 6 – Thermal Analysis
Summary
Module 3: Convection Heat Transfer
Page 12
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Heat transfer occurs mainly through convection, particularly in
engineering applications.
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Natural and forced convection both carry significance as they occur
in numerous applications.
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Because the presence of buoyancy forces lead to heat transfer in
natural convection, modeling the density variation is required.
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The Bousinesq model is most commonly used for modeling density
variation because of its simplicity.
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Section 6 – Thermal Analysis
Summary
Module 3: Convection Heat Transfer
Page 13
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Solutions to convection problems are mostly obtained through the
use of regressions which involve dimensionless parameters such as
Nusselt, Rayleigh and Peclet numbers.
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These regressions are available for a large number of generic cases
such as convection from a flat plate, sphere, cylinder, series of fins,
etc.

Numerical analysis for convection heat transfer is valuable
particularly when geometry strays from regular geometry.
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