Heat Transfer:
Establishing Boundary Conditions
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Section 6 – Thermal Analysis
Objectives
Module 2: Boundary Conditions
Page 2

Learn the boundary conditions for heat transfer which include:
Isothermal conditions
 Isoflux thermal conditions
 Adiabatic thermal conditions
 Mixed boundary (adiabatic-isothermal) conditions


Understand heat sources, heat generation and heat sinks.

Study conductive wall thickness.

Identify geometric symmetry, axis-symmetry and periodicity.

Study two examples:
Conduction across a multi-layered wall
 Critical thickness of insulation

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Boundary Conditions for Heat transfer
Section 6 – Thermal Analysis
Module 2: Boundary Conditions
Page 3

The user must set boundary conditions (BCs) in order to solve any
heat transfer problem.

Because many BCs may be a combination of two different types, it
requires experience and expertise in order to make simplifications
using appropriate distinct BCs instead.

Unless the heat transfer is unsteady, there should be a definite
source and sink for heat defined in the domain.

In many cases BCs may change with time, such as in unsteady cases
where the heat transfer coefficient for convection is coupled to
temperature. This adds to the complexity of problem.
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Isothermal Boundary Conditions
Section 6 – Thermal Analysis
Module 2: Boundary Conditions
Page 4

Isothermal boundary conditions are most commonly used in thermal
analysis.

Real life examples of pure isothermal boundary conditions are rare.

However, isothermal boundaries are a useful approximation and are
computationally inexpensive.

Examples include heat transfer from fins, electronic chips, engine
bays, piston-cylinder sleeves, and heat loss by animals and humans,
etc.
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Ta
(ambient)
Ts
(source)
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Section 6 – Thermal Analysis
Adiabatic Boundary Conditions
Module 2: Boundary Conditions
Page 5

An adiabatic boundary condition is said to exist where no heat crosses
the boundary.

In real life a 100% adiabatic boundary condition is difficult to achieve.

It is a reasonable approximation in cases of extremely heavy insulation
on walls or in a vacuum where heat can escape through other routes.
q=0
Ta (ambient)
q=0
W (work)
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Section 6 – Thermal Analysis
Isoflux Boundary Conditions
Module 2: Boundary Conditions
Page 6



An isoflux boundary condition is said to exist when a body is
uniformly losing or absorbing heat through a boundary.
Examples include an electric heater, heating element coil, solar flat
panel collectors, radiative loss to the night sky, and the human body.
Compared to isothermal, the analysis of isoflux systems are relatively
complex.

Q = (heat flux)AX

where
heat flux = The amount of heat flux (heat per unit area) applied to a surface,
entered by the user
 A = Surface area of the face
 X = The convection multiplier sometimes denoted by “h”

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Mixed (Isothermal and Isoflux)
Boundary Conditions
Section 6 – Thermal Analysis
Module 2: Boundary Conditions
Page 7

A mixed boundary condition is the best and most accurate
approximation of real life examples.

An example is a heat exchanger where the fluid in contact with a
heat transfer medium exchanges heat as it moves in the direction of
flow.
Cold Fluid In
Hot Fluid Out
Hot Fluid In
Cold Fluid Out
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Section 6 – Thermal Analysis
Heat Sources and Heat Generation
Module 2: Boundary Conditions
Page 8

Heat generation can occur within a body through chemical
processes, electrical resistance (Joule heating), etc.

In thermal analysis, heat generation or heat sources are frequently
used to model components that are giving away heat at a constant
rate.

Examples include heat generating electronic components such as
amplifiers and resistors. These can be represented by using a heat
source boundary condition.
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Section 6 – Thermal Analysis
Heat Sink
Module 2: Boundary Conditions
Page 9

Heat sink boundary conditions can be used where heat is being
dissipated fairly efficiently.

An ideal heat sink effectively does not allow temperature to rise
beyond a certain value.

Finned heat sinks, heat sinks with fans, and cooling jackets with
running water are good examples of heat sink boundary conditions.
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Section 6 – Thermal Analysis
Conductive Wall
Module 2: Boundary Conditions
Page 10

In a thermal analysis, when the effect of conduction through system
boundaries has to be accounted for, then a conductive wall boundary
condition can be used.

In such cases, solid walls need not to be modeled separately, thus
reducing the number of cells required for conjugate heat transfer
analysis.
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Section 6 – Thermal Analysis
Symmetry
Module 2: Boundary Conditions
Page 11

For a system that is continuous, symmetry boundary conditions help
to simplify the model, thus reducing analysis time while maintaining
the same level of accuracy.

For flow inside a pipe, only a quarter of the pipe needs
to be modeled.

Another example is flow across a pipe, where
only half of the pipe need to be modeled.

Care should be exercised in establishing symmetry, as
sometimes the presence of body forces such as gravity
can affect flow and render it asymmetrical.
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Wall
Symmetry
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Section 6 – Thermal Analysis
Axisymmetry and Periodic Conditions
Module 2: Boundary Conditions
Page 12


If the geometry is Axisymmetric, 3D geometry such as the cylinder
shown below can be simplified to a 2D plane.
If the geometry is repetitive then a portion of the domain can be
modeled and results can be extrapolated.
2D domain
Periodic Condition
Axisymmetric
Condition
3D
cylinder
Incoming air
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Hot tubes
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Axis of symmetry
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Section 6 – Thermal Analysis
Example: Conduction across
a multi-layered wall
Module 2: Boundary Conditions
Page 13
Δx


Δx/2
3Δx/2
Thermal resistance for each element can
be found and added directly to get overall
thermal resistance (K∙m/W).
Rtotal =RA+RB+RC
A video presentation for solving
conduction through multilayered
pipe insulation is available with this
module.
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A
RA
B
RB
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C
RC
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Section 6 – Thermal Analysis
Additional Example:
Critical Thickness of Insulation



Page 14
This is a case of conjugate heat transfer analysis.
Conduction and Convection both take place.
At critical thickness:
rcritical 

Module 2: Boundary Conditions
k
h
Where:
Rcritical = the critical insulation radius
k = the thermal conductivity of the insulation
h = the convection heat transfer coefficient
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Section 6 – Thermal Analysis
Summary
Module 2: Boundary Conditions
Page 15

For heat transfer cases to be solved through numerical methods, it is
important to select the right boundary conditions.

Occasionally it may be difficult to identify one distinct boundary
condition as real life conditions might be a combination of two
different boundary conditions.

However the user can make use of multiple analyses to counter this
situation.
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Section 6 – Thermal Analysis
Summary
Module 2: Boundary Conditions
Page 16

In addition to the boundary conditions, thermal loads which include
heat sources and heat sinks also need to be identified.

Heat sources are where heat energy is being generated.

Heat sinks dissipate heat energy and do not allow a body to rise
beyond a certain temperature.

Similarly the presence of geometric symmetry, if identified, can also
lead to substantial reductions in analysis times; this includes
periodicity and axisymmetry.
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