section6 module5 transient

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Heat Transfer:

Transient Heat Transfer


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Objectives

Understand the basics of transient heat transfer.

Examine lumped mass systems.

Compare linear unsteady heat transfer with nonlinear unsteady heattransfer.

Study two examples:

Heat sink assembly temperature riseTransient heat transfer through a rod

Section 6 Thermal Analysis

Module 5: Transient Heat Transfer

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Transient Heat Transfer

If systems can be approximated as lumped mass systems, transientheat transfer is easy to find.

Lumped mass systems rarely exist in reality, but particularly for large

systems, this can prove a valuable approximation with little loss inaccuracy.

For materials which are anisotropic rather than uniform, lumpedmass systems may not be a good assumption.

The Biot number (Bi) is normally used to find if a lumped masssystem would be applicable: 1.0 Bi



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Simplifying Heat Transfer Analysis

Lumped mass systems simplify transient simulation. The followingequation is normally used:

p

s

bt

i

t

VC hA

b

Where

eT T

T T

,

)(

T(t) = Temperature after time t

T = Ambient Temperature

h = Heat transfer coefficient

A s = Surface Area

V = Volume of lumped mass

C p = Specific heat of lumped mass



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Temperature Time Relationship

bt

i

t e

T T

T T )(

Where,

p

s

VC hA

b

The above relationships enable us to determine the temperature T(t)of a body at time t, or alternatively, the time t required for thetemperature to reach a specified value T(t).

The temperature of a lumped system approaches thetemperature of the environment as time progresses.



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Linear Unsteady Heat Transfer

Temperature distribution throughout time is required.The specific heat and the density of material is also required.Computationally less expensive than nonlinear cases.Very few cases for heat transfer in real life are linear unsteady

because many thermophysical properties do change withtemperature.

The graph shows asymptoticrise of temperature with time.



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Nonlinear Unsteady Heat Transfer

Problems with unsteady temperature dependent conduction orinvolving radiation are nonlinear.

Exact solutions do not exist and an iterative scheme is used to solve

such problems, as the number of unknowns is higher than thenumber of equations.

Because of nonlinearity, the time steps should be very small.

How often the nonlinear terms are updated can be controlledthrough programming.



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Example: Heat Sink AssemblyTemperature Rise

A heat sink assembly example thatwas used in the earlier modules isused again here. For this module,we will be looking at the rise intemperature with time as theprocessor starts to dissipate heatfrom an initial ambient temperatureof 20 C.

A video presentation is availablewith this module detailing thesetting up and solving of transientheat transfer analysis for thisexample.

B C

40Watts

20

Microprocessor(Silicon)

Heat Spreader(Copper)

Fins(Aluminium)



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Additional Example: TransientHeat Transfer Through a Rod

A solution for transient heat transfer of an insulated rod is availableand can be compared to a simulation.At the initial condition, the rod is hotter in the center and cooler atthe ends, with a parabolic temperature distribution.

T=T 0T=T 0

T(x, t=0) = f(x) and heat flux q=0

Problem Specification

2

2

xT

t T

Insulated rod is allowed to cool

t =0

T0 T0

x =0 x =L Cooling Temperature Profile

t



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Summary

Transient heat transfer analysis occurs mostly during thestarting/stopping of machinery, when the objective is to observetemperature variation with time; thus the additional variable oftime has to be solved.

When solving analytically, the approximation of lumped masssystems can simplify the analysis.

For this approximation to be valid, the dimensionless Biot Numberparameter is used.



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Summary

In the case of numerical analysis, the number of time steps willdictate the length of the analysis.

Therefore, provided that the gradient of temperature with time is

low, larger time steps can be taken.

Just like steady state problems, transient heat transfer problems canbe linear or nonlinear, with the latter adding another dimension ofcomplexity into the mix.



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section6 module5 transient

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