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Heat Transfer : Steady State Heat Transfer PowerPoint PPT Presentation


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Heat Transfer : Steady State Heat Transfer. Objectives. Section 6 – Thermal Analysis Module 4: Steady State Heat Transfer Page 2. U nderstand steady state heat transfer. Explore linear steady state analysis. Explore nonlinear steady state analysis. S tudy an example:

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Heat Transfer : Steady State Heat Transfer

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HeatTransfer:

Steady State Heat Transfer


Objectives

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 2

  • Understand steady state heat transfer.

  • Explore linear steady state analysis.

  • Explore nonlinear steady state analysis.

  • Study an example:

    • Thermal analysis of a heat sink assembly


Steady State Heat Transfer

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 3

  • Steady state heat transfer occurs when temperatures, thermo-physical properties, surface properties and bulk motion of fluid are constant over time.

  • Temperature has reached equilibrium.

Element under study

Heat In

Heat Out

Any machinery running at constant speed is a good example of steady state heat transfer.


Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 4

Linear Steady State Heat Transfer

  • A linear steady state problem is approximated when the thermophysical properties (e.g., conductivity, density, viscosity) are not dependent on temperature. Moreover, radiation loss is unaccounted for.

  • Thermal conductivity of a material in real life can vary significantly depending upon the material temperature.

  • If the material properties are fixed, the problem is said to be linear steady state.

  • If “k” in the above relationship is approximated as not dependent on temperature, then the problem is linear steady state.

  • An example where a linear steady state heat transfer approximation can be used is heat loss from domestic hot water pipes when the temperature differential is low.


Nonlinear Steady State Heat Transfer

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 5

  • Nonlinear steady state heat transfer occurs when thermophysical properties are assumed to vary with temperature.

  • This is closer to real life conditions; however more complex to solve.

  • To solve such problems, an iterative scheme is used by assuming initial temperatures and evaluating through calculations later.

  • The material properties are adjusted for new temperatures and calculated again until convergence is reached (for example, when heat entering and heat exiting the system boundaries are equal).

  • Most examples of heat transfer are nonlinear, such as heat loss from a car engine block (engine temperature varies significantly).

If “k” in this equation is a function of temperature f(T), than the problem becomes nonlinear.


Simplifying Heat Transfer Analysis

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 6

  • Problems can be simplified by avoiding the need to calculate for conjugate heat transfer.

  • For instance at low temperatures (<70⁰ C), radiation may be ignored.

  • If the material properties do not vary significantly (for example, the percentage change is < 20%), the problem can be assumed to be linear steady state.

  • Likewise, if the effect of body forces such as gravitational force is overwhelmed by forces responsible for bulk fluid flow, natural convection can be ignored.

  • Geometrical symmetry, if present, should be used to avoid the need to create a full model.


Example: Heat Sink Assembly

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 7

20°

  • A heat sink assembly is a common design element in electronics such as desktop computers, laptops and audio systems.

  • A two-part video presentation for this module using this example is available. The second part covers steady state heat transfer analysis.

B

C

Fins

(Aluminium)

Heat Spreader

(Copper)

40 Watts

Microprocessor

(Silicon)


Summary

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 8

  • Steady state heat transfer conditions are said to occur when a system is in equilibrium.

  • For instance, the engine on a car travelling at a constant speed on a highway would more or less lose a fixed amount of heat every second.

  • Steady state heat transfer can be linear or nonlinear.

  • Nearly all real life examples are nonlinear; however, systems can be approximated as linear if temperature variation is insignificant.


Summary

Section 6 – Thermal Analysis

Module4: Steady State Heat Transfer

Page 9

  • If the temperature variation is high, thermal properties of substances involved in heat transfer can change.

  • For instance: thermal conductivity, fluid density and viscosity changes due to temperature create a nonlinear system which is much more complicated to solve than a linear system.

  • If thermophysical properties do not vary significantly, linear analysis approximation should be used to reduce computational expense.


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