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Heat Transfer : Steady State Heat Transfer

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HeatTransfer:

Steady State Heat Transfer

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

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

- 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.

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.

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.

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)

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.

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.