1. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Heat Transfer: Steady State Heat Transfer

2. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Objectives  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 Module 4: Steady State Heat Transfer Page 2

3. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Steady State Heat Transfer  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 InHeat Out Any machinery running at constant speed is a good example of steady state heat transfer. Section 6 – Thermal Analysis Module 4: Steady State Heat Transfer Page 3

4. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community 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. Section 6 – Thermal Analysis Module 4: Steady State Heat Transfer Page 4

5. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Nonlinear Steady State Heat Transfer  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 Module 4: Steady State Heat Transfer Page 5

6. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Simplifying Heat Transfer Analysis  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 Module 4: Steady State Heat Transfer Page 6

7. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Example: Heat Sink Assembly  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. BC 40 Watts 20° Microprocessor (Silicon) Heat Spreader (Copper) Fins (Aluminium) Section 6 – Thermal Analysis Module 4: Steady State Heat Transfer Page 7

8. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Summary  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 Module 4: Steady State Heat Transfer Page 8

9. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Summary  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. Section 6 – Thermal Analysis Module 4: Steady State Heat Transfer Page 9