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© 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

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© 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

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© 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

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© 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

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© 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

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© 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

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© 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

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© 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

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© 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

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© 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the.

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