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: Establishing Boundary Conditions

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  Learn the boundary conditions for heat transfer which include:  Isothermal conditions  Isoflux thermal conditions  Adiabatic thermal conditions  Mixed boundary (adiabatic-isothermal) conditions  Understand heat sources, heat generation and heat sinks.  Study conductive wall thickness.  Identify geometric symmetry, axis-symmetry and periodicity.  Study two examples:  Conduction across a multi-layered wall  Critical thickness of insulation Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Boundary Conditions for Heat transfer  The user must set boundary conditions (BCs) in order to solve any heat transfer problem.  Because many BCs may be a combination of two different types, it requires experience and expertise in order to make simplifications using appropriate distinct BCs instead.  Unless the heat transfer is unsteady, there should be a definite source and sink for heat defined in the domain.  In many cases BCs may change with time, such as in unsteady cases where the heat transfer coefficient for convection is coupled to temperature. This adds to the complexity of problem. Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Isothermal Boundary Conditions  Isothermal boundary conditions are most commonly used in thermal analysis.  Real life examples of pure isothermal boundary conditions are rare.  However, isothermal boundaries are a useful approximation and are computationally inexpensive.  Examples include heat transfer from fins, electronic chips, engine bays, piston-cylinder sleeves, and heat loss by animals and humans, etc. TsTs TaTa (source) (ambient) Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Adiabatic Boundary Conditions  An adiabatic boundary condition is said to exist where no heat crosses the boundary.  In real life a 100% adiabatic boundary condition is difficult to achieve.  It is a reasonable approximation in cases of extremely heavy insulation on walls or in a vacuum where heat can escape through other routes. T a (ambient) W (work) q=0 Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Isoflux Boundary Conditions  An isoflux boundary condition is said to exist when a body is uniformly losing or absorbing heat through a boundary.  Examples include an electric heater, heating element coil, solar flat panel collectors, radiative loss to the night sky, and the human body.  Compared to isothermal, the analysis of isoflux systems are relatively complex.  Q = (heat flux)AX  where  heat flux = The amount of heat flux (heat per unit area) applied to a surface, entered by the user  A = Surface area of the face  X = The convection multiplier sometimes denoted by “h” Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Mixed (Isothermal and Isoflux) Boundary Conditions  A mixed boundary condition is the best and most accurate approximation of real life examples.  An example is a heat exchanger where the fluid in contact with a heat transfer medium exchanges heat as it moves in the direction of flow. Cold Fluid Out Cold Fluid In Hot Fluid In Hot Fluid Out Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Heat Sources and Heat Generation  Heat generation can occur within a body through chemical processes, electrical resistance (Joule heating), etc.  In thermal analysis, heat generation or heat sources are frequently used to model components that are giving away heat at a constant rate.  Examples include heat generating electronic components such as amplifiers and resistors. These can be represented by using a heat source boundary condition. Section 6 – Thermal Analysis Module 2: Boundary Conditions 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 Heat Sink  Heat sink boundary conditions can be used where heat is being dissipated fairly efficiently.  An ideal heat sink effectively does not allow temperature to rise beyond a certain value.  Finned heat sinks, heat sinks with fans, and cooling jackets with running water are good examples of heat sink boundary conditions. Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 9

10. © 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 Conductive Wall  In a thermal analysis, when the effect of conduction through system boundaries has to be accounted for, then a conductive wall boundary condition can be used.  In such cases, solid walls need not to be modeled separately, thus reducing the number of cells required for conjugate heat transfer analysis. Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 10

11. © 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 Symmetry  For a system that is continuous, symmetry boundary conditions help to simplify the model, thus reducing analysis time while maintaining the same level of accuracy.  For flow inside a pipe, only a quarter of the pipe needs to be modeled.  Another example is flow across a pipe, where only half of the pipe need to be modeled.  Care should be exercised in establishing symmetry, as sometimes the presence of body forces such as gravity can affect flow and render it asymmetrical. Symmetry Wall Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 11

12. © 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 Axisymmetry and Periodic Conditions  If the geometry is Axisymmetric, 3D geometry such as the cylinder shown below can be simplified to a 2D plane.  If the geometry is repetitive then a portion of the domain can be modeled and results can be extrapolated. 3D cylinder Axis of symmetry 2D domain Incoming airHot tubes Periodic ConditionAxisymmetric Condition Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 12

13. © 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: Conduction across a multi-layered wall  Thermal resistance for each element can be found and added directly to get overall thermal resistance (K∙m/W).  R total =R A +R B +R C RARA RBRB RCRC ΔxΔx3Δx/2Δx/2 ABC A video presentation for solving conduction through multilayered pipe insulation is available with this module. Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 13

14. © 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 Additional Example: Critical Thickness of Insulation  This is a case of conjugate heat transfer analysis.  Conduction and Convection both take place.  At critical thickness:  Where: R critical = the critical insulation radius k = the thermal conductivity of the insulation h = the convection heat transfer coefficient Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 14

15. © 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  For heat transfer cases to be solved through numerical methods, it is important to select the right boundary conditions.  Occasionally it may be difficult to identify one distinct boundary condition as real life conditions might be a combination of two different boundary conditions.  However the user can make use of multiple analyses to counter this situation. Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 15

16. © 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  In addition to the boundary conditions, thermal loads which include heat sources and heat sinks also need to be identified.  Heat sources are where heat energy is being generated.  Heat sinks dissipate heat energy and do not allow a body to rise beyond a certain temperature.  Similarly the presence of geometric symmetry, if identified, can also lead to substantial reductions in analysis times; this includes periodicity and axisymmetry. Section 6 – Thermal Analysis Module 2: Boundary Conditions Page 16