Heat Transfer : Establishing Boundary Conditions

1. HeatTransfer: Establishing Boundary Conditions

2. Objectives Section 6 – Thermal Analysis Module2: Boundary Conditions Page 2 • 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

3. Boundary Conditions for Heat transfer Section 6 – Thermal Analysis Module2: Boundary Conditions Page 3 • 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.

4. Isothermal Boundary Conditions Section 6 – Thermal Analysis Module2: Boundary Conditions Page 4 • 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. Ta (ambient) Ts (source)

5. Adiabatic Boundary Conditions Section 6 – Thermal Analysis Module2: Boundary Conditions Page 5 • 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. Ta(ambient) q=0 q=0 W (work)

6. Isoflux Boundary Conditions Section 6 – Thermal Analysis Module2: Boundary Conditions Page 6 • 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”

7. Mixed (Isothermal and Isoflux) Boundary Conditions Section 6 – Thermal Analysis Module2: Boundary Conditions Page 7 • 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 In Hot Fluid Out Hot Fluid In Cold Fluid Out

8. Heat Sources and Heat Generation Section 6 – Thermal Analysis Module2: Boundary Conditions Page 8 • 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.

9. Heat Sink Section 6 – Thermal Analysis Module2: Boundary Conditions Page 9 • 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.

10. Conductive Wall Section 6 – Thermal Analysis Module2: Boundary Conditions Page 10 • 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.

11. Symmetry Section 6 – Thermal Analysis Module2: Boundary Conditions Page 11 • 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, whereonly half of the pipe need to be modeled. • Care should be exercised in establishing symmetry, assometimes the presence of body forces such as gravitycan affect flow and render it asymmetrical. Wall Symmetry Symmetry

12. Axisymmetry and Periodic Conditions Section 6 – Thermal Analysis Module2: Boundary Conditions Page 12 • 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. 2D domain Periodic Condition Axisymmetric Condition 3D cylinder Incoming air Hot tubes Axis of symmetry

13. Example: Conduction across a multi-layered wall Section 6 – Thermal Analysis Module2: Boundary Conditions Page 13 Δx Δx/2 3Δx/2 • Thermal resistance for each element canbe found and added directly to get overallthermal resistance (K∙m/W). • Rtotal =RA+RB+RC A B C A video presentation for solving conduction through multilayered pipe insulation is available with this module. RA RB RC

14. Additional Example: Critical Thickness of Insulation Section 6 – Thermal Analysis Module2: Boundary Conditions Page 14 • This is a case of conjugate heat transfer analysis. • Conduction and Convection both take place. • At critical thickness: • Where:Rcritical = the critical insulation radiusk = the thermal conductivity of the insulationh = the convection heat transfer coefficient

15. Summary Section 6 – Thermal Analysis Module2: Boundary Conditions Page 15 • 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.

16. Summary Section 6 – Thermal Analysis Module2: Boundary Conditions Page 16 • 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.