XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> 1.4 Thermal Loads and Boundary Conditions
MD Nastran supports a full range of thermal boundary conditions and heat loads, starting with simple temperature constraints and heat flux boundary conditions, and moving on to more complicated heat transfer mechanisms associated with contact, convection and radiation. All of the thermal boundary conditions can be modeled as functions of time.
Thermal boundary conditions can be applied to finite element entities as well as geometric entities and include the following:
Table 1‑20 Typical UTable 1‑21 Temperature | Table 1‑22 oC oK | Table 1‑23 oF oR |
Table 1‑24 Normal Heat Flux | Table 1‑25 W/m2 | Table 1‑26 Btu/hr-ft2 |
Table 1‑27 Directional Heat Flux | Table 1‑28 W/m2 | Table 1‑29 Btu/hr-ft2 |
Table 1‑30 Nodal Source | Table 1‑31 W | Table 1‑32 Btu/hr |
Table 1‑33 Volumetric Generation | Table 1‑34 W/m3 | Table 1‑35 Btu/hr-ft3 |
Table 1‑36 Convection Heat Flow | Table 1‑37 W/m2 | Table 1‑38 Btu/hr-ft2 |
Table 1‑39 Advection Heat Flow | Table 1‑40 W | Table 1‑41 Btu/hr |
Table 1‑42 Convection Heat Transfer Coefficient | Table 1‑43 W/m2-oC | Table 1‑44 Btu/hr-ft2-oF |
Table 1‑45 Radiation to Space | Table 1‑46 W/m2 | Table 1‑47 Btu/hr-ft2 |
Table 1‑48 Radiation Enclosure | Table 1‑49 W/m2 | Table 1‑50 Btu/hr-ft2 |
Note: | Note: When applying flux type loads or boundary conditions to nodal points, the units will still be those of a flux, i.e., loads per unit area. Patran’s input data forms for thermal loads and boundary conditions require you to specify an associated nodal area. |
Temperature Boundary Conditions
Temperature constraints can only be applied to nodal points. Temperature constraints can be defined as constant, spatially varying, or time varying.
Normal Heat Flux
Normal heat flux is defined using the nodal, element uniform, or element variable loading operations. As with temperature boundary conditions, heat flux loads can be made to vary with space or time.
Directional Heat Flux
MD Nastran supports vector heat flux from a distant radiant heat source. This capability allows you to model phenomena such as diurnal or orbital heating. The required input for this capability includes:
• the magnitude of the flux vector
• the absorptivity of the surface on which the flux is being applied
• the vector components of the flux vector
The absorptivity can be dependent on temperature. The magnitude and components of the heat flux can be defined as constant, spatial varying, or time varying.
Nodal Source
Heat can be applied directly on nodal points (or “grid points” in MD Nastran terminology). Nodal source heat can be defined as constant, spatially varying in a global sense, or time varying.
Volumetric Heat Generation
Volumetric heat can be applied to one or more conduction elements and can be defined as constant, spatially varying, or time varying. The Patran MD Nastran interface also includes a heat generation multiplier for specifying temperature dependence. The multiplier feature is available in the input form used to specify the material property data.
Basic Convection
Basic convection boundaries can be defined. The approach to basic convection heat transfer in MD Nastran is to define the basic convection via a heat transfer coefficient and associated ambient temperature. The film coefficient is user specified and is available from a number of sources, including Reference 1. (p. 14). The film coefficient can be defined as a function of temperature; the ambient temperature can be defined as a function of time.
Advection, Forced Convection
Advection, forced convection, is a complicated heat transfer phenomenon that includes aspects of heat transfer as well as fluid flow. MD Nastran supports 1D fluid flow, which allows for energy transport due to streamwise advection and diffusion. Heat transfer between the fluid stream and the surroundings may be accounted for through a forced convection heat transfer coefficient based on locally computed Reynolds and Prandtl numbers; see Reference 1. (p. 14) and Reference 2. (p. 14) for more information on the underlying theory of this type of convection.
The input for forced convection includes:
• the mass flow rate of the fluid
• the diameter of the fluid pipe
• the material properties of the fluid
The calculation of the heat transfer coefficient between the fluid and the adjoining wall requires the specification of a film temperature. By default, this temperature will be internally calculated as the average of the temperatures of the fluid and the adjoining wall.
Additional forced convection inputs consist of the type of convection relationship used to calculate the energy transport and the method of calculating the heat transfer coefficient at the tube wall.
There are two choices with respect to the energy transport. The default method includes advection and streamwise diffusion, and its theoretical basis is the Streamwise-Upwind Petrov-Galerkin method, or SUPG.
There are also two choices for picking the method for calculating the heat transfer coefficient that applies between the fluid and the adjacent wall. The default method uses the following equation:
(1‑1)
The second method, chosen by picking the alternate formulation option, uses the following equation:
(1‑2)
h | = | =the heat transfer coefficient between the fluid and the adjacent wall (internally calculated) |
Coef | = | =a constant coefficient |
Re | = | =the Reynolds number based on the diameter (internally calculated) |
Pr | = | =the Prandtl number (internally calculated) |
Expr | = | =the Reynolds number convection exponent |
Expp | = | =the Prandtl number convection exponent |
k | = | =the fluid conductivity |
d | = | =the tube diameter |
Radiation to Space
Radiation to space is a boundary condition that defines radiant exchange between a surface and blackbody space. The inputs required for radiation to space are the absorptivity and emissivity of the surface, the ambient temperature of space, and the radiation view factor between the surface and space (usually equal to 1.0). The absorptivity and emissivity can both be temperature dependent. The ambient temperature can vary with time. The exchange relationship is defined to be:
(1‑3)
q | = | =the net energy flux in W/m2 (internally calculated) |
| = | =the Stefan-Boltzmann constant which has the value
5.668x10-8 W/m2 oK4 [0.1714x10-8 Btu/h ft2 oR4] |
Viewfac | = | =the view factor |
| = | = the emissivity |
| = | =the absorptivity (usually  ) |
Te | = | =the temperature of the element (internally calculated) |
Tamb | = | =the ambient temperature of space (user specified) |
Calculation of radiation exchange requires that the temperatures be defined on an absolute scale (Kelvin or Rankine). If the temperatures input in a problem involving radiation are either Celsius or Fahrenheit, an internal conversion can be defined.
Radiation Enclosures
Radiation Enclosure exchange is similar to the Radiation to Space boundary condition; however, this type of boundary condition takes into account the radiation exchange between discrete surfaces. As a result, subsequent to building a finite element mesh, the geometric relationship (view factor) between individual finite element surfaces must be determined. For enclosure radiation the view factors between surfaces are internally calculated. Also, for enclosure radiation, the absorptivity is taken as being equal to the emissivity (Kirchhoff’s Identity).
Calculation of the radiation view factors can be the most computationally intensive operation in heat transfer analysis. MD Nastran has implemented a unique set of algorithms for solving this problem which provides for both reasonable performance while maintaining an accurate calculation. To help facilitate this calculation, the Can Shade and Can Be Shaded options have been added for those situations where the shading is known. These options can help reduce the calculation time for radiation enclosures. Patran also allows you to define multiple radiation enclosures. The view factors within each Radiation Enclosure will be independently calculated from the view factors of the other enclosures.
In general, good view factor calculations require a reasonable surface mesh. Since the accuracy of the view factors tends to decrease as the distance between elements is reduced and becomes on the order of the element size, a mesh which prevents this sizing issue is recommended and is generally not too restrictive.
Contact Conduction
If contact bodies are present in the model for a SOL 153, 159 or 600 analysis heat transfer will occur between the contact bodies based on the properties defined on the contact bodies or via the contact table accessible from the subcase parameters for. as the bodies get closer the contact changes from radiation to convection to conduction. See the MSC Nastran Quick Reference Guide for more information.
