# Heat Transfer Analysis

Heat transfer describes the physical phenomena of the flow of thermal energy from regions of high temperature to a region of lower temperature, until thermal equilibrium is reached.

The heat transfer process takes place by three means:
• Conduction
• Convection

Heat is usually transferred in a combination of these three methods and rarely happens on a single form.

Steady-state heat transfer is the form of heat flow that happens when the temperature differences driving the heat transfer are constant, so once thermal equilibrium occurs, the temperature field does not change further.

Transient heat transfer takes place within a period of time, and the temperatures change in time toward a new equilibrium with the new thermal conditions. After equilibrium, heat flow into the system equals the heat flow out, and temperatures no longer change.

## Conduction

Conduction is the means of heat transfer within a part or between parts through thermal contact.

For example, heat is conducted from the body of a heated saucepan to the handle attached to it.

In OptiStruct, isotropic (MAT4) and anisotropic (MAT5) thermal conductivities are supported; temperature dependent conductivity and heat capacity (MATT4) are also available for nonlinear heat transfer analysis. Both steady-state and transient heat transfer are supported.

Conduction is resolved as:(1) $q={K}_{C}\text{Δ}T$
Where,
$q$
Heat transferred per unit time.
${K}_{C}$
Conductivity matrix.
$\text{Δ}T$
• Modeling:
• Thermal Conductivity is defined via the K, Kij, and T(K) fields on the MAT4, MAT5, and MATT4 Bulk Data Entries.
• The temperature boundary conditions can directly be defined on the structural GRID points via the SPC Bulk Data.
• The Heat Flux loads (QBDY1) require the definition of CHBDYE Bulk Data on the surface of the elements on which the loading is to be applied.
• The Heat Generation loads (QVOL) can be directly applied to the conduction elements in the model.
• Conduction across a contact interface can be modeled via the PCONTHT and PGAPHT entries.
• Conduction Across a Contact Interface:

Heat is propagated across a contact interface. If the PCONT entry is not defined for a contact interface, additional data is not required to define conductance properties for heat transfer across the interface. For such cases, the thermal conductivity is internally calculated based on the conductivity of the surrounding elements.

If the PCONT entry is defined for a contact interface, the PCONTHT entry can be used to defined thermal conductance properties.

If contact interface is defined via explicit CGAP(G) entries, the PGAPHT entry is used to define thermal conductance properties.

PARAM, THCNTPEN is available to control the penalty factor used in Thermal Contact analysis.

To setup conduction, refer to the following tutorials:
For Verification models regarding conduction, refer to:

## Convection

Heat transfer within solids is typically dominated by conduction, while within fluids (liquids and gases), although both conduction and convection modes exist, convection typically dominates.

Convective heat transfer within fluids is typically affected by the mass transport of fluids. Convection is the dominant form of heat transfer in liquids and gases. Thermal convection can be demonstrated by heating a saucepan filled with water and observing the changes in temperature in the water caused by the warmer water circulating into cooler areas.

OptiStruct supports both of the two types of convection, free convection and forced convection. When convection takes place under natural buoyancy forces that result from the density variations due to temperature differences, the process is called free convection. Forced convection occurs when the fluid is forced to flow over the object, for example, by a fan or pump.

### Free Convection

The simulation of free convection is activated by specifying the free convection coefficient via the H field of the MAT4 and T(H) field of MATT4 entries. Temperature dependent heat convection coefficient and time dependent heat convection are supported.

Heat is transferred by the process of free convection, as:(2) $q=\left(c*H\right)\left(T-{T}_{amb}\right)$
Where,
$q$
Heat transferred per unit time.
$H$
Free convection coefficient (defined on MAT4 entry and referenced by a PCONV entry).
$c$
Time-dependent multiplier defined via SPCD entry which constrains the control node identified by CNTRLND field on CONV entry.
$\left(T-{T}_{amb}\right)$
Temperature differential between the surface grid temperature and ambient point temperature.
Automatic free convection definition can be activated via CONVG Bulk/Subcase pair..
• Modeling:
• Free Convection Coefficient is defined on the H and T(H) fields of the MAT4 and MATT4 entries, respectively.
• User-defined time-dependent and temperature-dependent free convection coefficient can be defined using the PCONV and PCONVLIB Bulk Data Entries for Nonlinear Transient Analysis.
• The free convection material and boundary conditions are identified via the PCONV Bulk Data
• The free convection surface should be identified via CHBDYE Bulk Data.
• The CONV Bulk Data allows you to connect the free convection surface elements (CHBDYE) to both the free convection material/BCs via the PCONV entry and the ambient temperature via the TAi fields.
• The TAi fields define ambient temperature for the surrounding environment via the SPC/SPCD Bulk Data.
• The temperature boundary conditions can directly be defined on the structural GRID points via the SPC Bulk Data.
• The Heat Flux loads (QBDY1) require the definition of CHBDYE Bulk Data on the surface of the conduction elements on which the loading is to be applied.
• The Heat Generation loads (QVOL) can be directly applied to the conduction elements in the model
• Automatic free convection definition can be activated via CONVG Bulk/Subcase pair.
To setup Free Convection, refer to the following tutorials:
For Examples regarding Free Convection, refer to:
For Verification regarding Free Convection, refer to:

### Forced Convection

The simulation of forced convection is available by two methods in OptiStruct. Using 1D idealized heat transfer elements known as CAFLUID and by using Darcy-flow based forced convection heat transfer simulation. Using Darcy-flow, design optimization of cooling channels via topology design variables is also supported.

For more information on 1D forced convection, refer to CAFLUID Bulk Data and for Darcy-flow convection topology, refer to Darcy Flow Analysis and Convection Topology Optimization.
• Modeling:
• Forced Convection modeling depends on the approach used to simulate forced convection.
• 1D Forced Convection

CAFLUID elements are used to model fluid flow with element connection points, and additionally defines grid point IDs of ambient convection points via SPC entries. In addition, CAFLUID nodes can be defined as ambient points on the Tai fields of the CONV entry which turns on convection cooling from a surface via CAFLUID forced convection. PAFLUID property is used to define fluid flow properties like flow diameter, mass flow rate, and so on. Material properties are referenced on PAFLUID via MAT4 entry.

• Darcy Flow Analysis (and Convection Topology)

The SPCP Bulk/Subcase Entry pair are used to activate Darcy Fluid flow in a thermal subcase. Both inlet and outlet flow pressures can be defined using the SPCP entry. The INLETVEL Bulk/Subcase Entry pair are available instead of inlet pressure definition via SPC entry. The outlet pressure has to be defined using the SPCP entry. Solid and fluid thermal and flow material properties can be defined on the MAT4 entry. The DARCY continuation line is available to define fluid material properties.

Radiation is the transfer of energy in a form of electromagnetic waves.

Thermal radiation occurs through either vacuum or any transparent medium. All physical objects above absolute zero can produce electromagnetic waves. The waves carry the energy away from the emitting object. When they hit a body, the energy is absorbed, and the temperature of the body increases. Radiation can occur at all temperatures, with emissivity increasing with temperature. A common example is the heat from the sun travels to the earth as radiant energy.

OptiStruct supports the simulation of radiation to space, where the radiation heat transfer happens between surface elements and a blackbody space node. Radiation is a nonlinear solution. Both nonlinear steady-state and transient analyses are supported.

Heat transferred by the process of radiation, or the radiation heat flux is:(3) $q=\sigma \cdot \text{FAMB}\cdot \left({\epsilon }_{e}{\left({T}_{e}+{T}_{abs}\right)}^{4}-{\alpha }_{e}{\left({T}_{amb}+{T}_{abs}\right)}^{4}\right)$
Where,
$\sigma$
Stefan-Boltzmann constant (PARAM, SIGMA).
$q$
$\text{FAMB}$
Radiation view factor between the element face and the ambient space node (RADBC).
${\epsilon }_{e}$
Surface emissivity of the surface element, defined by EMIS1 on the RADM entry.
${\alpha }_{e}$
Surface absorptivity of the surface element, defined by ABSORP field on the RADM entry.
${T}_{e}$
Surface temperature.
${T}_{abs}$
Absolute temperature scale defined via PARAM, TABS.
${T}_{amb}$
Ambient temperature.
The temperatures and SIGMA should be defined in consistent units. Based on the input temperature units, the absolute temperature scale, ${T}_{abs}$, can be defined via PARAM,TABS. The value of SIGMA in SI units is 5.67E-8 Watts/m2K4.
• Modeling:
Radiation is modeled on the thermal boundary. To perform Radiation analysis, the following input are required:
• Nonlinear Steady-state and Nonlinear Transient Heat Transfer solutions are supported for radiation.
• PARAM,TABS defines the absolute temperature scale.
• PARAM,SIGMA defines the Stefan-Boltzmann constant.
• Define the ambient temperature for the blackbody in space via the SPC Bulk Data. This same grid is referenced via the NODAMB field on the RADBC Bulk Data.
• Radiation surface elements should be identified via CHBDYE Bulk Data.
• The RADM entry is used to specify the radiation material properties (emissivity and absorptivity) of a surface element. This is referenced on the CHBDYE Bulk Data.
• The RADBC entry is used to create radiation boundary conditions by specifying the ambient node for surface elements

Various loads and boundary conditions can be defined for Heat Transfer analysis, depending on the type of analysis being performed.
• Temperature

Fixed Temperatures for Heat Transfer Analysis can be defined using SPC, SPC1, and SPCD data with the Component ID blank or zero. MPC data can be used to specify the relationship between temperatures of different points using Component ID blank or zero.

Heat flux load is applied via QBDY1 Bulk Data Entry and can be applied via the CHBDYE Bulk Data Entry. The CHBDYE entry specifies the surface elements through which the heat flux loads are applied.

• Volumetric Heat Generation

Heat generation loads are activated via the QVOL Bulk Data Entry and can be directly assigned to elements which generate heat. The heat generation scale factor (HGEN) can be specified on the material entries (MAT4 and MAT5).

For Linear Transient and Nonlinear Transient Analysis, there are multiple options available to define time-dependent loading:
• Direct Definition

The EXCITEID field of the TLOAD1, TLOAD2 Bulk Data Entries should point to the IDs of QVOL (Heat Generation), QBDY1 (Heat Flux) Bulk Data Entries or a combination of them using LOADADD.

The EXCITEID field of the TLOAD1, TLOAD2 Bulk Data Entries should point to the ID of the SPCD Bulk Data Entry. Additionally, the TYPE field in the TLOAD1, TLOAD2 entries should be set to 1.

The QVOLLIB and QVOL entries can be used in combination to define time-dependent volumetric heat generation through user-defined external functions.

The QBDY1LIB and QBDY1 entries can be used in combination to define time-dependent uniform heat flux load through user-defined external functions.

The SPCDLIB and SPCD entries can be used in combination to define time-dependent temperature through user-defined external functions.

For Linear Transient and Nonlinear Transient Analysis, the options available to define temperature-dependent loading:

The QVOLLIB and QVOL entries can be used in combination to define temperature-dependent volumetric heat generation through user-defined external functions.

The QBDY1LIB and QBDY1 entries can be used in combination to define temperature-dependent uniform heat flux load through user-defined external functions.

The SPCDLIB and SPCD entries can be used in combination to define temperature-dependent temperature through user-defined external functions.

## Material

There are multiple options available to define material properties for Heat Transfer analysis in OptiStruct. Constant isotropic thermal material properties for conductivity, density and heat generation can be defined on the MAT4 Bulk Data Entry.

For anisotropic thermal material properties, the MAT5 Bulk Data can be used. It allows for the definition of direction-dependent thermal conductivity.
• Temperature-dependent Material

The MATT4 Bulk Data Entry is available to define temperature-dependent material properties for corresponding MAT4 Bulk Data Entry fields via the TABLEMi or TABLEG entries. The thermal conductivity, specific heat, and convection coefficient can be defined as temperature-dependent using the MATT4 Bulk Data Entry.

The MATUSHT Bulk Data is available for the definition of user-defined thermal material properties for Nonlinear Heat Transfer Analysis and includes the ability to define both temperature-dependent heat transfer material properties.

• Time-dependent Material

The MATUSHT Bulk Data is available also for the definition of user-defined time-dependent thermal material properties for Nonlinear Heat Transfer Analysis.