# MAT4

Bulk Data Entry Defines constant thermal material properties for conductivity, density, and heat generation.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT4 MID K CP RHO H   HGEN
DARCY KAPPA MU K CP RHO

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT4 24 200   2e5

## Definitions

Field Contents SI Unit Example
MID Unique material identification.
Integer
Specifies an identification number for this material.
<String>
Specifies a user-defined string label for this material entry. 2

No default (Integer > 0 or <String>)

K Thermal conductivity.

Default = 0.0 (Real ≥ 0.0)

CP Heat capacity per unit mass (specific heat). 4

(Real ≥ 0.0 or blank)

RHO Density. 4

Default = 1.0 (Real > 0.0)

H Free convection heat transfer coefficient.

Default = 0.0 (Real)

HGEN Heat generation capability used with QVOL entries. HGEN is the scale factor used with QVOL.

HGEN is the scale factor and QVOL is the power generated per unit volume, Pin = volume * HGEN * QVOL.

Default = 1.0 (Real ≥ 0.0)

DARCY Flag indicating fluid material properties to follow for Darcy Flow Analysis. 5
KAPPA Fluid permeability.

No default (Real)

MU Fluid dynamic viscosity.

No default (Real)

K Thermal conductivity of the fluid.

Default = 0.0 (Real ≥ 0.0)

CP Heat capacity per unit mass of the fluid (specific heat).

Default = 0.0 (Real ≥ 0.0 or blank)

RHO Density of the fluid.

Default = 0.0 (Real ≥ 0.0)

1. The material identification number/string may be the shared with structural material property definitions (MAT1, MAT2, MAT8, MAT9 or MGASK) but must be unique with respect to other thermal material property definitions (MAT4 or MAT5).
2. String based labels allow for easier visual identification of materials, including when being referenced by other cards. (example, the MID field of properties). For more details, refer to String Label Based Input File in the Bulk Data Input File.
3. MAT4 may specify material properties for any conduction elements. MAT4 also provides the heat transfer coefficient for free convection (CONV).
4. Heat capacity (CP) is defined per unit mass. It is multiplied by density (RHO) to calculate heat capacity matrix in transient heat transfer analysis. If RHO is not defined on MAT4, then positive density from a structural material entry with matching MID is used. If MAT4 does not have a corresponding matching structural material, then the default value of 1.0 is used.
5. Darcy Flow Analysis calculates flow of a fluid through porous medium. The porosity of the medium can be characterized via KAPPA and MU. In OptiStruct, Darcy Flow is used to determine fluid flow for forced convection heat transfer analysis and convective topology optimization.
• Darcy Flow is currently only supported for Steady-State Heat Transfer Analysis.
• Darcy Flow is supported for Topology Optimization via Steady-State Heat Transfer Analysis.
• For pure analysis, the model will have separate fluid and structural regions in the model. The fluid regions can be defined using a MAT4 entry with the DARCY continuation line (for analysis, even if the structural thermal material properties like K, CP, RHO on the first line are defined on a MAT4 entry which contains the DARCY continuation line, they are not used). The structure-only regions are defined using a MAT4 entry without a DARCY continuation line.
• The Darcy flow velocity is calculated as:(1)
$u=-\frac{\kappa }{\mu }\nabla p=-\frac{\kappa }{\mu }B{p}^{e}$
Where,
$u$
Flow velocity vector, an elemental quantity, which is output by default from a flow analysis subcase (can be controlled via VELOCITY I/O Entry).
$\kappa$
Fluid permeability specified via the KAPPA field.
$\mu$
Fluid dynamic viscosity specified via the MU field.
$\nabla p$
Pressure differential.
$B$
Derivative of shape functions in an element.
${p}^{e}$
Pressure vector in an element. Individual scalar nodal pressure output is turned off by default and can be activated using PRESSURE I/O Entry is specified in a flow analysis subcase.
• $\kappa }{\mu }$ is an estimate of ease of permeability of fluid into a porous medium. For regions defined as fully solid elements (MAT4 entry without DARCY continuation line), the lowest $\kappa }{\mu }$ from all other fluid MAT4 entries is used after it is multiplied with 10-9.
• For optimization, the Topology design space should have both fluid and structural thermal material properties defined on the same MAT4 entry.
• For more information and on how nodal pressures are calculated for flow analysis, refer to Darcy Flow Analysis in the User Guide.
6. Heat transfer via 1D fluid flow based on the CAFLUID entry is supported using the MAT4 entry. The MID field of the PAFLUID entry can be used to reference the MAT4 entry to define the fluid material properties.
7. This card is represented as a material in HyperMesh.