S h a r e d I n t e r f a c e F e a t u r e s

The following features are shared based on the selections made for the model. In this section:

•Fluid

•Wall

•Initial Values

•Pressure Work

•Viscous Heating

Fluid

The Fluid feature adds both the momentum equations and the temperature equation but without volume forces, heat sources, pressure work or viscous heating. Volume forces and heat sources can be added as separate features and Viscous Heating and

Pressure Work can be added as subnodes to the Fluid node.

When the turbulence model type is set to RANS, the Fluid node also adds the equations for k and .

D O M A I N S E L E C T I O N

By default, All domains are selected.

M O D E L I N P U T S

Define the model inputs. If no model inputs are required, this section is empty.

To define the Absolute Pressure, see the settings for the Heat Transfer in

Fluids node as described in the COMSOL Multiphysics User’s Guide.

Tip

S H A R E D I N T E R F A C E F E A T U R E S | 385

H E A T C O N D U C T I O N

The default uses the Thermal conductivity k (SI unit: W/(m·K)) From material. If User defined is selected, choose Isotropic, Diagonal, Symmetric, or Anisotropic based on the characteristics of the thermal conductivity and enter another value or expression in the field or matrix. The thermal conductivity describes the relationship between the heat flux vector q and the temperature gradient T as in q = k T which is Fourier’s law of heat conduction. Enter this quantity as power per length and temperature.

When the turbulence model type is set to RANS, the conductive heat flux includes the turbulent contribution: q = k+ TI) T where k is the thermal conductivity tensor, I the identity matrix and T the thermal turbulent conductivity defined by

Cp T

T = ------------- . PrT

T H E R M O D Y N A M I C S

Select a Fluid type—Gas/Liquid or Ideal gas.

•The heat capacity at constant pressure Cp describes the amount of heat energy required to produce a unit temperature change in a unit mass. For an ideal gas, choose to specify either Cp or the ratio of specific heats, , but not both since they in that case are dependent.

•The ratio of specific heats is the ratio of heat capacity at constant pressure, Cp, to

heat capacity at constant volume, Cv. When using the ideal gas law to describe a fluid, specifying is enough to evaluate Cp. For common diatomic gases such as air,1.4 is the standard value. Most liquids have 1.1 while water has 1.0. is

used in the streamline stabilization and in the results and analysis variables for heat fluxes and total energy fluxes. It is also used in the ideal gas law.

Gas/Liquid

If Gas/Liquid is selected properties of a non-ideal gas or liquid can be used. By default the Density (SI unit: kg/m3), Heat capacity at constant pressure Cp (SI unit: J/ (kg·K)), and Ratio of specific heats (unitless) use data From material. Select User defined to enter other values or expressions.

Ideal Gas

If Ideal gas is selected, the ideal gas law is used to describe the fluid. In this case, specify the thermodynamics properties by selecting a gas constant type and selecting between entering the heat capacity at constant pressure or the ratio of specific heats. For an ideal gas the density is defined as

386 | C H A P T E R 1 2 : N O N - I S O T H E R M A L F L O W B R A N C H

MnpA pA

= --------------- = ---------- ,

RT RsT

where pA is the absolute pressure, and T the temperature.

•Select a Gas constant type— Specific gas constant Rs (SI unit: J/(kg·K)) or Mean molar mass Mn (SI unit: kg/mol). In both cases, the default uses data From material. Select User defined to enter other values or expressions. If Mean molar mass is selected, the universal gas constant R 8.314 J/(mol·K), which is a built-in

physical constant, is also used.

•From the Specify Cp or list, select Heat capacity at constant pressure Cp (SI unit: J/(kg·K)), and Ratio of specific heats (unitless). The default setting is to use the

property value From material. Select User defined to enter another value or expression for either of material property.

D Y N A M I C V I S C O S I T Y

The dynamic viscosity describes the relationship between the shear rate and the shear stresses in a fluid. Intuitively, water and air have a low viscosity, and substances often described as thick, such as oil, have a higher viscosity. Non-Newtonian fluids have a shear-rate dependent viscosity. Examples of non-Newtonian fluids include yoghurt, paper pulp, and polymer suspensions.

Select a Dynamic viscosity (SI unit: Pa·s) from the list—From material (the default),

Non-Newtonian power law, Non-Newtonian Carreau model, or User defined. If User defined is selected, use a built-in variable for the shear rate magnitude, spf.sr, which makes it possible to define arbitrary expressions of the dynamic viscosity.

Non-Newtonian Power Law

If Non-Newtonian power law is selected, enter the Power law model parameter m and

Model parameter n (both unitless). This selection uses the power law as the viscosity model for a non-Newtonian fluid where the following equation defines dynamic

viscosity:

= m· n – 1

Non-Newtonian Carreau Model

If Non-Newtonian Carreau model is selected, enter these Carreau model parameters:

• The Zero shear rate viscosity 0 (SI unit: Pa·s)

S H A R E D I N T E R F A C E F E A T U R E S | 387

•The Infinite shear rate viscosity inf (SI unit: Pa·s)

•The Model parameters (SI unit: s) and n (unitless)

This selection uses the Carreau model as the viscosity model for a non-Newtonian fluid where the following equation defines the dynamic viscosity:

M I X I N G L E N G T H L I M I T ( T U R B U L E N C E M O D E L S O N L Y )

This section is only available for the k- and k- models, which need an upper limit on the mixing length. Select a Mixing length limit—Automatic (the default) or Manual.

• If Automatic is selected, the mixing length limit is automatically evaluated as:

where lbb is the shortest side of the geometry bounding box. If the geometry is for example a complicated system of very slender entities, Equation 12-1 tends to give a result that is too large. Then define lmixlim manually.

•If Manual is selected, enter a value or expression for the Mixing length limit lmixlim (SI unit: m).

D I S T A N C E E Q U A T I O N ( T U R B U L E N C E M O D E L S O N L Y )

This section is only available for the low-Reynolds number k- model and the Spalart-Allmaras model, which need the distance to the closest wall. Select a Reference length scale—Automatic (the default) or Manual.

• If Automatic is selected, the reference length scale is automatically evaluated as:

where lbb is the shortest side of the geometry bounding box. If the geometry is for example a complicated system of very slender entities, Equation 12-1 tends to give a result that is too large. Then define lref manually.

•If Manual is selected, enter a value or expression for the Reference length scale lref

(SI unit: m).

388 | C H A P T E R 1 2 : N O N - I S O T H E R M A L F L O W B R A N C H