Viscous Energy Model

The Viscous Energy model simulates the energy that drives the expansion of a viscous fluid due to shear stress.


Theory	See Non-Isothermal Flow
Provided by	[physics continuum] > Models > Optional Models
Example Node Path	Continua > Physics > Models > Viscous Energy
Requires	Flow: Viscous Flow
Properties	See Viscous Energy Properties.
Activates	Material Properties	Thermal Conductivity Specific Heat Horizontal Temperature Shift Factor. Vertical Temperature Shift Factor. See Viscous Energy Materials and Methods.
	Reference Values	Minimum Allowable Temperature Reference Temperature Maximum Allowable Temperature See Viscous Energy Reference Values.
	Initial Conditions	Static Temperature
	Boundary Inputs	See Viscous Energy Boundary Settings
	Region Inputs	See Viscous Energy Region Settings
	Monitors	Energy Temperature
	Field Functions	Specific Heat Temperature Thermal Conductivity

Viscous Energy Properties

SUPG: The value for the Streamline-Upwind-Petrov-Galerkin advection stabilization term. The default value is 1.0.
Transient Stabilization: The value for the degree of tolerance used to mitigate temperature spikes in combination with Minimum Allowable Temperature and Maximum Allowable Temperature. Corresponds to $α$ in Eqn. (1032). The default value is 0, normalized to 1.

Viscous Energy Materials and Methods

When temperature effects are present, the non-Newtonian liquid models use horizontal shift factor $a_{T}$ and vertical shift factor $b_{T}$ to adjust viscosity with temperature. These factors apply to both polymer viscosity and relaxation times of viscoelastic modes.

Horizontal Temperature Shift Factor

Method	Corresponding Method Node
Arrhenius	Arrhenius Exposes the following terms from Eqn. (733): Activation energy $E_{a}$ Reference temperature $T_{0}$ Use the Arrhenius model when the temperature is at least 100°C above the glass transition temperature of the polymer.
Nahme	Nahme Exposes the following terms from Eqn. (734): Activation energy $E_{a}$ Reference temperature $T_{0}$ Use the Nahme model when the temperature is close to the reference temperature $T_{0}$ .
Williams-Landel-Ferry (WLF)	Williams-Landel-Ferry Exposes the following terms from Eqn. (735): Coefficients $C_{1}$ and $C_{2}$ , positive empirical constants that depend on the material and the reference temperature. See [24] for tables of values for $C_{1}$ , $C_{2}$ Reference temperature $T_{0}$ Use the WLF model when the temperature is close to the glass transition temperature of the polymer.

Vertical Temperature Shift Factor

Method	Corresponding Method Node
Rouse	Rouse Exposes $T_{0}$ in Eqn. (736).

Viscous Energy Reference Values

Minimum Allowable Temperature: The smallest temperature value that is permitted anywhere in the continuum. The calculated temperature is restricted to the specified minimum allowable temperature by adding a source term to the energy equation to heat up the local temperature. See Eqn. (1032). For unsteady simulations only.
Reference Temperature: A temperature between Minimum and Maximum Allowable Temperature used as a basis for computing heat effects.
Maximum Allowable Temperature: The largest temperature value that is permitted anywhere in the continuum. The calculated temperature is restricted to the specified maximum allowable temperature by adding a source term to the energy equation to cool down the local temperature. See Eqn. (1032). For unsteady simulations only..

Viscous Energy Boundary Settings

Free Stream and Wall

Thermal Specification

Allows you to determine how the energy flow across the boundary is specified.


Method	Corresponding Physics Value Nodes
Heat Flux	Heat Flux Specifies the amount of energy flowing across the boundary in W/m², $q_{spec}$ in Eqn. (1065). A positive specified heat flux value $q_{spec}$ means that heat is flowing into the domain.
Temperature	Static Temperature Specifies the boundary temperature $T_{spec}$ in Eqn. (1063).
Adiabatic Specifies that there is no energy transfer across the boundary.	None.
Convection Specifies convection flux across the boundary in W/m².	Ambient Temperature Specifies the ambient temperature $T_{\infty}$ in Eqn. (1066). Heat Transfer Coefficient Specifies the heat transfer coefficient $h$ in Eqn. (1066).

Mass Flow Inlet, Stagnation Inlet, and Velocity Inlet

Static Temperature: The static temperature of the boundary.

Stagnation Inlet

Describes the resting conditions of the fluid.

Reference Frame Specification

Specifies the reference frame in which the fluid is at rest.

Method	Corresponding Physics Value Nodes
Lab Frame	Static Temperature The static temperature of the fluid.
Region Reference Frame	Static Temperature The static temperature of the fluid.
Local Reference Frame	Boundary Reference Frame Specification Applies the chosen reference frame to the containing boundary. Static Temperature The static temperature of the fluid.

Viscous Energy Region Settings

Applies to fluid regions.

Energy Source Option

Specifies whether you want to enter an energy source term, and of which type. The energy source corresponds to

q

in Eqn. (1035).

Energy Source Option	Corresponding Physics Value Nodes
None	None
Volumetric Heat Source	Volumetric Heat Source Specifies a user-defined volumetric heat source in W/m^3. Energy Source Temperature Derivative Represents linearization of the energy source with respect to temperature. Its value is set to zero by default. Providing a value for the derivative helps stabilize the solution when the function for the source term is a function of temperature. If the source is constant, or not a function of temperature, leave this value at zero.
Total Heat Source	Total Heat Source Specifies a user-defined total heat source in W. Energy Source Temperature Derivative Represents linearization of the energy source with respect to temperature. Its value is set to zero by default. Providing a value for the derivative helps stabilize the solution when the function for the source term is a function of temperature. If the source is constant, or not a function of temperature, leave this value at zero.
Specific Heat Source	Specific Heat Source Specifies a user-defined specific heat source in W/kg. Energy Source Temperature Derivative Represents linearization of the energy source with respect to temperature. Its value is set to zero by default. Providing a value for the derivative helps stabilize the solution when the function for the source term is a function of temperature. If the source is constant, or not a function of temperature, leave this value at zero.