Boundary conditions

Introduction

This page details all the boundary conditions a user has access to as well as what the required input is. A boundary condition makes it so that a problem only has one solution. For example, defining an inlet temperature for the coolant will (for a given heatsink, pump, and heat load) fix the temperatures for the rest of the entities. A boundary condition allows a user to match the model as close as possible to reality; is a pump driving the fluid motion and if so, is this pump positioned upstream or downstream, etc.?

General overview

The following list shows all the available boundary conditions, applicability, and input parameters. Parameters denoted with * are required, the others are optional entries. Click on the name of the boundary condition for more information.

Boundary type	Boundary condition	Applicable to		Input Parameters
		Fluid	Solid	Fluid	Solid
Inlet	FixedFlowRateInlet			$T^*$, $(U$, $\dot Q$ or $\dot m)^*$, $\omega$
	PressureInlet			$T^*$, $p^*$
	PumpInlet			$T^*$, Performance curve*
	FanInlet			$T^*$, Performance curve*
Outlet	PressureOutlet			$p$
	FanOutlet			Performance curve*
	PumpOutlet			Performance curve*
	MinFlowrateOutlet			$(U$, $\dot Q$ or $\dot m)^*$
Wall	FixedTemperatureWall			$T^*$	$T^*$
	HeatedWall			$Q^*$, $R_d$, $R_k$	$Q^*$
	ExternalWall			$h^*$, $T_a^*$, $R_d$, $R_k$, $\varepsilon_{external}$	$h^*$, $T_a^*$, $R_d$, $R_k$, $\varepsilon_{external}$
	InsulatedWall			$R_l^*$
	Slip
	Cyclic			Another boundary of type 'Cyclic'	Another boundary of type 'Cyclic'

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Important

Any boundary that isn't an interface or has any special boundary condition imposed is by default adiabatic. This means that it will be treated as if a wall with perfect insulation is placed next to it.

For fluids will also the no-slip condition be imposed.

Boundary Types

FixedFlowRateInlet

Name	fixedFlowRateInlet
Type	Inlet
Applicable to	Fluids
Input parameters	The temperature $T$ in $[K]$ at the patch should be specified, as well as either the velocity $U$ in $[m/s]$, the mass flow rate $\dot m$ in $[kg/s]$ or the volumetric flow rate $\dot Q$ in $[m^3/s]$, depending on the chosen option. Also a rotational velocity $\omega$ in $[rad/s]$ can be set.

With this boundary condition, a flow entering the domain at a certain velocity is specified. The flow can be described by:

• Fixed value velocity: the magnitude of the inlet velocity at the patch is specified.
• Mass flow rate: an average mass flow rate is specified, which is translated to a velocity at the patch with the fluid density by the software.
• Volumetric flow rate: the average volumetric flow rate at the patch is specified. The inlet velocity is then automatically calculated by the software.

A fixedFlowRateInlet boundary condition is typically used in combination with a pressureOutlet boundary condition.

PressureInlet

Name	pressureInlet
Type	Inlet
Applicable to	Fluids
Input parameters	The temperature $T$ in $[K]$ and pressure $p$ in $[Pa]$ at the patch should be specified.

This boundary condition defines an inflow condition based on the inputted total pressure at the boundary. A pressureInlet condition is typically used in combination with a pressureOulet boundary condition.

The total pressure $(P_{tot})$ in $Pa$ relates to the static pressure $(P_{stat})$ in $Pa$ through the following relation:

$$P_{tot} = P_{stat} + \frac{1}{2}\rho V^2 = P_{stat} +\frac{1}{2}\rho\frac{\dot Q^2}{A^2}$$

Where:

• $\rho$ represents the density of the fluid in $\frac{kg}{m^3}$

• $V$ represents the velocity of the fluid in $\frac{m}{s}$

• $\dot Q$ represents the volumetric flow rate of the fluid in $\frac{m^3}{s}$

• $A$ represents the area of the boundary patch in $m^2$

PumpInlet

Name	pumpInlet
Type	Inlet
Applicable to	Fluids
Input parameters	The temperature $T$ in $[K]$ at the patch should be specified, as well as the performance curve of the pump.

This boundary condition sets the total pressure at the patch based on the pressure drop as a function of the volumetric flow rate as specified in the performance curve of the pump. This boundary condition is typically used in combination with a pressureOutlet boundary condition at the outlet.

The total pressure $(P_{tot})$ in $Pa$ relates to the static pressure $(P_{stat})$ in $Pa$ through the following relation:

$$P_{tot} = P_{stat} + \frac{1}{2}\rho V^2 = P_{stat} +\frac{1}{2}\rho\frac{\dot Q^2}{A^2}$$

Where:

• $\rho$ represents the density of the fluid in $\frac{kg}{m^3}$

• $V$ represents the velocity of the fluid in $\frac{m}{s}$

• $\dot Q$ represents the volumetric flow rate of the fluid in $\frac{m^3}{s}$

• $A$ represents the area of the boundary patch in $m^2$

FanInlet

Name	fanInlet
Type	Inlet
Applicable to	Fluids
Input parameters	The temperature $T$ in $[K]$ at the patch should be specified, as well as the performance curve of the fan.

This boundary condition can be used to set a total pressure inlet condition for a fan. The total pressure at the patch is set based on the pressure drop which is specified in the performance curve of the fan as a function of the volumetric flow rate. This boundary condition is typically used in combination with a pressureOutlet boundary condition at the outlet.

The total pressure $(P_{tot})$ in $Pa$ relates to the static pressure $(P_{stat})$ in $Pa$ through the following relation:

$$P_{tot} = P_{stat} + \frac{1}{2}\rho V^2 = P_{stat} +\frac{1}{2}\rho\frac{\dot Q^2}{A^2}$$

Where:

• $\rho$ represents the density of the fluid in $\frac{kg}{m^3}$

• $V$ represents the velocity of the fluid in $\frac{m}{s}$

• $\dot Q$ represents the volumetric flow rate of the fluid in $\frac{m^3}{s}$

• $A$ represents the area of the boundary patch in $m^2$

PressureOutlet

Name	pressureOutlet
Type	Outlet
Applicable to	Fluids
Input parameters	Optionally, a pressure at the patch can be specified in $[Pa]$. If no pressure is specified, it is set to 0 $Pa$. This boundary patch fixes the static pressure at that boundary.

This boundary condition defines an outflow condition based on the specified static pressure at the boundary. A pressureOutlet boundary condition is typically used in combination with a fixedFlowRateInlet, a fanInlet, or a pumpInlet.

FanOutlet

Name	fanOutlet
Type	Outlet
Applicable to	Fluids
Input parameters	The performance curve of the fan should be specified.

This boundary condition sets the total pressure at the patch based on the pressure drop as a function of the volumetric flow rate as specified in the performance curve of the fan. A fanOutlet condition is typically used in combination with a pressureInlet condition at the inlet.

PumpOutlet

Name	pumpOutlet
Type	Outlet
Applicable to	Fluids
Input parameters	The performance curve of the fan should be specified.

This boundary condition sets the total pressure at the patch based on the pressure drop as a function of the volumetric flow rate as specified in the performance curve of the pump. A pumpOutlet condition is typically used in combination with a pressureInlet condition at the inlet.

MinFlowrateOutlet

Name	minFlowRateOutlet
Type	Outlet
Applicable to	Fluids
Input parameters	A minFlowRateOutlet only requires one input parameter: either the velocity $U$ in $[m/s]$ the mass flow rate $\dot m$ in $[kg/s]$ or the volumetric flow rate $\dot Q$ in $[m^3/s]$ at the patch.

This boundary condition ensures that a specified minimum flow rate is achieved through the outlet. This minimum flow rate can be described by:

• Fixed value velocity: the magnitude of the minimum outlet velocity at the patch is specified.
• Mass flow rate: the minimum average mass flow rate at the patch is specified. The minimum outlet velocity is then automatically calculated by the software.
• Volumetric flow rate: the minimum average volumetric flow rate at the patch is specified. The minimum outlet velocity is then automatically calculated by the software.

A minimumFlowRateOutlet boundary condition is typically used in combination with a pressureInlet boundary condition.

FixedTemperatureWall

Name	fixedTemperatureWall
Type	Wall
Applicable to	Fluids and solids
Input parameters	Fluid	The temperature $T$ in $[K]$ at the patch should be specified.
	Solid	The temperature $T$ in $[K]$ at the patch should be specified.

With the fixedTemperatureWall, you can fix the temperature assigned to the patch. This is useful if you want to model a constant temperature heat source or sink. The following input options are available:

1. A constant value over the entire patch, e.g.:
   $273.15$
2. A polynomial in function of spatial coordinates where 7 coefficients should be provided:
   $[1,2,3,4,5,6,7]$
   This array represents the coefficients of a polynomial:
   $1x^2+2y^2+3z^2+4x+5y+6z+7$
3. A table containing the coordinates and corresponding temperatures:
   $[[[1.0, 2.0, 3.0], 273.15],[[1.2, 2.4, 3.6], 283.15],[[2.4, 4.5, 7.8], 293.15]]$

HeatedWall

Name	fixedTemperatureWall
Type	Wall
Applicable to	Fluids and solids
Input parameters	Fluid	The heating power $Q$ in $[W]$ should be specified. Optionally, a thermal resistance can be applied by providing the thickness of the thermal resistance layer $R_d$ in $[m]$ and the conductivity $R_k$ of the resistance layer in $[W/(mK)]$.
	Solid	The heating power $Q$ in $[W]$ should be specified.

With the heatedWall, a constant heating power value can be assigned to the patch. The following input options are available:

1. A constant power value over the entire patch, e.g.:
   $150$
2. A polynomial in function of spatial coordinates where 7 coefficients should be provided:
   $[1,2,3,4,5,6,7]$
   This array represents the coefficients of a polynomial:
   $1x^2+2y^2+3z^2+4x+5y+6z+7$
3. A table containing the coordinates and corresponding power:
   $[[[1.0, 2.0, 3.0], 100],[[1.2, 2.4, 3.6], 150],[[2.4, 4.5, 7.8], 200]]$

ExternalWall

Name	fixedTemperatureWall
Type	Wall
Applicable to	Fluids and solids
Input parameters	Fluid	The heat transfer coefficient $h$ in $[W/(m^2K)]$ and the temperature of the environment $T_a$ in $[K]$ should be specified. Optionally, a thermal resistance layer can be defined by setting the thickness of the layer $R_d$ in $[m]$ and the conductivity $R_k$ of the thermal resistance layer in $[W/(mK)]$. Optionally, an external emissivity $\varepsilon_{external}$ in [−] can be set.
	Solid	The heat transfer coefficient $h$ in $[W/(m^2K)]$ and the temperature of the environment $T_a$ in $[K]$ should be specified. Optionally, a thermal resistance layer can be defined by setting the thickness of the layer $R_d$ in $[m]$ and the conductivity $R_k$ of the thermal resistance layer in $[W/(mK)]$. Optionally, an external emissivity $\varepsilon_{external}$ in [−] can be set.

With this boundary condition, heat losses to or gains from the environment can be modeled. Optional thin thermal resistance layers can be specified through the thicknesses and the conductivity of the layers.

InsulatedWall

Name	fixedTemperatureWall
Type	Wall
Applicable to	Fluids and solids
Input parameters	Fluid	The roughness length $R_l$ in $[m]$
	Solid	/

As the name suggests, this boundary condition represents an adiabatic wall. These boundaries do not thermally interact with the rest of the case setup.

Slip

Name	slip
Type	Wall
Applicable to	Fluids
Input parameters	/

This boundary condition ensures that there can be no flow perpendicular to the boundary itself, but there can be flow (with a non-zero velocity) parallel to or along this boundary patch.

Cyclic

Name	Cyclic
Type	Wall
Applicable to	Fluids and solids
Input parameters	Another boundary of type 'Cyclic'

ColdStream allows you to assign periodicity. By using the Cyclic boundary patch option, the heat leaving through this boundary will enter again through the second, linked boundary.

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Warning

To link 2 boundaries with one another, they must be assigned to the same parent region. The shape of the linked boundaries must also match with one another.