Description: "Correlations for convective heat flux"

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## Buildings.HeatTransfer.Convection.Functions.HeatFlux

Correlations for convective heat flux

### Information

This package contains functions for the convective heat transfer. Input into the functions is the temperature difference between the solid and the fluid. The functions compute the convective heat flux, rather than the convective heat transfer coefficient, because the convective heat transfer coefficient is not differentiable around zero for some flow configurations, such as buoyancy driven flow at a horizontal surface. However, the product of convective heat transfer coefficient times temperature difference is differentiable around zero.

### Package Content

Name | Description
--- | ---
ceiling | Free convection, ceiling
constantCoefficient | Constant convective heat transfer coefficient
floor | Free convection, floor
rayleigh | Rayleigh number with smooth transition to lower limit
wall | Free convection, wall
BaseClasses | Base classes for convective heat transfer coefficients

## Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling

Free convection, ceiling

### Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient for a ceiling, computed as

h=k |ΔT|0.3333,

where k=1.51 if the fluid is warmer than the ceiling, or k=0.76 otherwise.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
TemperatureDifference | dT |  | Temperature difference solid minus fluid [K]

### Outputs

Type | Name | Description
--- | --- | ---
HeatFlux | q_flow | Convective heat flux from solid to fluid [W/m2]

### Modelica definition

function ceiling "Free convection, ceiling" extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux; algorithm q_flow := noEvent(smooth(1, if (dT>0) then 0.76*dT^1.3333 else -1.51*(-dT)^1.3333)); end ceiling;

## Buildings.HeatTransfer.Convection.Functions.HeatFlux.constantCoefficient

Constant convective heat transfer coefficient

### Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
TemperatureDifference | dT |  | Temperature difference solid minus fluid [K]
CoefficientOfHeatTransfer | hCon | 3 | Constant for convective heat transfer coefficient [W/(m2.K)]

### Outputs

Type | Name | Description
--- | --- | ---
HeatFlux | q_flow | Convective heat flux from solid to fluid [W/m2]

### Modelica definition

function constantCoefficient "Constant convective heat transfer coefficient" extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux; input Modelica.SIunits.CoefficientOfHeatTransfer hCon = 3 "Constant for convective heat transfer coefficient"; algorithm q_flow :=hCon*dT; end constantCoefficient;

## Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor

Free convection, floor

### Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient for a floor, computed as

h=k |ΔT|0.3333,

where k=0.76 if the fluid is warmer than the floor, or k=1.51 otherwise.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
TemperatureDifference | dT |  | Temperature difference solid minus fluid [K]

### Outputs

Type | Name | Description
--- | --- | ---
HeatFlux | q_flow | Convective heat flux from solid to fluid [W/m2]

### Modelica definition

function floor "Free convection, floor" extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux; algorithm q_flow := noEvent(smooth(1, if (dT>0) then 1.51*dT^1.3333 else -0.76*(-dT)^1.3333)); end floor;

## Buildings.HeatTransfer.Convection.Functions.HeatFlux.rayleigh

Rayleigh number with smooth transition to lower limit

### Information

This function returns the Rayleigh number. The parameter `RaMin` is used to transition to a lower limit for the Rayleigh number. This is helpful to avoid a Rayleigh number of zero or to avoid an expression for a convection coefficient that has an infinite derivative near zero, i.e., if h=f(Ra(1/2)).

Extends from Modelica.Icons.Function (Icon for functions).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Length | x |  | Layer thickness [m]
Density | rho |  | Mass density [kg/m3]
SpecificHeatCapacity | c_p |  | Specific heat capacity [J/(kg.K)]
DynamicViscosity | mu |  | Dynamic viscosity [Pa.s]
ThermalConductivity | k |  | Thermal conductivity [W/(m.K)]
Temperature | T_a |  | Temperature of surface a [K]
Temperature | T_b |  | Temperature of surface b [K]
Real | Ra_min |  | Minimum value for Rayleigh number

### Outputs

Type | Name | Description
--- | --- | ---
Real | Ra | Rayleigh number

### Modelica definition

function rayleigh "Rayleigh number with smooth transition to lower limit" extends Modelica.Icons.Function; input Modelica.SIunits.Length x "Layer thickness"; input Modelica.SIunits.Density rho "Mass density"; input Modelica.SIunits.SpecificHeatCapacity c_p "Specific heat capacity"; input Modelica.SIunits.DynamicViscosity mu "Dynamic viscosity"; input Modelica.SIunits.ThermalConductivity k "Thermal conductivity"; input Modelica.SIunits.Temperature T_a "Temperature of surface a"; input Modelica.SIunits.Temperature T_b "Temperature of surface b"; input Real Ra_min "Minimum value for Rayleigh number"; output Real Ra "Rayleigh number"; protected Modelica.SIunits.TemperatureDifference dT "Temperature difference"; algorithm dT :=abs(T_a - T_b); Ra := rho^2*x^3*Modelica.Constants.g_n*c_p*dT/((T_a+T_b)/2*mu*k); Ra := Buildings.Utilities.Math.Functions.smoothMax(x1=Ra, x2=Ra_min, deltaX=Ra_min/10); end rayleigh;

## Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall

Free convection, wall

### Information

This function computes the buoyancy-driven convective heat flux as

q̇ = h ΔT,

where ΔT is the solid temperature minus the fluid temperature and h is the convective heat transfer coefficient for a wall, computed as

h=1.3 |ΔT|0.3333.

Extends from Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux (Partial function for convective heat flux).

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
TemperatureDifference | dT |  | Temperature difference solid minus fluid [K]

### Outputs

Type | Name | Description
--- | --- | ---
HeatFlux | q_flow | Convective heat flux from solid to fluid [W/m2]

### Modelica definition

function wall "Free convection, wall" extends Buildings.HeatTransfer.Convection.Functions.HeatFlux.BaseClasses.PartialHeatFlux; algorithm q_flow := noEvent(smooth(1, if (dT > 0) then 1.3*dT^1.3333 else -1.3*(-dT)^1.3333)); end wall;