Conductive Heat Transfer

Conductive thermal conductivity.

blockType: AcausalFoundation.Thermal.Elements.Conduction

Conductive Heat Transfer

Path in the library:

/Physical Modeling/Fundamental/Thermal/Elements/Conductive Heat Transfer

Variable Conductive Heat Transfer

Path in the library:

/Physical Modeling/Fundamental/Thermal/Elements/Variable Conductive Heat Transfer

Description

Block Conductive Heat Transfer It is the transfer of heat through conductive heat exchange between two layers of the same material.

The block icon changes depending on the parameter value. Conductivity type.

For a flat surface, the transfer is described by Fourier’s law:

where

— heat flow;
— thermal conductivity of the material;
— the cross-sectional area perpendicular to the direction of the heat flow;
— the distance between the layers, that is, the thickness of the material;
— layer temperature ;
— layer temperature .

The thermal conductivity through the cylindrical wall of the pipe is described by the equation:

where

— pipe length;
— inner diameter;
— outer diameter.

The method of setting the thermal conductivity can be specified using the parameter Conductivity type:

Constant — thermal conductivity remains constant during simulation. You set the thermal conductivity using the parameter Thermal conductivity.
Variable input — Thermal conductivity is set using the input signal on port K, which can change during simulation. Parameter Minimum thermal conductivity sets the lower limit of the signal.
Tabulated data — Thermal conductivity is indicated using temperature-based tabular data. In this case, the thermal conductivity may also change during the simulation process.

Option Tabulated data uses the average temperature of the unit to determine the thermal conductivity. For a flat wall geometry, the average temperature is

For the cylindrical geometry of the wall, the average temperature is

which suggests that it is located inside the cylinder.

A and B are the thermal ports corresponding to the material layers. The positive direction of heat transfer from port A to port B, in this case, the value of the heat flow is positive.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# A — layer
heat

Details

Thermal port corresponding to the layer .

Program usage name

port_a

# B — layer
heat

Details

Thermal port corresponding to the layer . In the case of a cylindrical wall, the layer — internal.

Program usage name

port_b

Input

# K — thermal conductivity control signal, W/(K*m)
scalar

Details

The input signal controlling the thermal conductivity. The signal is saturated when the value goes beyond the minimum limit set by the parameter Minimum thermal conductivity.

Dependencies

To use this port, set the parameter Conductivity type value Variable input.

Data types	`Float64`
Complex numbers support	I don’t

Parameters

# Conductivity type — the type of setting thermal conductivity properties
Constant | Variable input | Tabulated data

Details

Type of thermal conductivity assignment:

Constant — thermal conductivity remains constant during simulation. You set the thermal conductivity using the parameter Thermal conductivity.
Variable input — Thermal conductivity is set using the input signal on port K, which can change during simulation. Parameter Minimum thermal conductivity sets the lower limit of the signal.
Tabulated data — Thermal conductivity is indicated using temperature-based tabular data. In this case, the thermal conductivity may also change during the simulation process.

Values	`Constant` \| `Variable input` \| `Tabulated data`
Default value	`—`
Program usage name	`type`
Evaluatable	No

# Wall geometry — wall shape for calculating thermal conductivity
Planar | Cylindrical

Details

Wall shape for thermal conductivity:

Planar — heat transfer is carried out through a flat rectangular wall. The area and thickness of the wall are indicated.
Cylindrical — heat transfer is carried out through the cylindrical wall of the pipe. The inner diameter, outer diameter and length of the pipe are indicated.

Values	`Planar` \| `Cylindrical`
Default value	`Planar`
Program usage name	`wall_geometry`
Evaluatable	No

# Area — heat exchange area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area perpendicular to the direction of the heat flow.

Dependencies

To use this parameter, set for the parameter Wall geometry meaning Planar.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`1e-4 m^2`
Program usage name	`area`
Evaluatable	Yes

# Thickness — Material thickness
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The thickness of the material, that is, the distance between the layers.

Dependencies

To use this parameter, set for the parameter Wall geometry meaning Planar.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.1 m`
Program usage name	`thickness`
Evaluatable	Yes

# Inner diameter — inner diameter of the pipe
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The inner diameter of the pipe, that is, the diameter of the inner layer of the material.

Dependencies

To use this parameter, set for the parameter Wall geometry meaning Cylindrical.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.05 m`
Program usage name	`inner_diameter`
Evaluatable	Yes

# Outer diameter — The outer diameter of the pipe
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The outer diameter of the pipe, that is, the diameter of the outer layer of the material.

Dependencies

To use this parameter, set for the parameter Wall geometry meaning Cylindrical.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.1 m`
Program usage name	`outer_diameter`
Evaluatable	Yes

# Length — pipe length
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Pipe length.

Dependencies

To use this parameter, set for the parameter Wall geometry meaning Cylindrical.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`1.0 m`
Program usage name	`length`
Evaluatable	Yes

# Thermal conductivity — thermal conductivity of the material
W/(m*K) | mW/(m*K) | Btu_IT/(hr*ft*deltadegR)

Details

Thermal conductivity of the material.

Dependencies

To use this parameter, set for the parameter Conductivity type meaning Constant.

Units	`W/(mK)` \| `mW/(mK)` \| `Btu_IT/(hrftdeltadegR)`
Default value	`401.0 W/(m*K)`
Program usage name	`lambda_const`
Evaluatable	Yes

# Minimum thermal conductivity — the lower limit of thermal conductivity
W/(m*K) | mW/(m*K) | Btu_IT/(hr*ft*deltadegR)

Details

The lower limit of the thermal conductivity value. The input signal on the K port is saturated at this value to prevent further reduction of thermal conductivity.

Dependencies

To use this parameter, set for the parameter Conductivity type meaning Variable input.

Units	`W/(mK)` \| `mW/(mK)` \| `Btu_IT/(hrftdeltadegR)`
Default value	`10.0 W/(m*K)`
Program usage name	`lambda_min`
Evaluatable	Yes

# Thermal conductivity vector — vector of thermal conductivity values to use in the data table
W/(m*K) | mW/(m*K) | Btu_IT/(hr*ft*deltadegR)

Details

Vector of thermal conductivity values corresponding to the parameter values Temperature vector. The size of the vector must be the same as the parameter Temperature vector. The unit performs a one-dimensional search on the thermal conductivity table using the average temperature of the unit, linear interpolation and the nearest extrapolation.

Dependencies

To use this parameter, set for the parameter Conductivity type meaning Tabulated data.

Units	`W/(mK)` \| `mW/(mK)` \| `Btu_IT/(hrftdeltadegR)`
Default value	`[413.0, 401.0, 392.0, 383.0, 371.0, 357.0, 342.0] W/(m*K)`
Program usage name	`lambda_vector`
Evaluatable	Yes

Details

Vector of temperature values corresponding to parameter values Thermal conductivity vector. The vector must be strictly ascending. The values may be unevenly spaced. The vector must contain at least two values.

Dependencies

To use this parameter, set for the parameter Conductivity type meaning Tabulated data.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`[200.0, 273.0, 400.0, 600.0, 800.0, 1000.0, 1200.0] K`
Program usage name	`T_vector`
Evaluatable	Yes

Conductive Heat Transfer

Description

Variables

Ports

Conserving

Input

Parameters

Parameters

Examples