Conductive heat transfer#

The Conductive heat transfer block describes the transfer of heat by thermal conductivity between layers of the same material.

Wall geometry type

The block presents two types of geometry: plane and cylindrical.

Heat flow in a plate wall, according to Fourier’s law (1) :

(1)#\[ Q=\frac{\mathrm{k}\mathrm{F}\left(T_{1}-T_{2}\right)}{b} \]

where:

\(k\) - material thermal conductivity factor, [W/(m \(\cdot\) ℃)];

\(F\) - surface area of the heat exchange, [m\(^2\)];

\(b\) - wall thickness (distance between design layers), [m];

\(T_1\) - temperature of the calculated layer 1, [℃];

\(T_2\) - temperature of the calculated layer 2, [℃].

Heat flow in a cylindrical wall (2) :

(2)#\[ Q=\frac{2\cdot \pi \cdot \mathrm{k}\cdot \mathrm{L}\cdot \left(T_{1}-T_{2}\right)}{\mathrm{l}\mathrm{n}\left(\frac{d_{н}}{d_{\mathrm{в}\mathrm{н}}}\right)} \]

where:

\(L\) - tube length, [m];

\(d_н\) - pipe outer diameter, [m];

\(d_{in}\) - pipe inner diameter, [m].

Conductivity type:

“Constant” - user-specified thermal conductivity is used in the Thermal conductivity field.

“Table of values” - The thermal conductivity obtained by determining the polynomial constructed from the values entered by the user in the Thermal conductivity curve and Temperature curve fields is used.

“Material” - the thermal conductivity according to the selected material in the associated block is used Materials properties .

When calculating thermal conductivity using a polynomial, the average temperature.

For a plane wall (3) :

(3)#\[ T_{\mathrm{с}\mathrm{р}}=\frac{T_{1}+T_{2}}{2} \]

For a cylindrical wall (4) :

(4)#\[ T_{\mathrm{с}\mathrm{р}}=\left(T_{1}-T_{2}\right)\cdot \left(\frac{d_{н}}{d_{н}-d_{\mathrm{в}\mathrm{н}}}-\frac{1}{\mathrm{l}\mathrm{n}\left(\frac{d_{н}}{d_{\mathrm{в}\mathrm{н}}}\right)}\right)+T_{2} \]

1. Properties#

Property	Default value	Description	Units of measurement
Wall geometry type: Plane; Cylindrical	Plane	-	-
Surface area, available when selecting `Wall geometry type` - `Plane`	10.0	-	m\(^2\)
Wall thickness, available when selecting `Wall geometry type` - `Plane`	0.02	-	m
Inner diameter, available when selecting `Wall geometry type` - `Cylindrical`	0.02	-	m
Outer diameter, available when selecting `Wall geometry type` - `Cylindrical`	0.05	-	m
Length, available when selecting `Wall geometry type` - `Cylindrical`	10.0	-	m
Conductivity type: Constant; Table of values; Material	Constant	-	-
Thermal conductivity, available when selecting `Conductivity type` - `Constant`	1.7	-	\(\frac{W}{m \cdot ^\circ C}\)
Thermal conductivity curve, available when selecting `Conductivity type` - `Table of values`	401.9;391.5;385.4;376.9;	The format for completing the field: 401.9;391.5;385.4;376.9;	\(\frac{W}{m \cdot К}\)
Temperature curve, available when selecting `Conductivity type` - `Table of values`	26.85;126.85;226.85;326.85;	The format for completing the field: 26.85;126.85;226.85;326.85;	\(^\circ\)C
Material property, available when selecting `Conductivity type` - `Material`	-	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	Temperature of the preceding block	-	Heat exchange
Output	Output	-	-	Heat exchange

In order to see the connection capabilities of the block, you need to go to page Description of block ports

3. Examples of use#

Examples of using this block can be found in the following sections:

Tutorials;
How-to guides;
Description of Demo.

Tutorials

Library	Tutorial name
Heat exchange	Thermal conductivity in a flat wall; Transient thermal conductivity in a steel rod; Transient thermal conductivity in rods made of different materials
Automation	Modeling a DC motor using blocks from the “Automation” section
`Solving optimization problems`	Introduction to Optimization; Finding the root

How-to guides

Section	Guide name
Life support engineering	Development of room thermal state model
Machine learning approximation	A simple machine learning model of thermal conductivity