Thermal conduction

Under heat conduction - also known as heat conduction or diffusion - is understood in the physics of heat flow in a solid or a stationary fluid as a result of a temperature difference. Heat flows there - according to the second law of thermodynamics - only in the direction of lower temperature. Due to the energy conservation law it is lost no heat energy. Heat conduction is a mechanism for transporting thermal energy, without the need for a macroscopic flow of material is required, as in the alternative mechanism the convection. Also, the heat transfer by thermal radiation is considered as a separate mechanism. A measure of the heat conduction in a specific substance is the thermal conductivity.

For the calculation of heat transfer can often be used for the electrical analogy, refer to heat resistance. Then, thermal conductivity and temperature calculations using the methods of electrical engineering are possible.

Fourier 's law

The transmitted by conduction heat output is described by Fourier's law (1822, after Jean Baptiste Joseph Fourier ), which is for the simplified case of a solid body with two parallel wall surfaces:

Unit is watts ( W)

The individual symbols stand for the following sizes:

• The temperature of the hotter wall surface
• The temperature of the colder wall surface
• The area through which heat flows,
• The thermal conductivity, usually temperature-dependent material size, and
• The thickness of the body, measured from wall to wall.

The transferred heat power is therefore

• Proportional to surface, thermal conductivity and temperature difference
• Inversely proportional to the thickness of the material

From today's perspective, the heat transport is described by the sharper concept of heat flow density. The approaches to go back to Fourier and Newton. It applies the following definition:

Mathematically, described the phenomenon of " heat pipe " by a partial differential equation. She has a parabolic characteristic. In its general form, this partial differential equation can be given in the following form.

Specializing this equation to the so-called heat equation, must be restrictive noted that this form of heat conduction equation is valid only for homogeneous, isotropic media. So just for media everywhere have the same composition and no preferential orientation have ( at preferential orientations occurs, for example, fibers in composite materials, but also by so-called grain dilations in rolled sheets, etc.). In these cases - and only these - to the material properties of the medium under consideration are assumed to be dependent only on the temperature of sizes. Strictly speaking, the so- formulated equation applies only when no heat is due to foreign effects in the considered body introduced or removed from it. If this is the case, a so-called source term should be added. Under these restrictions then apply the following form of the heat equation:

The differential equation generally describes transport processes (such as diffusion processes - by which is meant a material transport due to a concentration difference, or in the case of the heat equation just a " wandering" of the temperature distribution in a body due to a temperature gradient ). The analytical solution to this equation is not possible in many cases. Today, we calculated technically relevant Wärmeleitaufgaben using the finite element method. As a result, we know the temporal and spatial temperature distribution (temperature field). Thus one can, for example, close to the spatial expansion behavior of the components, which in its turn influenced the local stress state. Thus, the temperature field calculation is an important foundation for all engineering design tasks in which the thermal component stress can not be neglected.

In inhomogeneous media with heat sources, the heat conduction equation is

Wherein the nabla operator, the bulk density, the specific heat capacity, thermal conductivity and the volume per introduced by external or internal source of heat flux.

Calculation method of stationary Wärmeleitvorgängen means of positive coefficients

In bodies, constant thermal conditions on their surfaces first type ( surface temperature), 2nd type ( heat flux ) or type 3 ( fluid temperature and heat transfer coefficient ) are present, form usually very complicated temperature fields. In special cases, these can be calculated analytically by solving the Laplace differential equation. In general, however, numeric working simulation models can be used. With knowledge of the temperature field and the heat flux can be determined. In many cases, the users are interested in any case only the self-adjusting to the body surface heat fluxes and / or the temperatures at specific locations within the solid. If such a body had been with the adjacent thermal conditions for such states among themselves which are not linear combinations studied, we can conclude determine a shape coefficient matrix. With its unique and specific matrix of coefficients, the heat flows can then be determined on the surfaces and selected local temperatures within the solid, for example, variable surface or adjacent fluid temperatures or for imprinted heat fluxes with simple spreadsheet programs.

Mechanisms

Dielectric Solids

In dielectric solids ( insulators ), the heat conduction is only through lattice vibrations, the phonons. The motion of the atoms is thus forwarded mechanically to the neighbors. All electrons are bound to atoms and can therefore not contribute to heat conduction.

Electrically conductive solid

In electrically conductive bodies such as metals, electrons can also transport heat. In metals predominates even heat conduction through electrons. This relationship leads to the Wiedemann -Franz 's law. Good electrical conductor such as copper transfer heat therefore better than poor electrical conductors such as iron.

Liquids and Gases

In liquids and gases, heat conduction is dominated by collisions between particles takes as long as not by differences in density or external mixing of the convection. The heat conduction in gas does not depend on the pressure, as long as the mean free path of the particles is small relative to the dimensions of the vessel. However, if the mean free path is limited by a vessel (eg thermos wall or by microporous materials with pore diameters in the nanometer range ), the thermal conductivity is directly proportional to the pressure. This effect make vacuum insulation panels advantage.

Light atoms or molecules conduct better than heavy. In contrast to the convection formed when pure thermal diffusion in liquids and gases whirls.

In general, gases are considered poor conductors of heat. The thermal conductivity of liquids is generally about one order of magnitude higher than that of gases. As an example of thermal conductivity at a pulp temperature of 20 ° C in W / (m · K ) ( detailed table can be found in the article to the thermal conductivity ).

Superfluid

In Supra fluids, the heat transfer is not carried out as usual by diffusion, but by temperature pulses with wave character. This effect is called the second sound.

Examples

• With a radiator, heat pipe or immersion heater, the heat energy from the hot interior passes by conduction through the housing to the outside.
• With a soldering iron a highly conductive metal such as copper to transmit the heat energy must be installed between the heating element and tip. Other metals such as iron do not conduct heat well enough.
• The total drive power of the external source of heat by means of heat conduction transfer to the working fluid in the cylinder chamber - in which the Stirling engine and Stirling engine must - in contrast to the gasoline engine. The thermal conductivity of the materials used is limited, the maximum achievable performance of the Stirling engine.
• Refrigerators are coated with glass wool or foamed polystyrene to maintain the flow of heat from the outside as small as possible.
• In a thermos flask or a vacuum tube collector for solar systems, inter alia, vacuum is used to prevent convection and conduction.
• In windows you can only use insulating glass with a very low heat transfer coefficient in order to meet the requirements of the Energy Conservation Act, and thus to keep the heating bills low.