Translate the following attributive constructions.

cross-sectional area, conduction equation, one-dimensional heat flow, conductor thickness, heat propagation,predominant transport mechanism, density gradients, conduction-band electrons, thermal potential difference.

Group the words into pairs of antonyms.

Decrease, solid, external, motion, more, rapid, elastic, high, microscopic, liquid, macroscopic, less, slow, inelastic, low, stagnation, internal, increase.

Group the words into pairs of synonyms.

Occur, similar, begin, simple, different, rarely, rapidly, seldom, easy, to take place, start, same, quickly, various.

Look through the text and say what you know about Fourier’s law of heat conduction. What kind of materials are called insulators? Can you give your own examples of heat conduction processes in different branches of engineering? Share your opinion with your fellow students.

Text 2 B

Heat Conduction

 The most efficient method of heat transfer is conduction. This mode of heat transfer occurs when there is a temperature gradient across a body. In this case, the energy is transferred from a high temperature region to low temperature region due to random molecular motion (diffusion). Heat flows through a solid by a process that is called thermal diffusion, or simply diffusion or conduction. In this mode, heat is transferred through a complex submicroscopic mechanism in which atoms interact by elastic and inelastic collisions to propagate the energy from regions of higher to regions of lower temperature. From an engineering point of view there is no need to delve into the complexities of the molecular mechanisms, because the rate of heat propagation can be predicted by Fourier’s law, which incorporates the mechanistic features of the process into a physical property known as the thermal conductivity.

Conduction occurs similarly in liquids and gases. Althoughconduction occurs in liquids and gases, it is rarely the predominant transport mechanism in fluids — once heat begins to flow in a fluid, even if no external force is applied, density gradients are set up and convective currents are set in motion. In convection, thermal energy is thus transported on a macroscopic scale as well as on a microscopic scale, and convection currents are generally more effective in transporting heat than conduction alone, where the motion is limited to submicroscopic transport of energy.

Regions with greater molecular kinetic energy will pass their thermal energy to regions with less molecular energy through direct molecular collisions. In metals, a significant portion of the transported thermal energy is also carried by conduction-band electrons. Different materials have varying abilities to conduct heat. Materials that conduct heat poorly (wood, styrofoam- пенополистирол) are often called insulators. However, materials that conduct heat well (metals, glass, some plastics) have no special name.

The simplest conduction heat transfer can be described as “one-dimensional heat flow”. The rate of heat flow from one side of an object to the other, or between objects that touch, depends on the cross-sectional area of flow, the conductivity of the material and the temperature difference between the two surfaces or objects.

Mathematically, it can be expressed as

 

where q is the heat transfer rate in watts (W), k is the thermal conductivity of the material (W/m.K), A is the cross-sectional area of heat path, and is the temperature gradient in the direction of the flow (K/m).

The above equation is known as Fourier’s law of heat conduction. Therefore, the heat transfer rate by conduction through the object can be expressed as

 

where L is the conductor thickness (or length), ∆ T is the temperature difference between one side and the other (for example, ∆ T = T ₁ – T₂ is the temperature difference between side 1 and side 2). The quantity (∆T/L) in equation is called the temperature gradient: it tells how many 0C or K the temperature changes per unit of distance moved along the path of heat flow. The quantity L/kA is called the thermal resistance.

 

Thermal resistance has SI units of kelvins per watt (K/W). Notice that the thermal resistance depends on the nature of the material (thermal conductivity k and geometry of the body d/A). From the above equations we realize the heat transfer rate as a flow, and the combination of thermal conductivity, thickness of material and area as a resistance to this flow.

Considering the temperature as a potential function of the heat flow, the Fourier law can be written as

 

If we define the resistance as the ratio of potential to the corresponding transfer rate, the thermal resistance for conduction can be expressed as

 

It is clear from the above equation that decreasing the thickness or increasing the cross-sectional area or thermal conductivity of an object will decrease its thermal resistance and increase its heat transfer rate.

Conduction heat transfer can readily be modeled and described mathematically. The associated governing physical relations are partialdifferential equations, which are susceptible to solution by classical methods. Famous mathematicians, including Laplace and Fourier, spent part of their lives seeking and tabulating useful solutions to heat conduction problems. However, the analytic approach to conduction is limited to relatively simple geometric shapes and to boundary conditions that can only approximatethe situation in realistic engineering problems. With the advent of the high-speed computer, the situation changed dramatically and a revolution occurred in the field of conduction heat transfer. The computer made it possible to solve, with relative ease, complex problems that closely approximate real conditions.

As a result, the analytic approach has nearly disappeared from the engineering scene. The analytic approach is nevertheless important as background.