Condensation is the phenomenon of vapor changing to liquid. There are two basic modes of condensation, namely, film condensation and dropwise condensation. During film condensation, vapor condenses in the form of a continuous liquid film over the condensing surface. During dropwise condensation, vapor condenses in the form of drops covering parts of the surface. Heat transfer coefficients during dropwise condensation are much higher than those during film condensation. Hence dropwise condensation is desirable. However, most common fluids condense in the film mode over ordinary metallic surfaces. Most of the condensers used in the industry today operate with film condensation. The mechanism of film condensation is well understood, and the rate of heat transfer during film condensation can be predicted with reasonable accuracy in most cases. Much research has been and is being done to develop durable heat exchangers with dropwise condensers but has not yet achieved success.

The various regimes in pool boiling were discussed in Section 3.1 and shown in Figure 3.1.1. The regimes in flow boiling are basically the same. In a surface temperature-controlled system, critical heat flux (CHF) is followed by transition boiling in which heat flux decreases with increasing wall temperature. This continues until the minimum film boiling temperature (MFBT) is reached. With further increase in wall temperature, film boiling starts during which heat flux increases with increasing wall temperature. In a heat flux-controlled system, film boiling starts immediately after CHF, and thus there is no transition boiling.

Heat transfer to mixtures of permanent gases with liquid flowing in tubes/pipes is frequently encountered in petroleum, nuclear power, chemical, food, and pharmaceutical industries. Injection of gas into liquid is also used for enhancing heat transfer. Hence prediction of heat transfer for such applications is of considerable practical importance. Topics discussed in this chapter include heat transfer during flow of pre-mixed gas–liquid mixtures inside channels as well as heat transfer with gas injected through the surface of tubes. Also discussed are cooling of objects of various shapes by mist cooling, cooling by jets, effects of gravity, and evaporation from water pools. Sections 8.2–8.6 discuss only non-metallic fluids. Liquid metal–gas mixtures are considered in Section 8.7.

Graphene is a two-dimensional (2D) material with the thickness of one single atom. This material is a carbon allotrope with nanostructure lattice of hexagonally arranged carbon atoms [1]. Due to the particular shape of graphene, it has an extraordinary thermal conductivity which has been reported to be up to 3000 W/(m⋅K) [2, 3] and 5300 W/(m⋅K) [4] while thermal conductivities of polymers are usually less than 1W/(m⋅K). This huge difference between thermal conductivities of graphene and polymers, introduces graphene as a highly efficient filler to significantly enhance the thermal conductivity of polymers [4, 5]. In the calculation of thermal conductivity of such nanocomposite materials, agglomeration formation and polymer–graphene interfacial thermal resistance are two significant parameters which can restrict the improvement of thermal behavior [6, 7].However, the dispersion of nanofillers based on functionally graded (FG) patterns in the host matrix usually improves the overall thermal and mechanical performances of nanocomposite materials. Moreover, FG dispersions of nanofillers provide a better management on the thermomechanical responses of nanocomposite structures [8–13].

In this chapter, radiant heating of spherical balls with different radii will be analyzed. A spherical ball (1) will be placed inside at the center of a spherical oven (2) which has a temperature controlled inner surface for infrared radiant heating. The spherical ball is heated by radiation in a vacuum environment, namely there is no convection heat transfer at the surface of the spherical ball. See Figure 15-1.

In the cooling of electronic equipment, liquid cooling is frequently applied to high power electronic equipment because of its high heat transfer capability. Liquid cooling can further be divided into single- and two-phase flow systems. The latter involves phase change processes such as boiling or condensation that greatly increases the heat transfer capability by utilization of the latent heat. In addition, the phase change process takes place at the constant temperature for a given pressure.

In order to better understand heat transfer from chip junctions (heat sources) to the ambient or coolant, one must have a clear picture of the construction of the chip packages. This chapter is to review the detailed chip packaging technology and other level packages of electronic equipment so that the heat transfer paths from the chip junctions to the ambient or liquid coolant and other surrounding structures of the system can be clearly identified. Then proper heat transfer schemes or technologies can be employed to every level of the system thermal design.

This chapter is to review variety of two phase heat transfer devices though the main focus will be at the heat pipes. All other de-vices are the derivatives products of the heat pipe, and hence all of them operate at the same principle. The heat transfer process of these devices involves the change of phase of working fluids. The advantages of two-phase boiling heat transfer over single phase flow are as follows: a) Extremely high heat transfer capability by utilization of the latent heat (heat of vaporization) of the fluids b) Uniform temperature distribution over heated devices because of the phase change taking place at a constant temperature for a given system pressure. Because of this unique feature, it can maintain the device at the constant temperature with various device heat loads (power) c) Quick thermal response d) Compact and light weight as compared with single phase heat transfer devices

In the cooling of electronic equipment, liquid cooling is frequently applied to high power electronic equipment because of its high heat transfer capability. Liquid cooling can further be divided into single- and two-phase flow systems. The latter involves phase change processes such as boiling or condensation that greatly increases the heat transfer capability by utilization of the latent heat of fluids. In addition, the phase change process takes place at the constant temperature under a given pressure.

So far we have only considered energy interactions between rays and surfaces. Two possible outcomes – absorption and reflection – have been identified, and corresponding models have been formulated and used to describe radiation heat transfer among surfaces. When a ray incident to a surface is neither absorbed nor reflected, it is said to be transmitted. Thermal radiation passing through lenses, filters, and the earth’s atmosphere are familiar examples of transmission. This chapter deals with emission, absorption, refraction, and scattering of thermal radiation within a medium through which it is propagating. Such media are said to be “participating.”

The subject of heat transfer is of fundamental importance in many branches of engineering. A mechanical engineer may be interested in knowing the mechanisms of heat transfer involved in the operation of equipment, such as boilers, condensers, air preheaters and economizers, and in thermal power plants, in order to improve performance. Refrigeration and air-conditioning systems also involve heat-exchanging devices, which need careful design. Electrical engineers are keen to avoid material damage due to hot spots, developed by improper heat transfer design in electric motors, generators and transformers. An electronic engineer is interested in knowing the most efficient methods of heat dissipation from chips and other semiconductor devices so that they can operate within safe operating temperatures. A computer hardware engineer wants to know the cooling requirements of circuit boards, as the miniaturization of computing devices is advancing rapidly. Chemical engineers are interested in heat transfer processes in various chemical reactions. A metallurgical engineer may need to know the rate of heat transfer required for a particular heat treatment process, such as the rate of cooling in a casting process, as this has a profound influence on the quality of the final product. Aeronautical engineers are interested in knowing the heat transfer rate in electronic equipment that uses compact heat exchangers for minimizing weight, in rocket nozzles and in heat shields used in re-entry vehicles. An agricultural engineer would be interested in the drying of food grains, food processing and preservation. Civil engineers need to be aware of the thermal stresses developed in quick-setting concrete, and the effect of heat and mass transfer on buildings and building materials. Finally, an environmental engineer is concerned with the effect of heat on the dispersion of pollutants in air, diffusion of pollutants in soils, thermal pollution in lakes and seas and their impact on life.

As it follows from the above discussion, the domain of any conjugate problem consists at least of two subdomains according to the interaction components. Therefore, to formulate conjugate problem, it is necessary to specify two sets of equations: initial and boundary conditions governing the problem in each of subdomains in order to further conjugation of the corresponding solutions.

In this section, we investigate the effect of different factors on conjugate heat transfer intensity considering the conjugate problem as a case of heat transfer from a surface with variable (nonisothermal) temperature or heat flux. Such an approach is founded on the conception (see Introduction) that a variable temperature (or temperature head) of a body/fluid interface is one of the basic characteristics of any conjugate problem. The results are obtained analyzing universal functions and are supplemented with relevant examples.

In the next two chapters, the applications of conjugate heat transfer problems are considered. First in Chapter 3, generally, without concrete usage, the flows past plates, around the bodies (external flows), and inside the channels and tubes (internal flows) are analyzed. Then in Chapter 4, the specific applications of conjugate heat transfer problems in industrial and technology areas are discussed. Analysis of examples include problem formulation and models as a basis of equations, short description of solution, and the most important results. An interested reader may get more detailed information using cited original papers. Besides analyzing examples, other related publications are shortly reviewed to give the reader extended knowledge of specific literature.

In this chapter, the examples are considered shortly as well as the conjugate solutions are discussed in the second part of third chapter, beginning from Section 3.2. Some of the examples might demand additional physical and mathematical information that one could get from the third part of the textbook. The author hopes that this knowledge is enough to understand the majority of presented solutions, otherwise, any course of Advanced Engineering Mathematics that consists of extra theory and exercises will do. For additional information of fluid flow and heat transfer, a reader is referred to Schlichting’s book “Boundary Layer Theory” and for more specific knowledge of turbulent flow to Wilcox’s monograph “Turbulence Modeling for CFD”.

The mathematical models describing the transfer processes are based on the system of the Navier-Stokes equations for momentum transfer and similar equations for energy and mass transfer. These equations are conservation laws expressed in terms of the velocity components, temperature, and concentration. For incompressible fluid flows with constant properties, these expressions are given by equations 1.4–1.8 (without dissipation function S ) from Chapter 1 supplemented by equation for mass transfer similar to energy equation, where C is dimension-less concentration and ρD m is the coefficient similar to μ .

Laminar flow exists only at relatively small Reynolds numbers. As the Reynolds number increases, the laminar regime of flow transients in turbulent flow. The laminar flow is well organized so that it looks like thin parallel layers (lamina in Greek means plate or layer) of fluid move unmixed along a pipe or a plate. In contrast to that, the mixing process inside a fluid leading to homogeneous disturbed medium is one of the basic characteristics of turbulent flow. The patterns of these two regimes were first observed by Reynolds in the nineteenth century, who put the dye inside the flow to make it visible. He was also the first to understand that there exists a universal dimensionless number (now known as critical Reynolds number) at which the transition occurs. The critical Reynolds numbers experimentally determined for flows in a circular section pipe and past a plate are: Re cr = ûD / v = 2300 and Re cr = Ux / v = 3.5 · 10 5 ÷ 10 6 , where û is an average velocity in a pipe. The value of critical Reynolds number depends on the conditions outside of a pipe or a body and increases as the level of disturbances in the inlet flow decreases. The just indicated critical Reynolds numbers correspond to usually disturbed environment, whereas in the experiments when the disturbance in the inlet flow was reduced, the flow in a pipe remained laminar up to Reynolds number 40000. At the same time at Reynolds numbers less than 2000, the flow in a pipe remains laminar independent of the level of inlet disturbances because these are dissipated by viscosity in flows with smaller than critical Reynolds numbers.

This chapter presents the mathematical methods frequently applied in applications. Although the reviewed methods are general, the following examples are mainly the problems of heat transfer in solids. That is because the other two topics laminar and turbulent fluid flow and heat transfer important for studying the basic text are considered with examples in previous chapters of this part of the book. As well as in previous chapters, here, the information from basic text is not repeated, rather at advising the additional explanations a reader is referred to the relevant basic text sections.

The foregoing chapters have focused mainly on the thermal considerations of geothermal energy systems. The focus of this chapter is hydraulic considerations of moving the heat transfer fluid from the geothermal resource to the point of use.

Another mechanism of heat transfer in addition to conduction and convection is radiative heat transfer, which involves the transport of thermal energy by electromagnetic waves. Since the application of thermal radiation to electronic equipment generally occurs in a relatively simple form, this chapter will be limited to basic knowledge of thermal radiation.