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.

Extending the surface of a body in contact with a fluid can enhance heat transfer in convection. Extended surfaces in practice often consist of small–cross section solids that protrude from the main body, such as fins attached to the walls of heat transfer equipment. The main reasons for using fins to enhance the heat transfer rate are (1) to increase the heat transfer surface area, (2) to break up the boundary layer of the flow, and (3) to increase the turbulence as flow passes over or across the fins.

It is common practice to use brackets, heat sinks, and circuit boards for mounting components that are to be cooled by conduction. The primary heat transfer mode inside a component is also heat conduction. Cooling by conduction often requires the transfer of heat across various materials and interfaces that may be laminated, bolted, riveted, clamped, or bonded together. A high temperature gradient may occur if a large amount of heat is transferred across these interfaces.

Industry uses water throughout the energy supply chains. The purpose and scope of this book is to describe water for the cooling needs of thermoelectric, or steam cycle, power plants. The book focuses on engineering fundamentals along with environmental and economic contexts. Water is an excellent heat transfer medium, and it has historically been abundant and cheap. Thus, thermoelectric , or thermal or steam-electric , power plant cooling needs are usually served by withdrawing and consuming fresh and saline water. Thermal power plants do not have to use water for cooling, but if the desired quantities of water are available, then water-cooling systems are the most economic.

The equations of fluid motion and accompanying boundary conditions are difficult to formulate and solve. For most practical problems, the equations and accompanying boundary conditions must be numerically solved. The types of numerical methods used by the majority of researchers and applications oriented engineers to solve these partial differential equations fall into three categories: 1) finite difference (or finite volume) methods (FDM), 2) finite element methods (FEM), and 3) other approaches (boundary integrals, hybrids, analytical, spectral, etc.). The FDM has been used for a wide variety of problems; nearly all of the early numerical simulations dealing with heat transfer and fluid flow revolved around various solution strategies for the FDM.

In this first section of the book, we have introduced the concept of numerical approximations using the finite element method. We started with the simplest one-dimensional, linear, steady-state conduction problem, expanded the method to two- and three-dimensional elements, and ended with the time-dependent, nonlinear incompressible and compressible Navier Stokes and energy equations. Once the basic concepts are understood, the method can be readily applied to fluid dynamics, heat transfer, wave propagation, structural analysis, species transport, as well as a multitude of other transport related processes. Hopefully you now have an appreciation of the power and versatility of the finite element technique. You are now ready to move to the next section of this book that deals with the Boundary Element Method (BEM).

In this chapter we will consider specialized applications of the BEM in heat transfer. Specifically, we will consider application of heat transfer for axisymmetric problems, that lays down the groundwork for a very useful result in certain cases of heat conduction in nonhomogeneous media with linearly varying thermal conductivity as well as heat transfer in thin plates and extended surfaces that utilizes a fundamental solution that can be utilized in treating linear heat diffusion problems by the Laplace transform method. This is followed by a discussion of practical applications of the BEM to large-scale three dimensional problems and detailed treatment of domain decomposition methods is provided along with some industrial applications. Finally, utilization of the BEM is presented as a suitable field solver for inverse problems problems, and consideration is given to the solution of the inverse geometric problem for the detection of subsurface flaw and cavities.

A series of multi-disciplinary field problem applications are now presented to demonstrate the robustness and range of the LCMM. The formulation of the field problem solution approach as well as the implementation on a variety of relevant problems is presented. Field problems ranging from Incompressible Fluid Flows, Conjugate Heat Transfer, Natural Convection, Turbulent Flows, Compressible Flows, Supersonic Flows, Solid Mechanics, Fluid-Structure Interaction, Two-Phase Flow, and Poro-Elasticity are among those discussed herein and applied to situations involving realistic problems in turbomachinery and bioengineering cases.

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.

Trends of dimensionless in-cylinder heat transfer parameters for single cylinder spark ignition port injection hydrogen fueled engine was investigated through simulation, while the experimental data utilized for validation purpose of the adopted numerical model. One-dimensional gas dynamics was used to describe the flow and heat transfer in the components of the engine model. The engine model is simulated with a variable engine speed and equivalence ratio (φ). Simulation has been executed for 1000 ≤ speed ≤ 6000 rpm rpm and 0.2 ≤ φ ≤ 1.2 . The baseline engine model with gasoline fuel has been verified with experimental data, and reasonable agreement has been achieved. Noticeable impacts for the engine speed and equivalence ratio on the overall heat transfer characteristics have been revealed. The dependency of dimensionless heat transfer parameters on the equivalence ratio strongly exists in case of hydrogen fueled engine, as well as the engine speed impact.