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This book presents the theory of periodic conjugate heat transfer in a detailed way. The effects of thermophysical properties and geometry of a solid body on the commonly used and experimentally determined heat transfer coefficient are analytically presented from a general point of view. The main objective of the book is a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation for the solid body. At the body surface, the true heat transfer coefficient is composed of two parts: the true mean value resulting from the solution of the steady state heat transfer problem and a periodically variable part, the periodic time and length to describe the oscillatory hydrodynamic effects. The second edition is extended by (i) the analysis of stability boundaries in helium flow at supercritical conditions in a heated channel with respect to the interaction between a solid body and a fluid; (ii) a periodic model and a method of heat transfer simulation in a fluid at supercritical pressure and (iii) a periodic quantum-mechanical model for homogeneous vapor nucleation in a fluid with respect to nanoscale effects

This chapter occupies a particular place in the book, whose title itself indicates an involvement in heat transfer problems of the conjugate convective–conductive nature. Unlike the first eight chapters, the ninth chapter is concentrated exclusively on nonconjugate periodic heat transfer. Thus, the aspect of conjugation “fluid–solid body” falls out of the topic of this chapter. The objective of the ninth chapter consists in modeling of heat transfer on the basis of an analysis of periodic internal structure of near-wall turbulence. The author deemed justifiable to make the following excursus. The model of thermohydraulic pulsations in helium flow considered in Chap. 8 means knowledge of intensity of heat transfer between the wall and turbulent flow. The thermophysical properties of helium in the area of supercritical pressures (SCP) exhibit rather complicated and even to a certain extent freakish character of variation. The second reason, which caused the author to recede from the analysis of conjugate problems, is pulsatory character of turbulent heat transfer by its very nature. The tempting possibility to undertake an approximate description of turbulent heat transfer in the area of SCP on the basis of a simple periodic model was a decisive argument to write the present chapter.

Numerous studies were devoted to the investigation of hydrodynamics and heat transfer in a close-packed fixed layer of pebbles (pebble bed), the results of such studies were generalized, in particular, in the monographs.

According to (Morel in Mathematical modeling of disperse two-phase flow. Springer, 2015), the distribution of spherical liquid droplets dispersed in a vapor flow significantly affects the characteristics of heat transport in a dispersed two-phase flow.

Let us carry out an analytical consideration of a boundary value problem for the two-dimensional transient heat conduction equation [1, 2, 3, 4]. An object of research is a flat plate of the thickness δ, 2.1. In accordance with the basic idea of the present research, on an internal surface of a plate (X=δ), a boundary condition (BC) of the third kind is used at the surface: $$h(z,\tau ) = h(\xi ).$$ (2.1)

In order to illustrate the influence of thermophysical properties of a solid body on the experimental heat transfer coefficient (EHTC) under conditions where heat transfer intensity is subjected to periodic oscillations, a special model experiment has been designed and carried out. Its purpose was to determine a dependence of the function \(\epsilon (\langle \tilde{h}\rangle )\) for a semi-infinite body under conditions of a time-dependent problem. This dependence has been theoretically computed in (3.56) and shown in Fig. 3.10. The basic element of the experimental rig (Fig. 7.1) was a long brass electrically heated rod (1) thermally insulated on its lateral cylindrical surface, with the end face being periodically washed with a colder water jet from the nozzles (2) of various diameters.

The problem of vapor condensation upon transversal flow around a horizontal cylinder is considered. The analytical solutions for the “boundary heat-exchange laws” are obtained. The solutions show the dependence of the heat transfer coefficient on the corresponding factor (gravity, interfacial friction, longitudinal pressure gradient) under the assumption that there is no effect of other factors. The boundary laws obtained for moving vapor are shown to depend on pressure in the same manner, while the temperature differential has different effects in specified asymptotics. The theoretical results obtained are used for qualitative analysis of the available experimental data.

Results from a research work on studying the effect of steam velocity on heat transfer during steam condensation on the surface of a horizontal cylinder are presented. An approximate model of interphase friction is proposed, using which the heat-transfer coefficients averaged over the cylinder surface are calculated. The calculation results are compared with the available experimental data obtained in a wide variation range of velocities and pressures.

An experimental investigation is performed of heat transfer under conditions of longitudinal flow of water moving in a bed of glass pebbles past a flat heated wall. Experiments involving the flow of single-phase liquid are performed in the ranges of variation of filtration velocities from 6 to 60 mm/s and of heat fluxes from 40 to 140 kW/m2; in the case of wall boiling, the experiments are performed in the ranges of variation of filtration velocities from 2 to 50 mm/s and of heat fluxes from 27 to 86 kW/m2. The temperature distribution is measured over the height of the heated wall and over the cross section (depth) of the channel at the outlet from the pebble bed. The experimental data are processed for single-phase flow using numerical optimization techniques. The values of the coefficient of “turbulent” thermal conductivity in the pebble bed are obtained as a function of the process parameters

A generalized inertial thermal model for the vapor bubble growth in an infinite volume of uniformly superheated liquid is developed. An approximate analytical solution to the problem is obtained. The solution provides exact asymptotic limiting processes over all defining problem parameters. The physically correct description of experimental data related to vapor bubble growth in the near-spinodal region, which were previously considered as paradoxical, is presented for the first time.

This work presents a proof of the inequality that determines the relation between two values of the heat-transfer coefficient averaged by different procedures in processes of heat exchange with periodic intensity.

A previously developed method of analysis of the processes of heat transfer with periodic intensity is generalized to the case of simultaneous fluctuations of the temperatures of the wall and the liquid. A final expression for the dependence of the coefficient of conjugation on the generalized parameter of the problem is obtained.

The limit of the stability of a heat carrier flow against small “density wave”-type perturbations is found. It is shown that stabilization of flow sets in on increase in the volume heat capacity and also in the amplitude of the heat-transfer coefficient fluctuations.

A method for solving a conjugate periodic convective-conductive problem for a "heat-transfer agent-wall" developed earlier system is used for calculation of the effect of the wall parameters on heat transfer under conditions of jet wetting.

Using an approximate method of analysis developed earlier for studying heat-exchange processes occurring with a periodic intensity, the problem of periodic evaporation of a liquid film from the surface of a heat-transfer wall is considered.

On the basis of an approximate analysis of flow in a liquid macrofilm on a heating surface the characteristics of nucleate boiling (surface density of nucleation sites, effect of the thermal conductivity of the wall on the averaged heat transfer) are estimated.

Using an analog of a Rayleigh equation the limiting law of vapor-bubble growth in a tube in coolant boiling in the region of very low pressures is obtained.

Processes of heat transfer with periodically varying intensity on the surface of heated bodies of three typical geometries (plate, cylinder, sphere) are considered. The true heat transfer coefficient, which varies in time by the law of a periodic step function having two free parameters - amplitude and asymmetry, is specified on the heat transfer surface. Resultant relations are obtained for calculating the experimental heat transfer coefficient, which is the quantity measured in a traditional heat transfer experiment and used in applied calculations.

Three basic characteristic functions ψ(ξ) investigated in Chap. 3 (harmonic, inverse harmonic, and symmetric stepwise) are single parametrical in the sense that their form is unequivocally characterized by the relative amplitude of oscillations b. An essential expansion of the class of the periodic conjugate problems can be achieved via prescribing an asymmetric step function ψ(ξ) (Fig. 6.1) $${h}_{\mathrm{m}} = \left \langle h\right \rangle \epsilon = {h}_{+}s\epsilon.$$ (6.1)

A simple method for calculation of heat transfer in transient boiling of liquids on a wall with a finite “coefficient of thermal activity≓ is suggested on the basis of model concepts available in the literature and also by an earlier developed method for analysis of processes.