Publisher Summary The chapter presents an overview of the background information needed to formulate and analyze heat transfer in semitransparent materials systematically and then reviews the literature in some specific problem areas Primary emphasis is placed on semitransparent solids, although the principles presented are general and apply to any phase The chapter also discusses the wide variety of applications and involves nature of heat transfer phenomena in semitransparent condensed phases The radiation characteristics of semitransparent materials are not only dependent on surface but also volume phenomenon since some of the emitted radiation originates at considerable depths In short, the radiation characteristics depend on the spectral absorption coefficient and index of refraction, thickness, boundary conditions, and temperature distribution The transient heating of semitransparent materials under idealized conditions in which the emission of radiation from the material is neglected is also discussed This implies that the body is cold and the rate of emission of radiation per unit volume is negligible compared to absorption This simplification limits the applicability of analysis and results to those early stages of heating during which temperatures have not raised high enough to render the assumption invalid The chapter also presents an analysis to show the influence of physical parameters on the temperature field in a semitransparent solid irradiated from a high temperature source such as the sun The results intend to aid the designer of solar collectors in selecting the optimum material by indicating physical parameters, which determine maximum efficiency of solar energy conversion in different semitransparent solids

Heat Transfer in Semitransparent Solids

A mathematical analysis of coupled heat transfer and natural convection in an all-electric glass furnace was conducted using a two-dimensional computer model. The model simulated numerically the complex interactions which occur among energy, mass, and momentum transfer in a vertical plane section through the melter. Computer-generated isotherm and streamline contour maps are presented for each of twelve different cases of vertical and horizontal rod-electrode pair configurations on the centerline section of a hypothetical all-electric glass furnace. The total electrical power consumption was held constant in all cases to establish a basis for comparison of the results. It is shown that both the temperature distribution and the circulation flow pattern in a glass melt can be markedly influenced by the power density distributions associated with electrodes of different length and orientation.

Use of Mathematical Modeling in Determining the Effects of Electrode Configuration on Convection Currents in an Electric Glass Melter

Chemical engineering problems of radioactive waste fixation by vitrification

The diffusion and P1 approximations for modeling buoyant flow of an optically thick fluid

A quantitative mathematical analysis of coupled electrical power dissipation, heat transfer, and natural convection in a hypothetical all-electric glass tank furnace was conducted using a two-dimensional computer model. The model simulated numerically the complex interactions which occur among charge, mass, energy, and momentum transport in a vertical plane section through the melter. Computer generated contour plots of the power density, isotherms, and stream-lines in the rectangular enclosure are presented for both a flint glass and an amber glass, each with and without the variation of electrical resistivity with temperature taken into account. The total electrical power consumption was held constant in all cases investigated in order to establish a common basis for comparison of the results. It is shown that although the variation in melt resistivity, associated with the range of temperatures encountered in the interior of the hypothetical glass furnace, approaches 10 percent of the mean isothermal value, it has subsequently very little effect on the calculated temperature and velocity distribution within the enclosure over a wide range of effective thermal conductivities. Hence the electrical resistivity can be assumed consistent for all practical purposes when these are the results of primary interest. It is also shown that the electric melting behavior of colored glasses may be quite different from that of a flint glass under the same basic furnace operating conditions.

Mathematical Model of an Electric Glass Furnace: Effects of Glass Color and Resistivity

Natural convection currents in a rectangular two-dimensional enclosure representative of the longitudinal section of an industrial glass-melting furnace have been established by both model experiments and numerical calculation. For the latter a finite-difference method has been employed to solve the time-dependent coupled flow and energy equations. The highly generalized mathematical model makes allowance for buoyancy, temperature-dependent viscosity, and diffusive radiation. Generalized boundary conditions are employed to permit specification of any combination of temperature, flux, or mixed thermal boundary conditions. Representative temperature and flow contour maps obtained from the calculations are shown to agree well with experimental results obtained with a 1/20 scale model in which glycerine was employed as the modeling fluid.

Mathematical and Experimental Modeling of the Circulation Patterns in Glass Melts

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Mathematical and Experimental Modeling of the Circulation Patterns in Glass Melts