Heat conduction in a semi-infinite solid when subjected to spatially decaying instantaneous laser source

A closed-form model for the computation of temperature and heat flux distribution in a semi-infinite solid when subjected to spatially decaying, instantaneous laser source is investigated. The appropriate dimensionless parameters are identified and the reduced temperature and heat flux as a function of these parameters are presented in the graphic form. Some special cases of practical interest are also discussed. It is demonstrated that the present analysis covers the classical case of no heat generation in the solid as well as some new solutions.

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Wärmeleitung in einem halbunendlichen Körper, der plötzlich durch eine mit zunehmender Eindringtiefe abklingende Laser-Wärmequelle beaufschlagt wird

Zusammenfassung Es wird ein geschlossenes Rechenmodell zur Ermittlung der Temperatur- und Wärmeflußverteilung in einem halbunendlichen Körper untersucht, der plötzlich durch eine mit der Eindringtiefe abklingende Laserquelle beaufschlagt wird. Die normierten Temperaturen und Wärmeflüsse sind als Funktionen relevanter Kenngrößen graphisch dargestellt. Spezialfälle von praktischem Interesse werden diskutiert. Die vorliegende Untersuchung liefert neben einigen neuen Lösungen auch das Ergebnis für den klassischen Fall, daß keine Wärmequellen wirksam sind.

     

Heat transfer in a vertically-layered porous medium heated from below

Some studies already made have investigated the criterion for onset of convection and heat and mass flow distributions in a porous slab composed of horizontal layers of different materials. This paper reports a study of such criteria for the case where the slab is composed of vertically-aligned strata with different permeabilities and thermal conductivities. This has particular relevance to where blocks of different materials abut in a vertical plane, as well as the case of very narrow highly permeable vertical layers which represent vertical faults in a geological structure. Results indicate that permeability and/or thermal conductivity contrasts between layers can significantly affect the flow pattern and the spatial distribution of the surface heat flux. The concentration of flow in highly permeable faults produces marked irregularities in the heat flow through the surface above them.     

Heat transfer in an unevenly heated porous layer

For a uniform saturated porous layer heated from below, the dependence of the quantity of heat transferred on the distribution of the heat source is investigated. It is found, using perturbation methods and numerical techniques, that very small nonuniformities in the heat source having the same wavelength as the preferred convection mode significantly reinforce natural convection.     

Heat transfer from a heated sphere in a rarefied gas at rest

We consider the problem of heat transfer from a slightly heated sphere in a resting rarefied gas. We assume that the Krook equation is valid in this case. Two forms of the basic equations are presented, and relations are given which are obtained as a result of calculations of the heat flux and the temperature jump at the sphere surface as a function of a parameter which is inversely proportional to the Knudsen number. The results obtained are compared with results given by the known approximate theories.In conclusion the author wishes to thank M. N. Kogan for proposing the problem and for numerous discussions.     

Heat transfer between a heated plate and an impinging transient diesel spray

An experimental investigation was performed to determine the heat-transfer distribution in the vicinity of a transient diesel spray impinging on a heated flat plate. The spray prior to impingement was characterised in terms of simultaneous droplet sizes and velocities by phase-Doppler anemometry while during its impingement on the plate, which was heated at temperatures between 150–205°C, the instantaneous surface temperature and associated rates of wall heat transfer were monitored by fast response thermocouples. The parameters examined in this work included the distance between the nozzle and the wall surface, the radial distance from the impingement point, the injection frequency, the injected volume and the pre-impingement wall temperature. The results showed that the wall heat transfer rates are dependent on the spray characteristics prior to impingement; the higher the velocity of arrival of the droplet is, the higher the heat transfer. A correlation was thus developed for the instantaneous and spatially-resolved spray/wall heat transfer based on experimentally-determined Nusselt, Reynolds, Prandtl and Weber numbers over a wide range of test conditions.     

Indentation of the semi-infinite elastic solid by a concave rigid punch

A solution is obtained for the relationship between load, displacement and inner contact radius for an axisymmetric, spherically concave, rigid punch, indenting an elastic half-space. Analytic approximations are developed for the limiting cases in which the ratio of the inner and outer radii of the annular contact region is respectively small and close to unity. These approximations overlap well at intermediate values. The same method is applied to the conically concave punch and to a punch with a central hole. , , . , . . .     

Heat conduction in a semi-infinite solid subject to time-dependent surface heat fluxes: an analytical study

A closed-form model for the computation of the transient temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The temperature and heat flux solutions are presented for time-dependent, surface-heat flux of the forms: (i) , (ii) , and (iii) , where is a real number and is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker function, the generalized representation of an incomplete Gamma functionI (b, x) which can also be expressed by the complementary error functions. It is also demonstrated that the present analysis covers some well known (classical) solutions as well as a family of new solutions for the heat transfer through a semi-infinite solid.

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Wärmeleitung in einem halbunendlichen Festkörper bei zeitveränderlichem Randwärmefluß: Eine analytische Untersuchung

Zusammenfassung Es wird ein geschlossenes Modell zur Berechnung der nichtstationären Temperatur- and Wärmestromverteilung für einen halbunendlichen Festkörper mit konstanten Stoffwerten untersucht. Die Lösungen für das Temperatur- und Wärmeflußfeld basieren auf folgenden Zeitgesetzen für den Randwärmefluß: (i) , (ii) , und (iii) wobei eine reelle Zahl und eine positive reelle Zahl ist. Die dimensionslosen Lösungen für das Temperatur- und Wärmflußfeld lassen sich in Form der Whittaker- Funktionen, der verallgemeinerten Darstellung einer unvollständigen Gamma-FunktionI (b, x) angeben, welche auch durch das komplementäre Fehlerintegral ausgedrückt werden kann. Es wird ferner gezeigt, daß die hier durchgeführte Untersuchung sowohl einige bekannte (klassische) Lösungen für die Wärmeleitung im halbunendlichen Festkörper liefert, wie auch eine Familie von neuen Lösungen.

     

Heat transfer from the heated concave wall of a return bend with rectangular cross section

The characteristics of the turbulent heat transfer along the heated concave walls of return bends which have rectangular cross sections with large aspect ratio have been examined for various clearances of the ducts in detail. The experiments are carried out under the condition that the concave walls are heated at constant heat flux while the convex walls are insulated. Water as the working fluid is utilized. Using three kinds of clearance of 9, 34, and 55 mm, the Reynolds number in the turbulent range are varied from 5×10³ to 8×10⁴ with the Prandtl numbers ranging from 4 to 13. As a result it is elucidated that both the mean and the local Nusselt numbers are always greater than those for the straight parallel plates or for the straight duct, respectively. This is attributed to Görtier vortices, which are visualized here. It is also found that the more the clearance increases, the more both the local and the mean Nusselt numbers increase. Correlation equations for the mean and the local Nusselt numbers are determined in the range of parameters covered. Introducing the Richardson number, it appears that the local Nusselt number,Nu _x , may be described as the following equation:Nu _x =447.745 ·Re _x ^1.497 ·De _x ^?1.596 ·F ^0.960 ·Pr ^0.412     

Heat transfer analysis of a particle-containing channel flow

This paper describes an analytical model of heat transfer in a two-dimensional, steady, nonreacting particle-containing channel flow. An idealized gas flow of specified uniform velocity between insulated parallel plates is assumed and the nonvaporizing particles are conceptualized as contained within an thin sheet injected at the symmetry plane. Two dimensionless parameters that affect the solution are described. These are the effective gas diffusivityK and the dimensionless particle number densityP. The linear, coupled differential equations governing the energy exchange between the gas and liquid phases are solved by means of the Green's function technique. This procedure yields a Volterra integral-series equation as the solution of the gas-phase energy equation. A series solution of this integral equation is obtained by the method of successive substitutions and terms up to second order are calculated.     

Heat transfer characteristics of internally heated liquid pools at high Rayleigh numbers

Detailed numerical analysis is presented for buoyancy driven flow of a Newtonian fluid contained in a square enclosure for high Rayleigh (Ra) numbers. Natural convection is due to internal heating sources, which are assumed to be uniformly distributed within the enclosure. All walls of the cavity are maintained at constant temperature. Flow and heat transfer characteristics are investigated for a Ra number range of 10⁷ to 10¹² while Prandtl (Pr) number is taken to be 7.0. Governing equations (in primitive variables) are discretised using control volume technique based on staggered grid formulation. These equations are solved using SIMPLER algorithm of Patankar. Flow and heat transfer characteristics, streamlines, isotherms and average wall Nusselt (Nu) number, are presented for whole range of Ra number considered. Finally, present results for average wall Nu numbers are compared with experimental observations obtained from open literature. It is concluded that both results are in very good agreement, which confirmed the accuracy of the scaling used for present investigation. Received on 15 November 1999     

Heat transfer characteristics of a vertical porous heat storage saturated by a liquid and spherical solid particles

A fundamental study on the transient characteristics of a vertical rectangular porous heat storage, which was composed of a fluid (liquid) and spherical solid particles, has been numerically carried out under one vertical wall exposed to a constantheat-flux condition while other walls thermally insulated. The present study has clarified the effects of the porosity, the heatflux as a receiving heat, thermophysical properties and the dimensions of the heat storage (aspect-ratioH/W, height to width of the rectangular cavity) on the transient characteristics of the porous heat storage proposed. It was concluded that the natural convection occurred in the heat storage had an important role in evaluating the transient heat transfer characteristics, that is, the convection occurred had contributed to shortening the time period until the quasi-steady state after starting the heating to the heat storage and to homogenizing thermally the porous heat storage. From the results obtained, it is possible to obtain optionally the time period until the quasi-steady state and the amount of the heat stored into or taken out from the porous heat storage proposed by selecting the proper combination of both phases and the dimension of the storage, in comparison with the single phase heat storage.     

Transient heat transfer between a perfect conductor with heat generated in it and a semi-infinite solid including a contact resistance

Analytical solutions are presented for heat conduction between a semi-infinite solid and a perfect conductor with internal heat generation, taking into account a thermal contact resistance at the interface.

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Nichtstationäre Wärmeübertragung zwischen einem idealen Leiter mit innerem Wärmeerzeuger und einem halbunendlichen Körper mit Kontakt wider stand

Zusammenfassung Es werden analytische Lösungen mitgeteilt für die Wärmeleitung zwischen einem halbunendlichen Körper und einem idealen Leiter mit innerer Wärmeerzeugung, wenn an der Grenzfläche ein thermischer Kontakt wider stand existiert.

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Nomenclature a constant 21 - b constant 21 - c kJ/kg K specific heat - H W/m² K heat-transfer coefficient - h m^–1 7 thermal conductivity of the solid - M kg/m² specific mass of the perfect conductor - Q W/m² energy input to the perfect conductor - q W/m² heat flux through the surface - p s^–1 Laplace variable - t s time - u K temperature of the perfect conductor - V K initial temperature - v K temperature of the solid - x m position - W/m²K overall heat transfer coefficient - energy flux 10 - capacity 11 - m²/s thermal diffusivity - time 14 - position 15 surfix + dimensionless variable - Laplace transformed variable     

Experimental analysis of the heat transfer in a cylindrical shell heated along a generator

Experimental Mechanics - An experimental program was conducted in order to determine the temperature profile in a cylindrical shell heated along two opposite generators. Many experimental tests...     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.