Showing papers in "Journal of Heat Transfer-transactions of The Asme in 1987"
TL;DR: In this paper, a modelisation of l'ecoulement dans la couche poreuse a l'aide de l'equation de Darcy et endue par Brinkman et Forchheimer is presented.
Abstract: Etude numerique et experimentale. Modelisation de l'ecoulement dans la couche poreuse a l'aide de l'equation de Darcy etendue par Brinkman et Forchheimer. Verification experimentale sur des ecoulements d'eau et de glycerine dans un milieu constitue de billes de verre
248 citations
TL;DR: In this article, the authors present a theoretical study of fully developed forced convection in a channel partially filled with a porous matrix, where the matrix is attached at the channel wall and extends inward, toward the centerline.
Abstract: This paper presents a theoretical study of fully developed forced convection in a channel partially filled with a porous matrix. The matrix is attached at the channel wall and extends inward, toward the centerline. Two channel configurations are investigated, namely, parallel plates and circular pipe. For each channel configuration, both the case of constant wall heat flux and constant wall temperature were studied. The main novel feature of this study is that it takes into account the flow inside the porous region and determines the effect of this flow on the heat exchange between the wall and the fluid in the channel. The Brinkman flow model which has been proven appropriate for flows in sparsely packed porous media and for flows near solid boundaries was used to model the flow inside the porous region. Important results of engineering interest were obtained and are reported in this paper. These results thoroughly document the dependence of the Nusselt number on several parameters of the problem. Of particular importance is the finding that the dependence of Nu on the thickness of the porous layer is not monotonic. A critical thickness exists at which the value of Nu reaches a minimum.
231 citations
TL;DR: In this paper, a control-volume-based finite difference procedure with appropriate averaging for the diffusion coefficients is used to solve the coupling between the solid and fluid regions, and the analysis is extended to study the optimum spacing between heat sources for a fixed heat input and a desired maximum temperature at the heat source.
Abstract: Conjugate heat transfer for two-dimensional, developing flow over an array of rectangular blocks, representing finite heat sources on parallel plates, is considered. Incompressible flow over multiple blocks is modeled using the fully elliptic form of the Navier-Stokes equations. A control-volume-based finite difference procedure with appropriate averaging for the diffusion coefficients is used to solve the coupling between the solid and fluid regions. The heat transfer characteristics resulting from recirculating zones around the blocks are presented. The analysis is extended to study the optimum spacing between heat sources for a fixed heat input and a desired maximum temperature at the heat source.
216 citations
TL;DR: In this paper, the authors focus on the discrete ordinate method as a method for analyzing radiative heat transfer in isotropically and anisotropic scattering media and demonstrate that if ordinate sets are chosen to satisfy key moments of the radiative intensity, the resulting Nth order solution with the proposed quadrature is superior to the Nth-order solution using Gauss quadratures.
Abstract: The objective of this note is to focus on the discrete ordinate method as a method for analyzing radiative heat transfer in isotropically and anisotropically scattering media. In particular, one dimension is chosen only for simplicity, since exact solutions are available for benchmarking the discrete ordinate method. One-dimensional radiative heat transfer has been analyzed in many previous investigations and has been extensively reviewed by Viskanta. The development of the discrete ordinate method has been described in detail by Chandrasekhar and Lathrop. The discrete ordinate method using Gauss quadrature has been compared with approximate solutions. In the cases previously analyzed solutions were obtained using ordinate sets that were larger than necessary. This note demonstrates that if ordinate sets are chosen to satisfy key moments of the radiative intensity, the resulting Nth order solution with the proposed quadrature is superior to the Nth order solution using Gauss quadrature.
208 citations
TL;DR: In this paper, it is shown that low-order discrete-ordinate solutions of the transport equation may be significantly improved when the quadrature is chosen to match the half-range first moment.
Abstract: Over the past decade, the discrete-ordinate method has been used by a number of researchers to solve multidimensional radiation transport problems in the field of engineering heat transfer. The method is based on a discrete representation for the angular variation in the radiation intensity. The angular quadrature is arbitrary, although restrictions arise from the need to preserve symmetries and invariance properties of the physical system. Moment-matching, completely symmetric quadratures are frequently selected because of their generality. However, some quadratures do not match half-range moments, in particular the half-range first moment which is related to the one-way radiation flux. It is the purpose of this note to point out that low-order discrete-ordinate solutions of the transport equation may be significantly improved when the quadrature is chosen to match the half-range first moment. These improvements are illustrated for the specific case of radiation in a two-dimensional rectangular enclosure, examined recently by Fiveland.
191 citations
TL;DR: In this article, a dimensional analysis of the Brinkman-extended Darcy formulation, which includes the transport and viscous terms, leads to four governing parameters for steady-state natural convection in a vertical porous cavity.
Abstract: A dimensional analysis of the Brinkman-extended Darcy formulation, which includes the transport and viscous terms, leads to four governing parameters for steady-state natural convection in a vertical porous cavity. They are: Rayleigh number, Darcy number, diffusion parameter {Omega}, and aspect ratio. Numerical results for 0 {le} Da {le} 10{sup {minus}1}, 10 {le} Ra* {le} 5 {times} 10{sup 3}, and A = 1 and 5, indicate that the temperature and velocity fields are significantly modified, the flow regimes are delayed, and the heat transfer rate is decreased when the Darcy number is increased beyond 10{sup {minus}5} for fixed Ra{sup {asterisk}} and A. The slope of the In (Nu) versus In (Ra*) curve in the boundary layer regime decreases from 0.53 at Da = 0 to 0.264 at Da = 10{sup {minus}1} when A = 5. The contribution of the transport term increases with {Omega}, Da, and Ra*, but the effect on the overall heat transfer is insignificant. However, the problem becomes ill formulated at high values of these parameters and may require the consideration of Forchheimer modifications. A scale analysis is also presented to show that the inertia term is of a low order of magnitude in comparison with the viscousmore » term at high Prandtl numbers.« less
178 citations
TL;DR: Fluid flow and heat transfer in two-dimensional finned passages were analyzed for constant property laminar flow as discussed by the authors, where the passage is formed by two parallel plates to which fins are attached in a staggered fashion.
Abstract: Fluid flow and heat transfer in two-dimensional finned passages were analyzed for constant property laminar flow. The passage is formed by two parallel plates to which fins are attached in a staggered fashion. Both the plates are maintained at a constant temperature. Streamwise periodic variation of the cross-sectional area causes the flow and temperature fields to repeat periodically after a certain developing length. Computations were performed for different values of the Reynolds number, the Prandtl number, geometric parameters, and the fin-conductance parameter. The fins were found to cause the flow to deflect significantly and impinge upon the opposite wall so as to increase the heat transfer significantly. However, the associated increase in pressure drop was an order of magnitude higher than the increase in heat transfer. Streamline patterns and local heat transfer results are presented in addition to the overall results.
175 citations
TL;DR: In this article, the effects of three jet-induced crossflow schemes on impingement heat transfer were made, referred to as minimum, intermediate, and maximum crossflow correspond, successively, to unrestricted flow of spent air away from the target surface, restriction of the flow to leave through two opposite sides, and though one side of a rectangular impeding surface.
Abstract: An experimental study of the effects of three jet-induced crossflow schemes on impingement heat transfer was made. The schemes, referred to as minimum, intermediate, and maximum crossflow correspond, successively, to unrestricted flow of spent air away from the target surface, restriction of the flow to leave through two opposite sides, and though one side of a rectangular impingement surface. The study covered jet Reynolds number. jet-to-surface spacing, and open area of 1,000-21,000, 2-16 jet hole diameters, and 1-4%, respectively. The best heat transfer performance is obtained with minimum scheme, intermediate and complete crossflow being associated with varying degrees of degradation. For a given blower power, heat transfer can be enhanced markedly by having greater number of jets over a fixed target area; notably when working with the minimum scheme at narrow jet-to-target spacings.
169 citations
TL;DR: In this paper, a series of numerical simulations with aim to document the problem of forced convection in a channel filled with a fluid-saturated porous medium is presented, where the effects of flow inertia, variable porosity and Brinkman friction are taken into account.
Abstract: This paper presents a series of numerical simulations with aim to document the problem of forced convection in a channel filled with a fluid-saturated porous medium. In modeling the flow in the channel, the effects of flow inertia, variable porosity and Brinkman friction are taken into account. Two channel configurations are investigated: parallel plates and circular pipe. In both cases, the channel wall is maintained at constant temperature. It is found that the general flow model predicts an overall enhancement in heat transfer between the fluid/porous matrix composite and the walls, compared to the predictions of the widely used Darcy flow model. This enhancement is reflected in the increase of the value of the Nusselt number. Important results documenting the dependence of the temperature and flow fields in the channel as well as the dependence of the thermal entry length on the problem parameters are also reported in the course of the study.
164 citations
TL;DR: In this paper, the effect of varying the Lewis number is documented by similarity solution valid for Le > 1 in heat-transfer-driven flows, and for Le < 1 in mass-transfer driven flows.
Abstract: The phenomenon of natural convection caused by combined temperature and concentration buoyancy effects is studied analytically and numerically in a rectangular slot with uniform heat and mass fluxes along the vertical sides. The analytical part is devoted to the boundary layer regime where the heat and mass transfer rates are devoted to the boundary layer regime where the heat and mass transfer rates are ruled by convection. An Oseen-linearized solution is reported for tall spaces filled with mixtures characterized by Le = 1 and arbitrary buoyancy ratios. The effect of varying the Lewis number is documented by similarity solution valid for Le > 1 in heat-transfer-driven flows, and for Le < 1 in mass-transfer-driven flows. The analytical results are validated by numerical experiments conducted in the range 1 {le} H/L {le} 4, 3.5 {times} Ra {le} 7 {times} 10{sup 6}, {minus}11 {le} n {le} 9, 1 {le} Le {le} 40, and Pr = 0.7, 7. Massline patterns are used to visualize the convective mass transfer path and the flow reversal observed when the buoyancy ratio n passes through the value {minus}1.
153 citations
TL;DR: In this paper, the effects of non-Darcian and non-uniform permeability conditions on the natural convection for a vertical plate in porous media were examined analytically.
Abstract: This work examines analytically the effects of non-Darcian and nonuniform permeability conditions on the natural convection for a vertical plate in porous media. The non-Darcian effects, which include the no-slip and inertia effects, decrease the flow and heat transfer rate, while the nonhomogeneity effect enhances the heat transfer. For packed spheres, in particular, the nonhomogeneity in permeability due to the packing of spheres near the solid wall results in a strong flow-channeling effect that significantly increases the heat transfer. The effect of transverse thermal dispersion is also examined. This dispersion effect causes an increase in the heat transfer.
TL;DR: In this paper, the heat transfer effects of an isolated longitudinal vortex embedded in a turbulent boundary layer were examined experimentally for vortex circulations ranging from GAMMA/U/sub infinity/delta/sub 99/ = 0.12 to 0.86.
Abstract: The heat transfer effects of an isolated longitudinal vortex embedded in a turbulent boundary layer were examined experimentally for vortex circulations ranging from GAMMA/U/sub infinity/delta/sub 99/ = 0.12 to 0.86. The test facility consisted of a two-dimensional boundary layer wind tunnel, with a vortex introduced into the flow by a half-delta wing protruding from the surface. In all cases, the vortex size was of the same order as the boundary-layer thickness. Heat transfer measurements were made using a constant-heat-flux surface with 160 embedded thermocouples to provide high resolution of the surface-temperature distribution. Three-component mean-velocity measurements were made using a four-hole pressure probe. Spanwise profiles of the Stanton number showed local increases as large as 24 percent and decreases of approximately 14 percent. The perturbation to the Stanton number was persistent to the end of the test section, a length of over 100 initial boundary-layer thicknesses. The weakest vortices examined showed smaller heat transfer effects, but the Stanton number profiles were nearly identical for the three cases with circulation greater than GAMMA/U/sub infinity/delta/sub 99/ = 0.53 cm. The local increase in the Stanton number is attributed to a thinning of the boundary layer on the downwash side of the vortex.
TL;DR: In this article, two modeles, tous les deux bases sur la definition de trois regions de transfert thermique, have been proposed, and experimentally evaluated.
Abstract: On propose deux modeles, tous les deux bases sur la definition de trois regions de transfert thermique. Etude experimentale mettant en evidence les effets des differents parametres sur le coefficient de transfert thermique
TL;DR: In this paper, a new correlation predicting critical heat flux (CHF) for a saturated forced convective boiling with an impinging jet was introduced, which is able to predict all the CHF data in V-regime with a good accuracy of +-20% to which the correlations existing until now could not be applicable for 15 36.
Abstract: The present study introduces a new correlation predicting critical heat flux (CHF) for a saturated forced convective boiling with an impinging jet. The new correlation is able to predict all the CHF data inV-regime with a good accuracy of +-20% to which the correlations existing until now could not be applicable for 15 36. The new correlation seems to support a new criterion of CHF mechanism applicable for not only pool boiling but also forced convective boiling, recently proposed by Katto and Haramura.
TL;DR: In this article, a finite volume methodology was developed to predict fully developed heat transfer coefficients, friction factors, and streamlines for flow in a corrugated duct, which can be adopted for other convection-diffusion problems in which two boundaries of the flow domain do not lie along the coordinate lines.
Abstract: A finite volume methodology was developed to predict fully developed heat transfer coefficients, friction factors, and streamlines for flow in a corrugated duct. The basis of the method is an algebraic coordinate transformation which maps the complex fluid domain onto a rectangle. The method can be adopted for other convection-diffusion problems in which two boundaries of the flow domain do not lie along the coordinate lines. Representative results were found for laminar flow uniform wall temperature, and for a range of Reynolds number, Prandtl number, corrugation angle, and dimensionless interwall spacing. As seen from the streamlines, the flow patterns are highly complex including large recirculation zones. The pressure drops and friction factor results are higher than the corresponding values for a straight duct. Finally, the performance of the corrugated duct was compared with the straight duct under three different constraints - fixed pumping power, fixed pressure drop, and fixed mass flow rate. There are small differences in the heat transfer rate ratios under these constraints.
TL;DR: In this paper, a method for predicting the average heat transfer coefficient for film condensation on horizontal low integral-fin tubes is presented, based on numerical analysis of surface tension drained condensate flow on the fin surface.
Abstract: A method for predicting the average heat transfer coefficient is presented for film condensation on horizontal low integral-fin tubes. Approximate equations based on the numerical analysis of surface tension drained condensate flow on the fin surface are developed for the heat transfer coefficients in the upper and lower portions of the flooding point below which the interfin space is flooded with condensate. For the unflooded region, the equations is modified to take account of the effect of gravity. These equations are used, along with the previously derived equation for the flooding point, to determine the wall temperature distribution, and in turn the average heat transfer coefficient within {plus minus} 20% for most of the available experimental data including 11 fluids and 22 tubes.
Abstract: Steady, laminar, axisymmetric and circumferentially uniform flow and heat transfer, including the effects of variable properties and buoyancy, have been modeled within a rotating disk chemical vapor deposition (CVD) reactor. The reactor is oriented vertically, with the hot, isothermal, spinning disk facing upward. The Navier-Stokes and energy equations have been solved for the carrier gas helium, at atmospheric pressure. The solutions have been obtained over a range of parameters which is of importance in CVD applications. The primary parameters are the ratio of the disk temperature to the free stream temperature T/sub ..omega..//T/sub infinity/, the disk Reynolds number Re = r/sub d//sup 2/..omega../..nu../sub infinity/, a mixed convection parameter Gr/Re/sup 3/2/ = g(1 - rho/sub ..omega..//rho/sub infinity/)/(..omega sqrt omega nu../sub infinity/), the dimensionless inlet velocity u/sub infinity//..sqrt omega nu../sub infinity/, and two geometric parameters r/sub 0//r/sub d/ and L/r/sub d/. Results are obtained for the velocity and the temperature fields and for the heat flux at the surface of the rotating disk. Comparisons are made with the one-dimensional, variable properties (excluding buoyant effects), infinite rotating disk solutions of Pollard and Newman. Results are presented in terms of a local Nusselt number. The potential uniformity of CVD in this geometry can bemore » inferred from the variation of the Nusselt number over the surface of the rotating disk. The effects of buoyancy and the finite size of the rotating disk within the cylindrical reactor evident.« less
TL;DR: In this article, 14 polymer coatings were evaluated for their ability to promote and sustain dropwise condensation of steam at atmospheric pressure, each coating was visually evaluated and selected for application to the outside of 19mm-dia copper tubes.
Abstract: Fourteen polymer coatings were evaluated for their ability to promote and sustain dropwise condensation of steam. Nine of the coatings employed a fluoropolymer as a major constituent; four employed hydrocarbons and one a silicone. Each coating was applied to 25-mm-square by approximately 1-mm-thick metal substrates of brass, copper, copper-nickel, and titanium. While exposed to steam at atmospheric pressure, each coating was visually evaluated for its ability to promote dropwise condensation. Observations were also conduction over a period of 22,000 hr. Hardness and adhesion tests were performed on selected specimens, On the basis of sustained performance, six coatings were selected for application to the outside of 19-mm-dia copper tubes in order to perform a heat transfer evaluation. These tubes were mounted horizontally in a separate apparatus through which steam flowed vertically downward. Steam-side heat transfer coefficients were inferred from overall measurements. Test results indicate that the steam-side heat transfer coefficient can be increased by a factor of five to eight through the use of polymer coatings to promote dropwise condensation.
TL;DR: In this paper, the irreversible generation of entropy for two limiting cases of combined forced-convection heat and mass transfer in a two-dimensional channel is investigated, where the flow is considered to be either laminar or turbulent with boundary conditions at the channel walls of either constant concentration or constant mass flux.
Abstract: The irreversible generation of entropy for two limiting cases of combined forced-convection heat and mass transfer in a two-dimensional channel are investigated. First, convective heat transfer in a channel with either constant heat flux or constant surface temperature boundary conditions are considered for laminar and turbulent flow. The entropy generation is minimized to yield expressions for optimum plate spacing and optimum Reynolds numbers for both boundary conditions and flow rigimes. Second, isothermal convective mass transfer in a channel is considered, assuming the diffusing substance to be an ideal gas with Lewis number equal to unity. The flow is considered to be either laminar or turbulent with boundary conditions at the channel walls of either constant concentration or constant mass flux. The analogy between heat and mass transfer is used to determine the entropy generation and the relations for optimum plate spacing and Reynolds number. The applicable range of the results for both limiting cases are then investigated by non-dimensionalizing the entropy generation equation.
TL;DR: In this article, entry-region hydrodynamic and thermal conditions have been experimentally determined for laminar mixed-convection water flow through a horizontal rectangular duct with uniform bottom heating.
Abstract: Entry-region hydrodynamic and thermal conditions have been experimentally determined for laminar mixed-convection water flow through a horizontal rectangular duct with uniform bottom heating. Direct heating of 0.05 mm stainless steel foil was used to minimize wall conduction, and the foil was instrumented to yield spanwise and longitudinal distributions of the Nusselt number. Flow visualization revealed the existence of four regimes corresponding to laminar forced convection, laminar mixed convection, transitional mixed convection, and turbulent free convection. The laminar mixed-convection regime was dominated by ascending thermals which developed into mushroom-shaped longitudinal vortices. Hydrodynamic instability resulted in breakdown of the vortices and subsequent transition to turbulent flow. The longitudinal distribution of the Nusselt number was characterized by a minimum, which followed the onset of mixed convection, and subsequent oscillations due to development of the buoyancy-driven secondary flow.
TL;DR: In this paper, an analysis of the problem assuming a constant wall temperature and a higher solid density, covering the entire melting process, is presented, which is an extension of Bareiss and Beer's analysis, but unlike their study no simplifying assumption for the film thickness has been made.
Abstract: In this note, an analysis of the problem assuming a constant wall temperature and a higher solid density, covering the entire melting process, is presented. The method used is an extension of Bareiss and Beer's analysis of the melting process in cylindrical enclosures, but unlike their study no simplifying assumption for the film thickness has been made. In fact, an earlier analysis by this investigator using such a relation gave results which failed to agree with experimental data.
TL;DR: In this article, the Berenson experiment has been recreated with a reduced thermal resistance in the heater, and an improved access to those portions of the transition boiling regime that have a steep negative slope.
Abstract: The Berenson (1960) flat-plate transition-boiling experiment has been recreated with a reduced thermal resistance in the heater, and an improved access to those portions of the transition boiling regime that have a steep negative slope. Tests have been made in Freon-113, acetone, benzene, and n-pentane boiling on horizontal flat copper heaters that have been mirror-polished, 'roughened', or teflon-coated. The resulting data reproduce and clarify certain features observed by Berenson: the modest surface finish dependence of boiling burnout, and the influence of surface chemistry on both the minimum heat flux and the mode of transition boiling, for example. A rational scheme of correlation yields a prediction of the heat flux in what Witte and Lienhard (1982) previously identified as the 'film-transition boiling' region. It is also shown how to calculate the heat flux at the boundary between the pure-film, and the film-transition, boiling regimes, as a function of the advancing contact angle.
TL;DR: In this article, a nonequilibrium two-phase flow model is described for the analysis of critical flows in variable diameter tubes, and the numerical resuls are compared with the experimental data involving critical flows with variable liquid subcoolings, stagnation pressures, and tube lengths.
Abstract: A nonequilibrium two-phase flow model is described for the analysis of critical flows in variable diameter tubes. Modeling of the two-phase flow mixture in the tube is accomplished by utilizing a one-dimensional form of conservation and balance equations of two-phase flow which account for the relative velocity and temperature differences between the phases. Closure of the governing equations was performed with the constitutive equations which account for different flow regimes, and the solution of the nonlinear set of six differential equations was accomplished by a variable step numerical procedure. Computations were carried out for a steam--water mixture with varying degrees of liquid subcooling and stagnation pressures in the vessel upstream of the tube and for different tube lengths. The numerical resuls are compared with the experimental data involving critical flows with variable liquid subcoolings, stagnation pressures, and tube lengths, and it is shown that the nonequilibrium model predicts well the critical flow rate, pressure distribution along the tube, and the tube exit pressure.
TL;DR: In this paper, a discussion of results of mesures de vitesse, temperature, concentration, and rayonnement is presented, together with evidence of correlations and interactions between turbulence/rayonnements.
Abstract: Presentation et discussion de resultats de mesures de vitesse, temperature, concentration et rayonnement. Mise en evidence de correlations et d'interactions turbulence/rayonnement
TL;DR: In this article, the heat transfer coefficients were obtained with two heater heights (5 mm, 10 mm) and varying width (2 mm, approximately 70 mm) in water and R-113.
Abstract: Microelectronic circuits were simulated with thin foil heaters supplied with d-c power. The heaters were arranged in two configurations: flush mounted on a circuit board substrate or protruding from the substrate about 1 mm. Heat transfer coefficients (midpoint) were obtained with two heater heights (5 mm, 10 mm) and varying width (2 mm {approximately} 70 mm), in water and R-113. The height effect for single flush heaters agrees qualitatively with convectional theory; however, even the widest heaters agrees qualitatively with convectional theory; however, even the widest heaters have coefficients higher than predicted due to leading edge effects. The heat transfer coefficient increases with decreasing width, with the coefficient for 2 mm being about 150% above that for 20 mm {approximately} 70mm. This is attributed to three-dimensional boundary layer effects. The protruding heaters have a coefficient about 15 percent higher. Data were obtained for in-line and staggered arrays of flush heaters with varying distance between heaters. Coefficients for the upper heaters are below those for lower heaters, with the differences diminishing as the vertical or horizontal spacing increases. For the protruding heaters, the upper heaters have higher coefficients than the lower heaters.
TL;DR: In this article, an experimental investigation of heat transfer by natural convection from a smooth, isothermal cubic cavity with a variety of side-facing aperatures is described, motivated by the desire to predict the convective loss from large solar thermal-electric receivers and to understand the mechanisms which control this loss.
Abstract: An experimental investigation of heat transfer by natural convection from a smooth, isothermal cubic cavity with a variety of side-facing aperatures is described in this paper. The study was motivated by the desire to predict the convective loss from large solar thermal-electric receivers and to understand the mechanisms which control this loss. Hence, emphasis is placed on the large Rayleigh number, Ra, regime with large ratios of the cavity wall temperature T{sub w} to the ambient temperature T{sub {infinity}}. A cryogenic wind tunnel with test section temperatures which are varied between 80 K and 310 K is used to facilitate deduction of the influences of the relevant parameters and to obtain large temperature ratios without masking the results by radiative heat transfer. A 0.4-m cubic cavity, which is mounted in the side wall of this tunnel, is used. The area of the aperture A{sub a} and its location are key variables in this study. The data which are presented cover the ranges: 1 < T{sub w}/T{sub {infinity}} < 3, L{sup 2}/18 {le} A{sub a} {le} L{sup 2}, and 3 {times} 10{sup 10}.
TL;DR: In this article, a numerical study dealing with combined free and forced laminar convection in a parallel plate vertical channel with asymmetric wall heating at uniform heat fluxes (UHF) is presented.
Abstract: Results are presented of a numerical study dealing with combined free and forced laminar convection in a parallel plate vertical channel with asymmetric wall heating at uniform heat fluxes (UHF). The forced flow at the inlet is assumed to be spatially uniform and directed vertically upward. Quantitative information is provided pertaining to the effects of buoyancy and asymmetric heating on the hydrodynamic and thermal parameters. For values of Grashof number/Reynolds number up to 500 no flow reversal is predicted, in contrast to the case of uniform wall temperatures (UWT) recently reported. Other fundamental differences between UHF and UWT also are indicated.
TL;DR: In this paper, the authors introduced a general transformation procedure appropriate to the problem of combined free and forced convection in a porous medium and showed that particular transformations proposed in the previous papers by Cheng and Minkowycz and co-workers are simply the specific forms of the present general transformation.
Abstract: It is the purpose of the present paper to introduce a general transformation procedure appropriate to the problem of combined free and forced convection in a porous medium. It will be shown that particular transformations proposed in the previous papers by Cheng and Minkowycz and co-workers are simply the specific forms of the present general transformation. Pure forced convection will be treated first as a limiting case of combined free and forced convection. The analysis reveals that any two-dimensional or axisymmetric body of arbitrary shape possesses its corresponding class of wall temperature distributions which permit similarity solutions. Secondly, combined free and forced convection will be considered to seek similarity solutions. It is found that, unlike in pure forced convection, similarity solutions in mixed convection are possible only when the external free-stream velocity varies every where in proportion to the product of the streamwise component of the gravity force and the wall-ambient temperature difference.
TL;DR: In this paper, an approach similar to those employed in the theories of lubrication and film condensation is applied to the problem of melting within a sphere, and an approximate closed-form solution is obtained which yields relationships between the solid speed, position, and time.
Abstract: An approach similar to those employed in the theories of lubrication and film condensation is applied to the problem of melting within a sphere. An approximate closed-form solution is obtained which yields relationships between the solid speed, position, and time. The results are compared with those obtained by Bareiss and Beer (1984) for the case of melting in a horizontal cylinder.
TL;DR: In this article, the effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate was studied using the integral method, and closed-form solutions were obtained using a finite difference approximation and the expansion method.
Abstract: The effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate is studied using the integral method. The closed-form solutions found are in good agreement with the available numerical results and also with the results obtained using a finite difference approximation and the expansion method. For the large values of the flow resistance (due to the presence of the solid matrix), the asymptotic value for the heat transfer rate shows a Prandtl number dependency of 1/2 power, while the results for the intermediate values of the resistances show a 1/3 power dependency. The effect of the presence of the solid matrix on the heat transfer rate is shown through a regime diagram marking the boundaries of the regime of no significant alteration, the non-Darcian regime, and the Darcian regime.