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Showing papers on "Combined forced and natural convection published in 1987"


Book
01 Jan 1987
TL;DR: In this paper, the effect of temperature-dependent Fluid properties on convective heat transfer has been investigated in the context of closed-loop convection in Ducts and cross-flow convection over Rod Bundles.
Abstract: Basics of Heat Transfer (S. Kakac & Y. Yener) External Flow Forced Convection (R. Pletcher) Laminar Convective Heat Transfer in Ducts (R. Shah & M. Bhatti) Turbulent and Transition Flow Convective Heat Transfer in Ducts (M. Bhatti & R. Shah) Convective Heat Transfer in Curved Ducts (R. Shah & S. Joshi) Convective Heat Transfer in Cross Flow (A. Zukauskas) Convective Heat Transfer over Rod Bundles (K. Rehme) Convective Heat Transfer in Liquid Metals (C. Reed) Convective Heat Transfer with Electric and Magnetic Fields (F. Kulacki et al.) Convective Heat Transfer in Bends and Fittings (S. Joshi & R. Shah) Transient Forced Convection in Ducts (Y. Yener & S. Kakac) Basics of Natural Convection (Y. Jaluria) Natural Convection in Enclosures (K. Yang) Mixed Convection in External Flow (T. Chen & B. Armaly) Mixed Convection in Internal Flow (W. Aung) Convective Heat Transfer in Porous Media (A. Bejan) Enhancement of Single-phase Heat Transfer (R. Webb) The Effect of Temperature-dependent Fluid Properties on Convective Heat Transfer (S. Kakac) Interaction of Radiation with Convection (M. Ozisik) Non-Newtonian Fluid Flow and Heat Transfer (T. Irvine, Jr & J. Karni) Fouling with Convective Heat Transfer (W. Marner & J. Suitor) Thermophysical Properties (P. Liley) Index.

1,589 citations


Journal ArticleDOI
TL;DR: In this paper, the mass, momentum and energy balance equations for two-dimensional natural convective flow in a tilted rectangular porous material saturated with fluid are analyzed by solving numerically the mass and momentum equations, using Darcy's law and the Boussinesq approximation.

176 citations


Journal ArticleDOI
TL;DR: In this article, the effect of surface heat flux and channel orientation on the local Nusselt number was studied for Pr = 0.7, 125 3 6, and 0.

118 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the entry effects in mixed convection between horizontal, differentially heated plates in nitrogen by laser Doppler anemometry in a range 1368 < Ra < 8300 and 15 < Re < 170.

114 citations


Journal ArticleDOI
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

106 citations


Journal ArticleDOI
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.

93 citations


Journal ArticleDOI
TL;DR: In this article, the two-dimensional natural convection of fluid under both a magnetic and a gravitational field was modeled by conservation equations and the numerical computations converged successfully and the Nusselt numbers obtained were correlated to give an empirical equation for the rate of heat transfer.
Abstract: The two-dimensional natural convection of fluid under both a magnetic and a gravitational field was modeled by conservation equations. Sample computations were carried out for the fluid in a square enclosure for Rayleigh number of from 104 to 106, for Hartman number of from 1 to 103 and for Prandtl number equal to 0.054, equivalent to melted silicon. The numerical computations converged successfully and the Nusselt numbers obtained were correlated to give an empirical equation for the rate of heat transfer. The steady state solutions were graphically visualized. At Ha=103 and Ra=106, the point at which the temperature profile was almost linear, the flow was almost suppressed and elongated in a regime with high wave numbers.

84 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of buoyancy-induced secondary flow on forced flow in a horizontal rectangular duct with uniform bottom heating were evaluated numerically using a vectorized finite-difference marching technique.
Abstract: Using a vectorized finite-difference marching technique, the steady-state continuity, momentum, and energy equations are solved numerically to evaluate the effects of buoyancy-induced secondary flow on forced flow in a horizontal rectangular duct with uniform bottom heating. Combined entry region conditions are considered, and the secondary flow is found to consist of longitudinal plumes and vortices that first develop at the vertical sidewalls and subsequently propagate to interior spanwise positions. Sequential stages of the secondary flow development are computed in detail and used to interpret the nonmonotonic longitudinal distribution of the spanwise average Nusselt number. The distribution is characterized by oscillations that, under certain conditions, are damped and yield a fully developed Nusselt number that substantially exceeds the value for pure forced convection.

78 citations


Journal ArticleDOI
TL;DR: In this paper, the transverse velocities of longitudinal convection rolls in mixed convection between horizontal plates were measured in nitrogen by laser Doppler anemometry for a range 2472 < Ra < 8300 and 15 < Re < 150.

76 citations


Journal ArticleDOI
Win Aung1, G. Worku
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.

73 citations


Journal ArticleDOI
TL;DR: In this article, the k-e models of turbulence for low Reynolds number flows were adopted for predicting the fully developed upward flow in a uniformly heated, vertical pipe by taking account of the buoyancy force.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: In this article, the Brinkman-extended Darcy model (Brinkman flow) of a laminar mixed-convection flow in an annular porous region is discussed.
Abstract: This study addresses the Brinkman-extended Darcy model (Brinkman flow) of a laminar mixed-convection flow in an annular porous region. The primary objective of the present study is to help clarify the conditions under which the Brinkman term can be neglected in this flow without producing an unacceptable error. The simple geometry considered and the closed-form nature of the solution are advantageous in the demonstration of the importance of the wall effect. The results of this study can also be used in the evaluation of the accuracy of the numerical computations in more complex non-Darcian annular flows in the limiting case of the fully developed flow.

Journal ArticleDOI
TL;DR: In this paper, the conjugate conduction connection problem of a free convection fin embedded in a thermally stratified porous medium is examined, and it is shown that the influence of the thermal stratification on the heat transfer is quite significant.
Abstract: Free convection over a vertical flat plate embedded in a thermally stratified porous medium is analyzed by exploiting the similarity transformation procedure. Numerical integration results are presented for a series of wall and ambient temperature distributions which permit similarity solutions. The conjugate conduction connection problems of a free convection fin embedded in a thermally stratified porous medium is examined, and it is shown that the influence of the thermal stratification on the heat transfer is quite significant. 8 references.

Journal ArticleDOI
TL;DR: In this article, the problem of natural convection of a non-Newtonian power-law fluid about a horizontal impermeable surface in the porous medium is considered, where the plate is assumed with a nonuniform heat flux distribution.
Abstract: The problem of natural convection of a non-Newtonian power-law fluid about a horizontal impermeable surface in the porous medium is considered, where the plate is assumed with a nonuniform heat flux distribution. The present study is based on the boundary layer approximation and only suitable for a high Rayleigh number. Similarity solutions are obtained by using the fourth-order Runge-Kutta method and the Nachtsheim-Swigert iteration scheme. The effects of the nonuniform wall heat flux q w (x) and the new power-law index n on the heat transfer characteristics are discussed.

Journal ArticleDOI
TL;DR: In this article, it was shown that compressible convective motions in a density-stratified rotating fluid give rise to non-diffusive fluxes of the angular momentum (Λ-effect), thus leading to differential rotation.
Abstract: It is shown that compressible convective motions in a density-stratified rotating fluid give rise to non-diffusive fluxes of the angular momentum (Λ-effect), thus leading to differential rotation. This also occurs for the case of extremely small convection anisotropy. Attention is focused on this case of quasi-isotropic convection and the Λ-effect of quasi-isotropic convection is derived. The corresponding fluxes of the angular momentum, as well as the resulting deviation of the rotation from homogeneity, are shown to be proportional to the second spatial derivative of the fluid density squared. The solution of the Reynolds equation is found for a particular density profile. Isorotational surfaces corresponding to different values of the Rossby number, Ro, are considered. The angular velocity increases with depth and towards the equator when Ro≾0.3 which corresponds to the middle and lower parts of the solar convection zone. The results obtained are compared with observations. A possible physical...

Journal ArticleDOI
TL;DR: In this paper, a boundary layer analysis is presented for the problem of melting of a flat plate embedded in a porous medium, where the melting phenomenon is induced by forced convection of the ambient fluid.

Journal ArticleDOI
TL;DR: In this paper, the heat transfer by natural convection and radiation between an isothermal vertical surface, having a staggered array of discrete vertical plates of finite thickness, and the surroundings is investigated.

Journal ArticleDOI
TL;DR: In this paper, the authors re-examine the free-convection effect as a perturbation quantity and show that for a vertical plate, two limits can exist for {xi, yields} {infinity], depending on whether Re {yields] O, or Gr {yours} O, or Gr{yourss} ∞.
Abstract: For a horizontal plate, the axial pressure gradient induced by the buoyancy force is 0(Gr/Re{sup 5/2}). Numerous solutions have been developed by considering the free-convection effect as a perturbation quantity. Again, forced convection exists as a limit for small Gr/Re{sup 5/2} and the free-convection limit can be reached as the parameter approaches infinity. The critical difference between the flow over a horizontal plate and a vertical plate has been pointed out by Cheng and his co-workers. The buoyancy force normal to the plate can induce a vortex instability. The governing parameter for the development of this instability is Gr/Re{sup 3/2}. In this paper, the authors re-examine this problem. For a vertical plate, they show that two limits can exists for {xi} {yields} {infinity}, depending on whether Re {yields} O, or Gr {yields} {infinity}. The mixed-convection, boundary-layer solution is valid for the limit Re {yields} {theta}. The solution for the limit, Re {yields} O, is the free-convection solution, but the forced-convection effect cannot be obtained by solving mixed-convection, boundary-layer equations alone. Also, they demonstrate by order-of-magnitude arguments that Cr/Re{sup 5/2} is not the governing parameter for mixed convection along a horizontal plate. For an inclined plate, as long as no vortexmore » instability develops, Gr/Re{sup 2} is the sole parameter for mixed-convection flows. This conclusion is confirmed by recent measurements (24). The physical model of the analysis is kept simple in order to point out the important physics; thus, the forced flow is assumed along the same direction as the free convection (assisting flow), and the value of the Prandtl number is set to one (Pr = 1).« less

Journal ArticleDOI
TL;DR: In this paper, the gevernine equation for fully developed laminar natural convection in a vertical annulus has been analytically solved for the isothermal wall boundary conditions, and the resulting flow rates and Nusselt numbers are a function of a annulus gap and a non-dimensional temperature ration.

Journal ArticleDOI
TL;DR: In this article, a linear stability analysis for the onset of convection with anisotropic linear rheology is presented, where the critical Rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity.

Journal ArticleDOI
TL;DR: In this paper, a heat flux-based Rayleigh number, Ra/sub T/, is used to estimate the thermal and kinematic states of a convecting magma.
Abstract: Estimates of the Rayleigh number are necessary for determining the thermal and dynamic states of convecting magma. Calculation of a temperature based Rayleigh number, Ra/sub T/, is complicated by the thermal coupling that exists between an intrusion and its host. However, the typically greater thermal resistance of the host regime compared to that of convecting magma can allow the host to control heat flux from a magma chamber in a manner somewhat independent of the state of convection in the chamber. In a system where heat flux is controlled rather than temperature, a heat flux based Rayleigh number, Ra/sub F/, is a more natural parameter to employ, although it has not been used in most magmatic convection models. While the insulating properties of the host regime tend to reduce the value of the thermal Rayleigh number, whether temperature or flux based, this value can be very large compared to any critical value of the Rayleigh number that might exist. The quantity Ra/sub F/ is used to obtain useful relationships for estimating the thermal and kinematic regime in magma. Conservative models of a cooling lava lake, which include temperature dependent viscosity, show that convection will be vigorous enough to circulate phenocrysts.more » However, the time dependent nature of magmatic convection and the tendency of whole body convection to vanish before crystallization is complete severely complicate any attempt to infer convective amplitudes from the observed distribution of crystals ''frozen'' into the interior of the body. copyright American Geophysical Union 1987« less

Journal ArticleDOI
TL;DR: In this paper, the laminar flow patterns and heat transfer for air contained in the enclosure formed between two vertical, concentric cylinders and two horizontal planes have been studied numerically.

Journal ArticleDOI
TL;DR: In this article, an aiding flow of turbulent, combined convection along a vertical flat plate is investigated experimentally in the range of high values of Rax∗ and Rex numbers.

Journal ArticleDOI
TL;DR: In this paper, a boundary-layer analysis for the nonlinear convection of an infinite-Prandtl-number fluid in a rectangular enclosure, in the limit of large Rayleigh numbers, is presented.
Abstract: A boundary-layer analysis is presented for the two-dimensional nonlinear convection of an infinite-Prandtl-number fluid in a rectangular enclosure, in the limit of large Rayleigh numbers. Particular emphaais is given to the analysis of the periodic boundary layers, and on the removal of the singularities that appear near the corners of the cell. It is argued that this later step is necessary to ensure the correctness of the boundary-layer assumptions. Numerical values are obtained for the heat transfer and stress characteristics of the flow.

Journal ArticleDOI
TL;DR: In this paper, the mixed convection boundary layer on a horizontal plate is considered for two separate cases when there is a uniform free stream with the plate held fixed and when there was no outer flow but the plate was moving continuously with a uniform velocity along its length.
Abstract: The mixed convection boundary layer on a horizontal plate is considered for the two separate cases when there is a uniform free stream with the plate held fixed and when there is no outer flow but the plate is moving continuously with a uniform velocity along its length. In both cases we assume that power law temperature distribution on the plate which enables the governing equations to be reduced to similarity form. For the first problem we consider the range of buoyancy parameter for which there are dual solutions, showing how these dual solutions arise from a bifurcation and how the lower branch of solutions terminate as the buoyancy parameter tends to zero. For the second problem we show that there is a unique solution for all positive values of the buoyancy parameter and that for negative values the solution terminates at a singular solution with algebraic decay.

Journal ArticleDOI
Adrian Bejan1
TL;DR: In this article, the parallel structure of the fields of natural convection in fluids and non-Darcy flow in porous media is reviewed in terms of the most basic scales of flow, heat and mass transfer.


Journal ArticleDOI
TL;DR: In this paper, an electronic voltage to frequency conversion technique was developed to record thermocouple signals inside a vertical, air cooled graphite cylinder rotating in molten cryolite, which allowed determination of the interfacial heat transfer coefficient under both free and forced convection conditions.
Abstract: The need to maintain a solid electrolyte ledge on the sidewalls of aluminum smelting cells has recently provoked interest in the heat transfer rate from the molten to the frozen phase at this interface. In this work an electronic voltage to frequency conversion technique was developed to record thermocouple signals inside a vertical, air cooled graphite cylinder rotating in molten cryolite. Precise measurement of the solid electrolyte which freezes around the internally-cooled cylinder allowed determination of the interfacial heat transfer coefficient under both free and forced convection conditions. Correlation of the local Nusselt numbers for heat transfer to the stationary cylinder yields an expression similar to that obtained for natural convection in a rectangular enclosure. However, rotation of the cylinder at peripheral velocities of 0.09 to 0.12 m s−1 caused forced convection to dominate in the cavity and increased the heat transfer coefficients by 34 to 45 pct, respectively. The data provide a basis on which to calculate the convective heat flow to the sidewall ledge for a range of hydrodynamic conditions in the cell.

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional, hydrostatic, nonrotating numerical model with a cumulus paramelerizafion is developed to study the early stages of mesozcale convective systems.
Abstract: A two-dimensional, hydrostatic, nonrotating numerical model with a cumulus paramelerizafion is developed to study the early stages of mesozcale convective systems. Amplifying, forced gravity waves occur when peneirative downdrafts are present. Updraft heating by itself is unable to cause convective sysiems to intensify. Propagation speeds are in rough agreement with those observed in midlatitude mesoscale convective systems. The conditionalityof the convection and the horizontal advection of precipitation by the relative wind produce las between lifting and convection that are not found in conventional wave-CISK models. These lags slow the growth and reduce the propasation speeds of forced gravity waves.