Showing papers on "Combined forced and natural convection published in 1990"
TL;DR: In this paper, the free convection boundary layer flow with simultaneous heat and mass transfer in a porous medium is studied when the boundary wall moves in its own plane with suction, and asymptotic approximate solutions are obtained for the flow variables for various values of the activation energy.
Abstract: The free convection boundary layer flow with simultaneous heat and mass transfer in a porous medium is studied when the boundary wall moves in its own plane with suction. The study also incorporates chemical reaction for the very simple model of a binary reaction with Arrhenius activation energy. For large suction, asymptotic approximate solutions are obtained for the flow variables for various values of the activation energy.
262 citations
TL;DR: In this paper, a comparison of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid is presented.
Abstract: Comparisons of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid are presented. The good comparisons indicate that the simulation is capturing the important features of the flow. Several features are identified and discussed in detail; in particular, the presence of travelling wave instabilities on the vertical-wall boundary layers and horizontal intrusions, the existence of a rapid flow divergence in the region of the outflow of the intrusions, and the presence of cavity-scale oscillations, caused by the interaction of the intrusions with the opposing vertical boundary layer. The utilization of both numerical and experimental investigations has allowed a more complete exploitation of the available resources than would have been possible had each been conducted separately.
174 citations
TL;DR: In this paper, the effects of convection on chemical waves in which density gradients result from the exothermicity as well as from the isothermal volume change of the reaction are considered.
Abstract: We consider the effects of convection on chemical waves in which density gradients result from the exothermicity as well as from the isothermal volume change of the reaction. If the signs of the enthalpy (ΔH) and volume (ΔV) of the reaction are opposite, then simple convection will occur, and the increase in the front propagation velocity will be equal to the velocity of the convective fluid flow. If the signs are the same, then simple convection will not occur. Instead multicomponent convection may be present, even though the overall density gradient may appear to be stable. The stability conditions for both mechanisms as functions of ΔH and ΔV and of the direction of front propagation (ascending, descending or horizontal) are analyzed
172 citations
TL;DR: In this paper, three fundamental combinations of thermal boundary conditions on the respective wall surface (i.e., isoflux-isoflux, isoftluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern.
Abstract: The present analysis is concerned with flow reversal phenomena and heat transfer characteristics of the fully developed laminar combined free and forced convection in the heated vertical channels. Three fundamental combinations of thermal boundary conditions on the respective wall surface (namely isoflux-isoflux, isofluxisothermal, and isothermal-isothermal) are considered separately so as to investigate extensively their distinct influence on the flow pattern. Results of the velocity distribution and temperature distribution as well as the Nusselt number in terms of bulk mean temperature are carried out. Based on the analytical solutions obtained, flow reversal adjacent to the relatively colder wall is found to exist within the channel as Re/Gr is below than a threshold value, which is related to the thermal boundary conditions. Parameter zones for the occurrence of reversed flow are presented. Comparisons and verification are made using the existing numerical solutions at locations far downstream of developing flow.
124 citations
TL;DR: In this paper, the authors investigated vortex shedding from a heated/cooled circular cylinder in the mixed natural and forced convection regimes using the fourth-order Hermitian relation applied to the contravariant velocity components.
Abstract: The phenomenon of vortex shedding from a heated/cooled circular cylinder has been investigated numerically in the mixed natural and forced convection regimes. Accuracy of the computation was achieved by the fourth-order Hermitian relation applied to the contravariant velocity components in the convection terms of the vorticity transport equation, and by the far-boundary stream-function condition of an integral-series form developed by the authors.
118 citations
TL;DR: In this paper, the authors describe the combined heat and mass-transfer natural convection mechanisms, which are considered an important subfield in contemporary heat andmass transfer research, and consider the phenomena of convection through fluid-saturated porous media generally in terms of volume-averaged quantities.
Abstract: Publisher Summary The chapter describes the combined heat and mass-transfer natural convection mechanisms, which are considered an important subfield in contemporary heat and mass-transfer research. This subfield essentially brings together the studies concerned with the combined heat and mass-transfer or double-diffusive processes that are driven by buoyancy through porous media saturated with fluid. The density gradients that provide the driving buoyancy effect are induced by the combined effects of temperature and species concentration nonuniformities present in the porous medium. The chapter considers the phenomena of convection through fluid-saturated porous media generally in terms of volume-averaged quantities. There are four conservation principles considered in the study of convection with more than one buoyancy effect. These include conservation of mass, energy, species, and momentum. Heat and mass transfer in the vertical direction and in horizontal direction are discussed in detail. Another category of studies of combined buoyancy effects in porous media deals with the local fields around buried sources of heat and mass. The recent work in this field focuses on the multilayer structure of flows of the boundary-layer or concentrated-source type.
104 citations
TL;DR: In this paper, the Launder and Sharma low-Reynolds-number k ~ ϵ turbulence model is used for developing flow in a tube and the results show that the model is in agreement with a range of experimental heat transfer data and flow profile measurements for air, except for strongly buoyancy-influenced descending flow.
89 citations
TL;DR: In this article, mixed convective heat transfer results for laminar, buoyancy-assisting, two-dimensional flow in a vertical duct with a backward-facing step are reported.
86 citations
TL;DR: In this article, the authors investigated the structure of laminar wakes and heat transfer in the presence of thermal buoyancy art in a two-dimensional horizontal channel with a built-in square cylinder and showed that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone.
Abstract: Structures of laminar wakes and heat transfer in the presence of thermal buoyancy art investigated from the numerical solution of complete Navier-Stokes and energy equations in a two-dimensional horizontal channel with a built-in square cylinder. Results show that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone. For a given Reynolds number, the heating of the fluid in the channel is improved by mixed convection up to a certain Grashof number and deteriorates if the Grashof number is further increased.
75 citations
TL;DR: In this article, heat transfer enhancement in mixed convection flow between parallel plates heated uniformly from below is investigated, and the onset of secondary flow is found to precede appreciable heat transfer enhancements.
69 citations
TL;DR: In this article, the stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries was investigated using numerical calculations in three-dimensional rectangles.
Abstract: The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. At low Rayleigh numbers (Ra 2.22 (aspect ratio 1.6) are time dependent for Ra > 4 × 104. For every case in which the initial condition was a time-dependent large-aspect-ratio roll, two-dimensional convection was found to be unstable to three-dimensional convection. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth. The bimodal planforms are steady states for Ra [les ] 105, but one case at Ra = 5 × 105 exhibits time dependence in the form of pulsating knots. Calculations at Ra = 105 in larger domains resulted in fully three-dimensional cellular planforms. A steady-state square planform was obtained in a 2.4 × 2.4 × 1 rectangular box. started from random initial conditions. Calculations in a 3 × 3 × 1 box produced steady hexagonal cells when started from random initial conditions, and a rectangular planform when started from a two-dimensional roll. An hexagonal planform started in a 3.5 × 3.5 × 1 box at Ra = 105 exhibited oscillatory time dependence, including boundary-layer instabilities and pulsating plumes. Thus, the stable planform in three-dimensional convection is sensitive to the size of the rectangular domain and the initial conditions. The sensitivity of heat transfer to planform variations is less than 10%.
TL;DR: In this article, a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e., transparent) fluid was described.
Abstract: SUMMARY This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e. transparent) fluid. One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls. The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non-isothermal walls. A two-band radiation model has been employed. Results are presented for a square cavity with a vertical hot wall at 15O"C, the ambient at 20°C and lo4 I Ra _< 3 x LO5, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers.
TL;DR: The role played by the retardation time, characteristic of the Jeffreys model, is emphasised in this article, where threshold values of the parameters (critical Rayleigh number, critical wavenumber, onset frequency, etc.) for stationary and oscillatory convection are obtained.
Abstract: The onset of convection in a viscoelastic fluid that obeys the Jeffreys model is investigated. Two boundary conditions have been considered separately: free-free and rigid-rigid. The role played by the retardation time, characteristic of the Jeffreys model, is emphasised. The threshold values of the parameters (critical Rayleigh number, critical wavenumber, onset frequency, etc.) for stationary and oscillatory convection are obtained. The frontier between oscillatory and stationary convection is calculated and the possibility to obtain a codimension-two point is discussed.
TL;DR: In this article, the equations of motion for buoyancy-driven convection and the equation of induction for the magnetic field are solved for a fluid of infinite Prandtl number in a rotating spherical shell of radius ratio η = 0.4.
TL;DR: In this article, analytical solutions for fully developed natural convection in open-ended vertical concentric annuli are presented and four fundamental boundary conditions have been investigated and corresponding fundamental solutions are obtained.
Book•
01 Jan 1990
TL;DR: In this article, the authors presented a simulation of buoyancy-driven Oscillatory Flows in Shallow Cavities Filled With Low-Prandtl Number Fluids using the TURBIT Code.
Abstract: Benchmark Definition.- 1. Finite Difference Methods.- Fine Mesh Solutions Using Stream Function-Vorticity Formulation.- A Comparison of Velocity-Vorticity and Stream Function-Vorticity Formulations for Pr=0.- Buoyancy-Driven Oscillatory Flows in Shallow Cavities Filled With Low-Prandtl Number Fluids.- A Finite-Difference Method With Direct Solvers for Thermally-Driven Cavity Problems.- Contribution to the GAMM Workshop.- Low Prandtl Number Convection in a Shallow Cavity.- Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids With the TURBIT Code.- Marangoni Flows in a Cylindrical Liquid Bridge of Silicon.- Numerical Simulation of Oscillatory Convection in a Low Prandtl Fluid.- Steady-State Natural Convection in a Rectangular Cavity Filled With Low Prandtl Number Fluids.- Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids Using AQUA Code.- Pressure Correction Splitting Methods for the Computation of Oscillatory Free Convection in Low Pr Fluids.- Influence of Thermocapillarity on the Oscillatory Convection in Low-Pr Fluids.- 2. Finite Volume Methods.- Numerical Simulation of Oscillatory Convection in Low-Pr Fluids.- An Implicit Pressure Velocity Algorithm Applied to Oscillatory Convection in Low Prandtl Fluid.- Oscillatory Natural Convection in a Long Horizontal Cavity.- Contribution of the Heat-Transfer Group at DELFT University.- Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids.- 3. Finite Element Methods.- Application of the N3S Finite Element Code to Simulation of Oscillatory Convection in Low Prandtl Fluids.- Two- and Three-Dimensional Finite Element Simulations of Buoyancy-Driven Convection in a Confined Pr=0.015 Liquid Layer.- Two and Three-Dimensional Study of Convection in Low Prandtl Number Fluids.- Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids.- The Solution of the Boussinesq Equations by the Finite Element Method.- Numerical Simulation of Oscillatory Convection in Low Pr Fluids by Using the Galerkin Finite Element Method.- 4. Spectral Methods.- Oscillatory Convection in Low Prandtl Fluids: A Chebyshev Solution With Special Treatment of the Pressure field.- Contribution to the GAMM Workshop With a Pseudo-Spectral Chebyshev Algorithm on a Staggered Grid.- Spectral Calculations of Convection in Low-Pr Fluids.- Spectral Method for Two-Dimensional Time-Dependent Pr?0 Convection.- Steady-State Solution of a Convection Benchmark Problem by Multidomain Chebyshev Collocation.- 5. Synthesis.- Synthesis of Finite Difference Methods.- Synthesis of the Results With the Finite-Volume Method.- Analysis of Finite Element Results.- Analysis of Spectral Results.- General Synthesis of the Numerical Results.- 6. Stability Results.- Linear and Non-Linear Analysis of the Hadley Circulation.- A Bifurcation Analysis of Oscillatory Convection in Liquid Metals.- 7. Experimental Results.- A Laboratory Study of Oscillations in Differentially Heated Layers of Mercury.- Subharmonic Transitions in Convection in a Moderately Shallow Cavity.- Convection in a Shallow Cavity.- Conclusions.- List of Participants.- Support and Sponsoring Acknowledgements.
TL;DR: In this paper, the authors investigated thermal instabilities in forced convection boiling in a vertical single channel system, with Freon-11 as the working fluid, and they used finite difference techniques to determine the wall conditions, fluid properties and flow conditions at any point along the test section.
TL;DR: In this article, the authors investigated mixed convection heat transfer from a four-row, in-line array of 12, square heat sources which are flush mounted to the lower wall of a horizontal, rectangular channel.
TL;DR: The transition from thermal convection in the form of rolls in a fluid layer heated from below to traveling wave convection occurs at the Rayleigh number RII=1854 in the limit of low Prandtl numbers and in the presence of no slip boundaries as mentioned in this paper.
Abstract: The transition from thermal convection in the form of rolls in a fluid layer heated from below to traveling wave convection occurs at the Rayleigh number RII=1854 in the limit of low Prandtl numbers and in the presence of no‐slip boundaries. While the traveling wave convection exhibits similar properties at moderately low and very low Prandtl numbers, the tertiary transition to asymmetric waves experiences a qualitative change at a Prandtl number of about 0.02. Instead of the double frequency asymmetric waves that occur at higher Prandtl numbers the traveling wave convection becomes just asymmetric, but remains stationary with respect to the moving frame of reference. The heat transport carried by the new form of convection is larger than for symmetric traveling wave convection.
TL;DR: In this paper, the combined heat and mass transfer in natural convection along a vertical cylinder in a saturated porous medium is studied, and boundary layer analysis is formulated in terms of the combined thermal and solutal buoyancy effect.
TL;DR: In this article, the authors extended two-dimensional, compressible convection to three dimensions using a higher order Godunov scheme and showed that the flow readily becomes supersonic in the upper boundary layer, where shock structures form intermittently in the vicinity of strong downflow lanes.
Abstract: Previous numerical calculations of two-dimensional, compressible convection are extended to three dimensions, using a higher order Godunov scheme. The results show that the flow readily becomes supersonic in the upper boundary layer, where shock structures form intermittently in the vicinity of the strong downflow lanes. The convection as a whole is strongly time-dependent and evolves on a time scale comparable to the sound crossing time. The motions in the upper layers are characterized by the rapid expansion of the upward-moving fluid elements. In the interior, most of the heat is carried by a small fraction of the fluid residing in strong, highly coherent downflows. The remaining fluid is dominated by small-scale, disorganized turbulent motions.
TL;DR: In this article, a 3D laminar flow model of a constant property fluid is used to establish the pattern of three-dimensional convection and to determine the value of the critical Grashof number, Grcrit, at which the flow becomes time dependent.
Abstract: Numerical experiments of natural convection of a zero Prandtl (Pr) number fluid in 4×1×2 (length to height to width) and 4×1×1 rectangular cavities (with a free top surface) and enclosures (having a solid top surface) are performed. The cavities are referred to as R‐F (rigid‐free) while enclosures are referred to as R–R (rigid–rigid). The objective of this study is to establish the pattern of three‐dimensional convection and to determine the value of the critical Grashof number, Grcrit, at which the flow becomes time dependent. A three‐dimensional laminar flow model of a constant property fluid is used. The model equations are solved numerically by a finite volume method. The flow field is steady at relatively low Grashof number (Gr), and is represented by one cell, unlike the multicellular flow predicted by two‐dimensional studies. When Gr reaches Grcrit, the flow becomes oscillatory. Transition to time dependence is a function of the geometry and the type of top surface (rigid or free). The R–R flow is more stable than that of the R‐F case, for both widths considered (one and two). The width of cavity and/or enclosure has an important effect on transition to oscillatory convection, for it is found that reducing the width from two to one, leads to a much higher Grcrit, making the results of two‐dimensional numerical simulations completely inadequate.
TL;DR: In this paper, the mixed convection on a vertical slender adiabatic paraboloid with a tip heat source was studied and the boundary layer equations admit similarity solutions that are governed by a nondimensional free-stream parameter γ and a heat source parameter α.
Abstract: The mixed convection on a vertical slender adiabatic paraboloid with a tip heat source is studied. The boundary layer equations admit similarity solutions that are governed by a nondimensional free‐stream parameter γ and a heat source parameter α. Numerical results show for aiding flow (α>0) the solutions are unique and for opposing flow (α<0) the solutions may be unique, dual, or nonexistent. Velocity and temperature profiles are obtained.
TL;DR: In this article, a theoretical and experimental study of laminar forced convection in the thermal entrance region of a rectangular duct, subjected to a sinusoidally varying inlet temperature, is presented.
Abstract: A theoretical and experimental study of laminar forced convection in the thermal entrance region of a rectangular duct, subjected to a sinusoidally varying inlet temperature, is presented. A general boundary condition of the fifth kind that accounts for both external convection and wall thermal capacitance effects is considered, and an analytical solution is obtained through extending the generalized integral transform technique. The variations of amplitudes and pahse lags of centerline and bulk temperatures are determined as functions of modified Biot number, fluid-to-wall thermal capacitance ratio, and dimensionaless inlet frequency. An apparatus has been designed, built, and used for the experimental study to provide validation of the mathematical modeling employed. Good agreement is obtained when the nonuniform sinusoidally varying inlet temperature profile obtained by experiments is incorporated into the theoretical model.
TL;DR: In this article, an experimental study of the mixed convective heat transfer from an isolated source of finite thickness, located on a horizontal surface in an externally induced forced flow, has been carried out.
Abstract: An experimental study of the mixed convective heat transfer from an isolated source of finite thickness, located on a horizontal surface in an externally induced forced flow, has been carried out. This problem is of particular interest in the cooling of electronic components and also in the thermal transport associated with various manufacturing systems, such as ovens and furnaces. The temperature distribution in the flow as well as the surface temperature variation are studied in detail. The dependence of the heat transfer rate on the mixed convection parameter and on the thickness of the heated element or source, particularly in the vicinity of the source, is investigated. The results obtained indicate that the heat transfer rate and fluid flow characteristics vary strongly with the mixed convection variables. The transition from a natural convection dominated flow to a forced convection dominated flow is studied experimentally and the basic characteristics of the two regimes determined. This transition has a strong influence on the temperature of the surface and on the heat transfer rate. As expected, the forced convection dominated flow is seen to be significantly more effective in the cooling of a heat dissipating component than a natural convection dominated flow. Themore » location of the maximum temperature on the module surface, which corresponds to the minimum local heat transfer coefficient, is determined and discussed in terms of the underlying physical mechanisms. The results obtained are also compared with these for an element of negligible thickness and the effect of a significant module thickness on the transport is determined. Several other important aspects of fundamental and applied interest are studied in this investigation.« less
TL;DR: In this article, the fluid flow and heat transfer characteristics are found to be dependent on a modified Grashof number Gr+, Prandtl number Pr, number of fins M and the relative fin height H. Satisfactory agreement is obtained between the present numerical results and previous experimental data.
TL;DR: In this article, the authors studied thermoconvective instabilities in horizontal porous layers heated from below using the Brinkman-Forchheimer extended Darcy formulation and found that the onsets of stable and oscillatory convection are strong functions of the governing parameters: fluid Rayleigh and Prandtl numbers, Darcy number, and conductivity ratio.
Abstract: Thermoconvective instabilities in horizontal porous layers heated from below are studied numerically by employing the Brinkman-Forchheimer extended Darcy formulation. The onsets of stable and oscillatory convection are found to be strong functions of the governing parameters: fluid Rayleigh and Prandtl numbers, Darcy number, and conductivity ratio. The effects of porosity and specific heat ratio are pronounced only in the fluctuating convection regime. At the onset, the oscillatory convection is highly periodic, but with an increase in convective motions the disorder increases monotonically and the fluctuations become highly random. These results do not confirm the possibility of reverse transition from a more-disordered to a less-disordered state as predicted by the Darcy model (Kimura et al., 1986). The applicability of Darcy formulation is thus highly restrcited in the case of a Benard convection problem. In a randomly oscillating convective state, the heat transfer rate varies substantially with time.
TL;DR: In this article, the authors considered the laminar, natural convection of air in a slender, laterally-heated square-section cavity situated in a uniform gravitational field.