Optimal Spacings for Mixed Convection

2004 ◽  
Vol 126 (6) ◽  
pp. 956-962 ◽  
Author(s):  
T. Bello-Ochende ◽  
A. Bejan
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Mixed Convection ◽  
Forced Convection ◽  
Geometry Optimization ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Dimensionless Groups ◽  
Drop Number ◽  
Single Formula

This paper completes the description of geometry optimization in stacks of parallel plates that generate heat. The spacing between plates, or the number of plates in a fixed volume, has been maximized in two limits: pure natural convection and pure forced convection. In this paper, the in-between regime of mixed convection is modeled numerically. After simulating the flow and temperature fields in configurations with a variety of spacings, this paper reports the optimal spacings and the dimensionless groups that govern them (Rayleigh number, pressure drop number, mixed convection ratio). It shows that the numerical results match the results in the limits of natural convection and forced convection. The paper constructs a correlation that bridges the gap between the two limits, and provides a single formula for optimal spacings covering the entire domain, from natural convection to forced convection.

On Combined Free and Forced Convection in Channels

1960 ◽  
Vol 82 (3) ◽  
pp. 233-238 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Forced Convection ◽  
Rectangular Channel ◽  
Complex Function ◽  
Vertical Channel ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Free And Forced Convection ◽  
Energy Equations ◽  
Helmholtz Wave Equation ◽  
Transfer Problems

The heat-transfer problems of combined free and forced convection by a fully developed laminar flow in a vertical channel of constant axial wall temperature gradient with or without heat generations are approached by a new method. By introducing a complex function which is directly related to the velocity and temperature fields, the coupled momentum and energy equations are readily combinable to a Helmholtz wave equation in the complex domain. This greatly reduces the complexities of the problems. For illustrations, the cases of flows between parallel plates and in a rectangular channel are treated. It shows that this method is more direct and powerful than those of previous investigations.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

Unsteady Laminar Pulsating Flow in a Saturated Porous Microchannel in the Presence of Electrical Double-Layer Effects

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Muhammad Dilawar Khan Niazi ◽  
Hang Xu
Keyword(s):  
Angular Velocity ◽  
Forced Convection ◽  
Double Layer ◽  
Analytical Solutions ◽  
Electrical Double Layer ◽  
Darcy Number ◽  
Pulsating Flow ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Periodic Pressure

Abstract The forced convection of a pulsating flow in a saturated porous parallel-plates microchannel driven by a periodic pressure in the presence of an electrical double layer is investigated. Such configuration is very important but seldom considered in literature. Analytical solutions for electrical, momentum, and temperature fields are obtained by means of a substitution approach. The results show that the flow fields depend highly on the electro-osmotic parameter κ, the angular velocity parameter Ω, as well as the Darcy number Da.

A Pseudospectral Analysis of Laminar Natural Convection Flow and Heat Transfer Between Two Inclined Parallel Plates

2006 ◽  
Author(s):  
Serkan Kasapoglu ◽  
Ilker Tari
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Convection Flow ◽  
Parallel Plates ◽  
Natural Convection Flow ◽  
Constant Wall Temperature ◽  
Laminar Natural Convection

Three dimensional laminar natural convection flow of and heat transfer in incompressible air between two inclined parallel plates are analyzed with the Boussinesq approximation by using spectral methods. The plates are assumed to be infinitely long in streamwise (x) and spanwise (z) directions. For these directions, periodic boundary conditions are used and for the normal direction (y), constant wall temperature and no slip boundary conditions are used. Unsteady Navier-Stokes and energy equations are solved using a pseudospectral approach in order to obtain velocity and temperature fields inside the channel. Fourier series are used to expand the variables in × and z directions, while Chebyshev polynomials are used to expand the variables in y direction. By using the temperature distribution between the plates, local and average Nusselt numbers (Nu) are calculated. Nu values are correlated with φ, which is the inclination angle, and with Ra·cosφ to compare the results with the literature.

Numerical Simulation of Natural Convection of Water Near Its Density Maximum Around a Cylinder Inside a Concentric Triangular Enclosure

2012 ◽  
Author(s):  
Yu-Peng Hu ◽  
You-Rong Li ◽  
Chun-Mei Wu
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Inclination Angle ◽  
Temperature Fields ◽  
Density Inversion ◽  
Density Maximum ◽  
Triangular Enclosure ◽  
Density Inversion Parameter ◽  
Boussinesq Fluid

In this paper, a series of numerical simulations for natural convection of water near its maximum-density around a cylinder inside a concentric triangular enclosure were conducted using finite volume method. The effects of the density inversion parameter, the aspect ratio, the Rayleigh number and the inclination angle on natural convection were discussed. Furthermore, the flow and temperature fields, the local and average Nusselt numbers at different parameters were obtained and analyzed. The results show that the flow pattern and temperature distribution are unique for various density inversion parameters and inclination angles. The density inversion parameter, the aspect ratio, the Rayleigh number all have significant effects on the overall heat transfer rates, except for the inclination angle. The present results can also contribute further information on the natural convection of non-Boussinesq fluid in enclosures.

Optimization of Parallel, Horizontal, and Laminar Forced Air-Cooled Heat Generating Boards

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
M. O. Özdemir ◽  
H. Yüncü
Keyword(s):  
Forced Convection ◽  
Heat Dissipation ◽  
Rectangular Channel ◽  
Numerical Procedure ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Constant Property ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Optimal Spacing

The objective of this study is to predict numerically the optimal spacing between parallel heat generating boards. The isothermal boards are stacked in a fixed volume of electronic package enclosed by insulated lateral walls, and they are cooled by laminar forced convection of air with prescribed pressure drop. In the numerical procedure, governing equations for the solution of forced convection of constant property incompressible flow through one rectangular channel are solved. Resulting flow and temperature fields in each rectangular channel yield the optimal board-to-board spacing by which maximum heat dissipation rate from the package to the air is achieved. Next, generalized correlations for the determination of the maximum heat transfer rate from the package and optimal spacing between boards are derived in terms of prescribed pressure difference, board length, and density and kinematic viscosity of air. Finally, corresponding correlations are compared with the available two-dimensional studies in literature for infinite parallel plates.

Bouyancy Effect on Forced Convection in Vertical Tubes at High Reynolds Numbers

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
LiDong Huang ◽  
Kevin J. Farrell
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Mixed Convection ◽  
Transfer Coefficient ◽  
Flow Regime ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Buoyancy Effect ◽  
Vertical Tubes

The complex interaction of forced and natural convections depends on flow regime and flow direction. Aiding flow occurs when both driving forces act in the same direction (heating upflow fluid and cooling downflow fluid), opposing flow occurs when they act in different directions (cooling upflow fluid and heating downflow fluid). To evaluate mixed convection methods, Heat Transfer Research, Inc. (HTRI) recently collected water and propylene glycol data in two vertical tubes of different tube diameters. The data cover wide ranges of Reynolds, Grashof, and Prandtl numbers and differing ratios of heated tube length to diameter in laminar, transition, and turbulent forced flow regimes. In this paper, we focus the buoyancy effect on forced convection of single-phase flows in vertical tubes with Reynolds numbers higher than 2000. Using HTRI data and experimental data in literature, we demonstrate that natural convection can greatly increase or decrease the convective heat transfer coefficient. In addition, we establish that natural convection should not be neglected if the Richardson number is higher than 0.01 or the mixed turbulent parameter Ra1/3/(Re0.8 Pr0.4) is higher than 0.05 even in forced turbulent flow with Reynolds numbers greater than 10,000. High resolution Reynolds-averaged Navier–Stokes simulations of several experimental conditions confirm the importance of the buoyancy effect on the production of turbulence kinetic energy. We also determine that flow regime maps are required to predict the mixed convection heat transfer coefficient accurately.

Natural Convection at the Interface Between a Vertical Porous Layer and an Open Space

1983 ◽  
Vol 105 (1) ◽  
pp. 124-129 ◽  
Author(s):  
A. Bejan ◽  
R. Anderson
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Open Space ◽  
Saturated Porous Medium ◽  
Temperature Fields ◽  
Interface Temperature ◽  
Fluid Systems ◽  
Two Fluid ◽  
Fluid Reservoir

This paper examines the interaction by natural convection between a fluid-saturated porous medium and a fluid reservoir separated by a vertical impermeable partition. The two fluid systems are maintained at different temperatures. The analysis is simplified by assuming Pr > > 1 in the fluid reservoir. It is shown analytically that the flow and temperature fields in the boundary layer regime consist of two fluid layers in counterflow. The interface temperature is shown to increase monotonically with altitude. The important dimensionless group which governs the fluid mechanics is B = (kRaK1/2) / (k′Ra1/4), where k, k′, RaK and Ra are, respectively, the porous medium conductivity, reservoir fluid conductivity, Darcy-modified Rayleigh number based on partition height, and the reservoir Rayleigh number based on partition height. The effect of parameter, B, on the flow, temperature, and heat transfer is documented in the range 0 < B < ∞.

Combined forced and natural convection with low-speed air flow over horizontal cylinders

1970 ◽  
Vol 42 (1) ◽  
pp. 17-31 ◽  
Author(s):  
A. P. Hatton ◽  
D. D. James ◽  
H. W. Swire
Keyword(s):  
Natural Convection ◽  
Mixed Convection ◽  
Forced Convection ◽  
Experimental Work ◽  
Air Flow ◽  
Limited Range ◽  
Convection Regime ◽  
Flow Parameters ◽  
Horizontal Cylinders ◽  
Good Agreement

This article describes experimental work on the mixed convection régime with flow normal to electrically heated cylinders. The forcing velocities used were in the range 0·0085–3 ft./sec (i.e. 10−2 < Ref < 45) and temperature differences in the range 30°C to 200°C (i.e. 10−3 < Ra < 10) were covered.Correlations are proposed for the forced convection and natural convection conditions. A correlation is also developed for the combined forced and natural convection region by a vectorial addition of the flow parameters, which gives good agreement with the experiments except over a limited range in the contraflow régime.

High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel

1989 ◽  
Vol 111 (3) ◽  
pp. 649-656 ◽  
Author(s):  
B. W. Webb ◽  
D. P. Hill
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Channel ◽  
Local Heat Transfer ◽  
Heated Wall ◽  
Uniform Heat Flux ◽  
Parallel Plates ◽  
Heating Rates ◽  
Wide Range

Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.

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