Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number

1988 ◽  
Vol 8 (3) ◽  
pp. 247-281 ◽  
Author(s):  
Keith H. Winters
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Rectangular Cavity ◽  
Laminar Natural Convection

scholarly journals Lattice Boltzmann Simulation of Natural Convection in an Annulus between a Hexagonal Cylinder and a Square Enclosure

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
L. El Moutaouakil ◽  
Z. Zrikem ◽  
A. Abdelbaki
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Square Enclosure ◽  
Lattice Boltzmann Simulation ◽  
Laminar Natural Convection ◽  
Heat Transfers ◽  
Boltzmann Method ◽  
Vertical Case

Laminar natural convection in a water filled square enclosure containing at its center a horizontal hexagonal cylinder is studied by the lattice Boltzmann method. The hexagonal cylinder is heated while the walls of the cavity are maintained at the same cold temperature. Two orientations are treated, corresponding to two opposite sides of the hexagonal cross-section which are horizontal (case I) or vertical (case II). For each case, the results are presented in terms of streamlines, isotherms, local and average convective heat transfers as a function of the dimensionless size of the hexagonal cylinder cross-section (0.1≤B≤0.4), and the Rayleigh number (103≤Ra≤106).

Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Şahin Yİğİt ◽  
Robert J. Poole ◽  
Nilanjan Chakraborty
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Yield Stress ◽  
Local Minimum ◽  
Bingham Fluids ◽  
Bingham Number ◽  
Yield Stress Fluids ◽  
Laminar Natural Convection ◽  
The Mean

The effects of inclination 180deg≥φ≥0deg on steady-state laminar natural convection of yield-stress fluids, modeled assuming a Bingham approach, have been numerically analyzed for nominal values of Rayleigh number Ra ranging from 103 to 105 in a square enclosure of infinite span lying horizontally at φ=0deg, then rotated about its axis for φ>0deg cases. It has been found that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number but Nu¯ values for yield-stress fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to the weakening of convective transport. For large values of Bingham number Bn (i.e., nondimensional yield stress), the mean Nusselt number Nu¯ value settles to unity (Nu¯=1.0) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number Nu¯ for both Newtonian and Bingham fluids decreases with increasing φ until reaching a local minimum at an angle φ* before rising with increasing φ until φ=90deg. For φ>90deg the mean Nusselt number Nu¯ decreases with increasing φ before assuming Nu¯=1.0 at φ=180deg for all values of Ra. The Bingham number above which Nu¯ becomes unity (denoted Bnmax) has been found to decrease with increasing φ until a local minimum is obtained at an angle φ* before rising with increasing φ until φ=90deg. However, Bnmax decreases monotonically with increasing φ for 90deg<φ<180deg. A correlation has been proposed in terms of φ, Ra, and Bn, which has been shown to satisfactorily capture Nu¯ obtained from simulation data for the range of Ra and φ considered here.

Natural convection flow in an open rectangular cavity with cold sidewalls and constant volumetric heat source

2011 ◽  
Vol 225 (5) ◽  
pp. 1191-1201 ◽  
Author(s):  
M Saleem ◽  
S Asghar ◽  
M A Hossain
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Heat Source ◽  
Prandtl Number ◽  
Rectangular Cavity ◽  
Maximum Temperature ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Volumetric Heat Source

The transient two-dimensional natural convection flow of Newtonian fluid in an open rectangular cavity has been studied numerically. The flow is induced due to constant internal heat generation. The alternate direct implicit (ADI) finite difference, together with upwind finite-difference scheme and successive over relaxation method, are used to solve the non-dimensional equations numerically. Effects of Rayleigh number, Ra, Prandtl number, Pr, and cavity aspect ratio, A, on the flow patterns and isotherms as well as on the heat transfer rate are studied graphically. The maximum temperature induced due to the constant volumetric heat source is found with the increase in cavity width, and to decrease with the increase in Prandtl number and Rayleigh number. The numerical model employed here is found to be in good agreement with the previous work.

Numerical analysis of laminar natural convection in isosceles triangular enclosures

2009 ◽  
Vol 223 (5) ◽  
pp. 1157-1169 ◽  
Author(s):  
E F Kent
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Rayleigh Number ◽  
Flow Field ◽  
Water Heaters ◽  
Thermal Boundary Conditions ◽  
Laminar Natural Convection ◽  
Solar Water Heaters ◽  
Rayleigh Numbers

In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 103 to 105. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.

Numerical Study of Laminar Natural Convection From a Plate to its Cylindrical Enclosure

1991 ◽  
Vol 113 (3) ◽  
pp. 194-199 ◽  
Author(s):  
M. M. Elshamy ◽  
M. N. Ozisik
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Hot Plate ◽  
Cell Pattern ◽  
Laminar Natural Convection

The steady-state laminar natural convection for air bounded by a hot plate and a cold cylindrical enclosure has been studied numerically for the case of cold isothermal cylinder and hot isothermal plate. A correlation is presented for the average Nusselt number over the range of Rayleigh number from 105 to 106 for different values of the width-aspect ratio Sw and thickness aspect-ratio St of the plate. It is found that the average Nusselt number increases with increasing Sw and Rayleigh number. A two-cell pattern is observed for Sw=1.5 and less. The effect of Sw on the average Nusselt number is found to be stronger than that of St.

Natural convection in a shallow cavity with differentially heated end walls. Part 3. Experimental results

1974 ◽  
Vol 65 (2) ◽  
pp. 247-260 ◽  
Author(s):  
Jorg Imberger
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Boundary Layers ◽  
Vertical Wall ◽  
Steady Motion ◽  
Rectangular Cavity ◽  
Longitudinal Temperature Gradient ◽  
Longitudinal Temperature ◽  
Shallow Cavity

The steady motion of water in an enclosed rectangular cavity with differentially heated vertical end walls was studied experimentally, and the results are compared with the findings of parts 1 and 2. The depth-to-length ratios of the cavities were 102 and 1·9 × 102, and the Rayleigh number was allowed to vary sufficiently to enable a study to be made of the transition from a flow driven by the vertical wall boundary layers to one sustained by a longitudinal temperature gradient in the central sections of the cavity.

Numerical Investigation of Laminar Natural Convection in a Square Cavity With Wavy Wall and Horizontal Fin Attached to the Hot Wall

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Ahmed Kadari ◽  
Nord-Eddine Sad Chemloul ◽  
Said Mekroussi
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Thermal Conductivity Ratio ◽  
Wavy Wall ◽  
Square Cavity ◽  
Laminar Natural Convection ◽  
Fin Length

Laminar natural convection in differentially heated square cavity with right cold wavy wall and horizontal conducting fin attached to its left hot wall has been investigated numerically. The vertical walls are maintained at different isothermal temperatures, while the horizontal walls are insulated. The fluid that filled the cavity is air with Prandtl number of 0.71. The investigation has been performed for Rayleigh number in the range of 103–106, the thermal conductivity ratio was varied from 10 to 105, three fin lengths and positions have been examined (0.25, 0.5, and 0.75), and three numbers of undulation were tested (one, two, and three undulations). The wave amplitude and the fin thickness were kept constant at 0.05 and 0.04, respectively. The results obtained show that increasing the fin thermal conductivity or the Rayleigh number increases the average Nusselt number especially when the fin length increases. It was also found that the fin position enhances the heat transfer when the fin is placed opposite to the crest of the wavy wall. The trend of the local Nusselt number is wavy. The effect of undulations number appears when the fin length is greater than 0.5. The average Nusselt number enhanced when a conducting fin is added to the cavity with wavy wall and without fin by 51.23% and 56.85% for one and three undulations, respectively, when the Rayleigh number is 105 and the fin length is 0.75.

scholarly journals Laminar natural convection from a vertical array of horizontal heated cylinders inside a water-filled rectangular enclosure cooled at sides

2019 ◽  
Vol 30 (5) ◽  
pp. 2607-2623 ◽  
Author(s):  
Marta Cianfrini ◽  
Massimo Corcione ◽  
Alessandro Quintino ◽  
Vincenzo Andrea Spena
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Control Volume ◽  
Maximum Heat ◽  
Content Type ◽  
Rectangular Enclosure ◽  
Cylinder Diameter ◽  
Maximum Heat Transfer ◽  
Laminar Natural Convection

Purpose The purpose of this study is to investigate numerically the laminar natural convection from a pair of horizontal heated cylinders, set one above the other, inside a water-filled rectangular enclosure cooled at sides, with perfectly insulated top and bottom walls, through a control-volume formulation of the finite-difference method, with the main aim to evaluate the effects of the center-to-center cylinder spacing, the size of the cavity and the temperature difference imposed between the cylinders and the cavity sides. Design/methodology/approach The system of the conservation equations of the mass, momentum and energy, expressed in dimensionless form, is solved by a specifically developed computer code based on the SIMPLE-C algorithm for the pressure-velocity coupling. Numerical simulations are executed for different values of the Rayleigh number based on the cylinder diameter, as well as the center-to-center cylinder spacing and the width of the cavity normalized by the cylinder diameter. Findings The main results obtained may be summarized as follows: the existence of an optimum cylinder spacing for maximum heat transfer rate is found at any investigated Rayleigh number; as a consequence of the downstream confinement, a periodic flow arises at sufficiently high Rayleigh numbers; the amplitude of oscillation of the periodic heat transfer performance of the cylinder array decreases as the cylinder spacing is increased and the cavity width is decreased, whereas the frequency of oscillations remains almost the same; at very small cavity widths, a transition from the typical two-cell to a four-cell flow pattern occurs. Originality/value The computational code used in the present study incorporates an original composite polar/Cartesian discretization grid scheme.

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