Natural Convection In Trapezoidal Cavity Research Articles

Natural Convection in Trapezoidal Cavity containing Hybrid Nanofluid

In this paper, a numerical study of natural convection in a trapezoidal cavity with left heated wall, right cold wall and filled with Cu – Al2 O3 and water hybrid nanofluid. The remaining walls of the cavity are kept at adiabatic. An enhancement in heat transfer is observed with the increase of three different parameters. Based upon the numerical predictions, the effect of Rayleigh number, inclination of the slopping wall, solid volume fraction of nanoparticles on flow and patterns as well tested. We found that acute slopping wall, high Rayleigh number and Cu – Al2 O3 nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle, effective thermal conductivity and viscosity as well as Rayleigh number.

Casson Hybrid Nanofluid Natural Convection in Trapezoidal Cavity containing a Partially Heated Wall

A computational analysis has been performed for Casson hybrid nanofluid natural convection heat transfer in trapezoidal cavity containing a partially heated at bottom wall, and the incline walls are set to be at the cold temperature while the top wall is supposed to be adiabatic. The hybrid nanoparticles, alumina and copper are dispersed in ethylene glycol and water mixture has been used as a working fluid. The finite element method is used to solve the nondimensional governing partial differentials equations. The numerical results are carried out for different governing parameters such as Casson parameter Rayleigh number and hybrid nanoparticles volume fraction and heated zone length. The influence of these parameters on streamlines, isotherms, velocities and average Nusselt number will be the focus in this study.

WITHDRAWN: Heatlines Visualization of Natural Convection in Trapezoidal Cavity Filled with Nanofluid and Divided by Porous Medium Partition

Abstract Heatlines visualization of natural convection heat transfer in trapezoidal-shape cavity filled with nanofluid (TiO2-water) and divided by horizontal porous media partition has been studied numerically using finite element method. Non-uniform temperature is applied at the bottom wall and cold temperature applied to the top wall while two inclined vertical walls were insulated. In this work the influence of many parameters such as, Rayleigh number (103≤Ra≤105), partition porous thickness (0.05≤TH≤0.6), partition porous position (0.15≤HD≤0.75), Darcy number (10−5≤Da≤10−1) and volume of fraction (0≤φ≤0.1). Results are exhibited by means heatlines, isotherms, streamlines rather than local and average Nusselt number. The results show that at a constant Rayleigh number equal to (105) and thickness of porous partition (0.1), the percentage enhancement of heat transfer along the bottom wall with the addition of nanoparticles (ϕ=0.1) is greater than enhancement with the base fluid. While, the maximum value of the percentage enhancement of heat transfer is (4.22%) occurred at porous position equal to 0.5. Also, for a constant position of porous partition (HD=0.5) the percentage enhancement of heat transfer with volume fraction of nanoparticles (0.1) along the bottom wall decreases as the thickness of porous partition and Rayleigh number increased. It can be noticed that there is a good agreement between the current study and those of Chamka and Ismeal, with an approximated absolute error 1.829%.

Analysis of entropy production vs. energy efficiencies during natural convection in porous trapezoidal cavities exposed to various thermal ambience

Natural convection in trapezoidal cavities is important in industrial processing applications and the entropy generation technique has been used for the assessment of the energy efficiency. The results are obtained in terms of the isotherms (θ), streamlines (ψ), entropy generation due to the heat transfer (Sθ) and fluid friction Sψ), total entropy generation (Stotal), average Bejan number (Beav) and average Nusselt numbers (Nul¯ and Nub¯). It was found that, Sθ, max occurs at the top corners for the case 1 (uniformly heated bottom wall, adiabatic top wall and linearly heated side walls) whereas, Sθ, max occurs at the bottom right corner for the case 2 (linearly heated left wall and isothermally cold right wall with other walls identical with the case 1). On the other hand, Sψ, max occurs along the side walls for the case 1 whereas, Sψ, max occurs along the bottom or right walls for the case 2. The local maxima of entropy generation terms (Sθ, max, Sψ, max) contribute significantly on the total entropy generation (Stotal). Finally, the optimal strategy for natural convection involving the cases 1 and 2 are decided based on the interplay between Stotal and Nub¯ for various ranges of modified Darcy numbers (Dam).

Magnetohydrodynamic double diffusive natural convection in trapezoidal cavities

A numerical work has been carried out to study the effects of magnetic field on double diffusive natural convection in a trapezoidal enclosure. Both inclined walls and bottom wall were kept at constant temperature and concentration where the bottom wall temperature and concentration are higher than those of the inclined walls. Top wall of the cavity is adiabatic and impermeable. The trapezoidal enclosure is subjected to a horizontal magnetic field. To investigate the effects, finite volume method is used to solve the governing equations for different parameters such as Grashof number, inclination angle of inclined wall of the enclosure, Hartmann number and buoyancy ratio. The numerical results are reported for the effect of studied parameters on the contours of streamline, temperature, and concentration. In addition, results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study is done for constant Prandtl number, Pr=0.7; aspect ratio=1 and Lewis number, Le=2. The studied range of Grashof number is from Gr=103 to 106, inclination angle from 0° to 75°, Hartmann number from 0 to 15 and buoyancy ratio from −2 to 2 which covers the double diffusive range in the cases of aiding and opposing flows. It is found that heat and mass transfer decreased as φ increases from 0° to 75°. Also heat and mass transfer decreased as Hartman number increased from 0 to 15. Finally, the predicted results for both average Nusselt and Sherwood numbers were correlated in terms of the studied parameters.

Magnetohydrodynamic natural convection in trapezoidal cavities

A computational numerical work has been done to see the effects of magnetic field on natural convection for a trapezoidal enclosure. Both inclined walls and bottom wall have constant temperature where the bottom wall temperature is higher than the inclined walls. Top wall of the cavity is adiabatic. To investigate the effects, finite element method is used to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure. It is found that heat transfer decreased by 20.70% and 16.15% as φ increases from 0 to 60 at Ra=105 and 106 respectively. On the other hand, heat transfer decreased by 20.28% and 13.42% as Ha increases from 0 to 50 for Ra=105 and 106 respectively.

Numerical investigation of several physical and geometric parameters in the natural convection into trapezoidal cavities

Natural convection in trapezoidal cavities, especially those with two internal baffles in conjunction with an insulated floor, inclined top surface, and isothermal left-heated and isothermal right-cooled vertical walls, has been investigated numerically using the Element based Finite Volume Method (EbFVM). In numerical simulations, the effect of three inclination angles of the upper surface as well as the effect of the Rayleigh number (Ra), the Prandtl number (Pr), and the baffle’s height (Hb) on the stream functions, temperature profiles, and local and average Nusselt numbers has been investigated. A parametric study was performed for a wide range of Ra numbers (103⩽Ra⩽106) Hb heights (Hb=H∗/3, 2H∗/3, and H∗), Pr numbers (Pr=0.7, 10 and 130), and top angle (θ) ranges from 10 to 20. A correlation for the average Nusselt number in terms of Pr and Ra numbers, and the inclination of the upper surface of the cavity is proposed for each baffle height investigated.

The Influence of Baffles on the Natural Convection in Trapezoidal Cavities

This article presents an investigation into natural convection in trapezoidal cavities. It examines a cavity whose floor and upper inclined walls are both adiabatic, while the vertical walls are isothermal. For these isothermal walls, we consider two thermal boundary conditions. Under the first condition, the short wall on the left side is heated as the tall one on the right side is cooled. The second condition is the reverse of the first—the short wall is cooled as the tall one is heated. Considering laminar conditions and a two-dimensional system, steady-state computations are carried out to assess the effects of one and two baffles, the baffle's height (H b ), Rayleigh number, 103 ≤ Ra ≤ 106, and three Prandtl number values. To demonstrate the various effects, the results from several designed case studies are shown in terms of isotherms, streamlines, and local and average Nusselt numbers in order. Predictions reveal that the second baffle decreases the cavity's fluid flow and heat transfer. As the height of the baffle rises, the heat transfer drops drastically. Also, two baffles produce more pronounced thermal stratification than only one.

Natural Convection in Trapezoidal Cavities

This note was inspired by a paper published recently in this journal by T, S. Lee [I]. Here, results of calculations of the same problem are presented, which differ both qualitatively and quantitatively from those of Lee [I]. By using a series of systematically refined grids from 10 x 10 to 160 X 160 control volumes, a second-order discretization method, and an efficient multigrid algorithm, the convergence of the results toward grid independent solutions is demonstrated, and the errors are proven to negligibly small. Features of flows are discussed, and disagreements with results of Lee [I] are analyzed.

Experimental and Numerical Studies of Natural Convection in Trapezoidal Cavities

Natural convection heat transfer has been studied experimentally and numerically for horizontal prismatic cavities of trapezoidal section having a hot horizontal base, a cool inclined top, and insulated vertical walls. Experimental results are presented for a cavity with width-to-mean height ratio of 4, Rayleigh numbers (based on the mean cavity height) from 103 to 107, and top surface inclinations from 0 to 25 deg to the horizontal. For a given top surface inclination, the Nusselt–Rayleigh relationship follows the usual trend, but with an interesting anomaly, in which higher Nusselt numbers than expected are obtained in the range 8 × 103 < Ra < 2 × 105 for inclinations of 0 and 5 deg. Overall, as the inclination of the top surface is increased, the Nusselt number decreases, an effect that becomes greater at higher angles. The proportions of convective heat flow rate into the high side and low side of the cavity were measured and show distinct maxima at particular Rayleigh numbers (which are independent of the top surface inclination angle). The equation Nu = 0.168 [Ra (1 + cos θ)/2]0.278 [(1 − cos θmax)/(cos θ − cos θmax)]−0.199 correlates the experimental results to within 6.9 percent for the ranges 4 × 103 < Ra < 107 and 0 deg ≤ θ ≤ 25 deg, apart from the anomalous region previously indicated. It is suggested that this correlation applies for A ≥ 4. The numerical model uses a false transient ADI finite difference scheme to solve the governing two-dimensional vorticity and energy transport equations. Nusselt numbers computed by the model are in good agreement with the experimental values. The convective flow patterns generated by the model exhibit changes in number and in size of cells for different Rayleigh numbers and different top surface inclinations.