Trapezoidal Enclosure Research Articles

Hydromagnetic double-diffusive mixed convection in trapezoidal enclosure due to uniform and nonuniform heating at the bottom side: Effect of Lewis number

This paper presents unsteady numerical results of double diffusive mixed convection flow in a trapezoidal enclosure with the uniform magnetic field effect applied in negative horizontal direction. At the bottom wall, the uniform and non-uniform heat and mass are applied while the heat and mass absorbed uniformly at the top wall. Other side walls are impermeable and adiabatic. The top wall moves along x-axis direction with a constant velocity. The transport phenomenon of this problem can be expressed by the coupled governing equation derived from the conservation of mass and momentum along with the energy equation for temperature and concentration. The finite element method (FEM) based on Galerkin weighted residual technique is used to compute the numerical result from these governing equations. The numerical computation is carried out for Lewis number (Le=0.1–50) and Richardson’s number (Ri=0.1–100). Computed numerical results of mass, temperature and velocity distribution are expressed graphically as iso-concentration lines, isotherm lines and streamlines respectively. Average Sherwood and Nusselt number values are used to show the mass and heat transfer rate from the heated and concentrated surface of the enclosure. It is found from the analysis that mass transfer strongly depends on Lewis number. Heat and mass transfer for uniformly heated and concentrated bottom wall is larger than the non-uniformly heated and concentrated bottom wall. Finally, a correlation has been done for average Nusselt and Sherwood numbers for both of the cases.

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.

Numerical study of double diffusive buoyancy forces induced natural convection in a trapezoidal enclosure partially heated from the right sidewall

A study of double-diffusive natural convection in a trapezoidal enclosure with a partial heated active right sidewall has been conducted numerically using the finite difference method. The length of the heated active part is equal to half of the inclined wall. Uniform different temperatures and concentrations are imposed along the active parts of the enclosure. The top and bottom boundaries of the enclosure, as well as inactive part of the right sidewall, are being insulated and impermeable. The species diffusivity of the fluid is considered to be constant, but the density varies linearly with the temperature and concentration. Double-diffusive convection for laminar two-dimensional incompressible flow with negligible radiation is expressed in terms of vorticity, temperature or energy, concentration and stream function. A Partial Differential Equation (PDE) technique is adopted to generate regular grid distribution in the physical space. The numerical results are reported for the effect of different heating cases, thermal Grashof numbers, and inclination angles on the contours of streamline, temperature, and concentration. Also, the relevant results for the average Nusselt and Sherwood numbers are demonstrated for several parameters including thermal Grashof number (103⩽GrT⩽106), Lewis number (0.5⩽Le⩽10), Prandtl number (0.7⩽Pr⩽10) at a fixed aspect ratio Ar=1 and buoyancy ratio N=-0.2.

Control of natural convection heat transfer in ferrofluid filled trapezoidal cavities with a magnetic dipole source

In this study, a numerical study of natural convection ferrofluid filled trapezoidal enclosure was performed under the influence of a magnetic dipole source. The left inclined wall of the cavity is heated and the right inclined wall is kept at constant temperature lower than that of the heater. Other horizontal walls of the trapezoidal enclosure are assumed to be adiabatic. The governing equations are solved with finite element method. The influence of the Rayleigh number, inclination angle of the side walls, strength of the magnetic dipole, horizontal and vertical location of the magnetic dipole on fluid flow and heat transfer are numerically investigated. It is observed that increasing values of Rayleigh number and inclination angles enhance the heat transfer. The external magnetic field parameters (strength and location) can be used to control the heat transfer and fluid flow inside the trapezoidal cavity.

Numerical study of magnetic field on mixed convection and entropy generation of nanofluid in a trapezoidal enclosure

The flow under influence of magnetic field is experienced in cooling electronic devices and voltage transformers, nuclear reactors, biochemistry and in physical phenomenon like geology. In this study, the effects of magnetic field on the flow field, heat transfer and entropy generation of Cu–water nanofluid mixed convection in a trapezoidal enclosure have been investigated. The top lid is cold and moving toward right or left, the bottom wall is hot and the side walls are insulated and their angle from the horizon are 15°, 30°, 45° and 60°. Simulations have been carried out for constant Grashof number of 104, Reynolds numbers of 30, 100, 300 and 1000, Hartmann numbers of 25, 50, 75 and 100 and nanoparticles volume fractions of zero up to 0.04. The finite volume method and SIMPLER algorithm have been utilized to solve the governing equations numerically. The results showed that with imposing the magnetic field and enhancing it, the nanofluid convection and the strength of flow decrease and the flow tends toward natural convection and finally toward pure conduction. For this reason, for all of the considered Reynolds numbers and volume fractions, by increasing the Hartmann number the average Nusselt number decreases. Furthermore, for any case with constant Reynolds and Hartmann numbers by increasing the volume fraction of nanoparticles the maximum stream function decreases. For all of the studied cases, entropy generation due to friction is negligible and the total entropy generation is mainly due to irreversibility associated with heat transfer and variation of the total entropy generation with Hartmann number is similar to that of the average Nusselt number. With change in lid movement direction at Reynolds number of 30 the average Nusselt number and total entropy generation are changed, but at Reynolds number of 1000 it has a negligible effect.

Unsteady MHD free convection nanofluid flows within a wavy trapezoidal enclosure with viscous and Joule dissipation effects

ABSTRACTThis article examines the unsteady magnetohydrodynamic free convection flows of Al2O3 (alumina)-water and single-walled carbon nanotube (SWCNT)-water nanofluids within a symmetrical wavy trapezoidal enclosure with viscous and Joule dissipation effects. The governing equations and the corresponding initial and boundary conditions are nondimensionalized and the resulting initial boundary value problem is solved using the mixed finite-element method with polynomial pressure projection stabilization. Streamline and isotherm plots are used to represent the numerical results for the velocity and temperature, respectively. The effects of time t, Hartmann number Ha, wall amplitude a, and solid volume fraction ϕ on the fluid flow and heat transfer are studied.

Mixed convection heat transfer in a CuO–water filled trapezoidal enclosure, effects of various constant and variable properties of the nanofluid

Different models for the thermophysical properties of the CuO–water nanofluid have been proposed in recent years. In the more sophisticated variable-property models, the thermophysical properties of the nanofluid are considered to be functions of the temperature and the volume fraction of the nanoparticles; while, in the constant-property models, they depend on the nanoparticles volume-fraction only. In this study, a new variable-property model is proposed for the thermophysical properties of the CuO–water nanofluid based on the experimental and the theoretical results available in the literature. The impacts of using the newly generated as well as the existing models on the flow and temperature fields during numerical simulation of mixed convection heat transfer in a trapezoidal enclosure filled with the CuO–water nanofluid are investigated. The simulation results are presented in terms of the average Nusselt number and the entropy generation within the enclosure for a wide range of Richardson numbers and volume fractions of the nanoparticles. In general, more heat transfer enhancements and higher entropy generations are observed employing the variable-property models which consider the effect of the Brownian motion as compared to using the constant-property Maxwell–Brinkman model. Furthermore, the results indicate that the effective thermal conductivity of the nanofluid for a variable-property model plays a pre-eminent role in the heat transfer and the entropy generation inside the enclosure. However, the differences between the average Nusselt number and the entropy generation obtained using the different considered variable-property models decrease with increasing the nanoparticles volume fraction.

Natural convection in a trapezoidal enclosure filled with carbon nanotube–EG–water nanofluid

In the present study, natural convection heat transfer inside a trapezoidal enclosure filled with carbon nanotube–EG–water nanofluid using variable properties has been numerically investigated. The bottom and top walls of trapezoidal enclosure are kept at constant temperatures Th and Tc, respectively, while the side walls of the cavity are thermally insulated. Using the finite volume method and the SIMPLER algorithm, the governing equations have been discretized. Simulations have been carried out for different aspect ratios, Rayleigh numbers of 103–106 as well as solid volume fractions of 0.0015, 0.03, and 0.045. The results show that at low Rayleigh number (Ra⩽104), the average Nusselt number NuAvg decreases with increasing the inclination angle (aspect ratio) at all solid volume fractions. While for Ra=106, the NuAvg increases and then decreases with inclination angle (aspect ratio) with maximum NuAvg occurring at γ=30°. Moreover, NuAvg increases with increasing Rayleigh number at fixed inclination angle (aspect ratio) and solid volume fraction.

Hydromagnetic Double-Diffusive Unsteady Mixed Convection in a Trapezoidal Enclosure Due to Uniform and Nonuniform Heating at the Bottom Side

This article focuses on exploring the effect of the magnetic field on double-diffusive mixed convection in a lid-driven trapezoidal enclosure with a uniformly (case I) and nonuniformly (case II) heated and concentrated bottom wall for unsteady flow. Numerical calculation is carried out for different values of Hartmann number (0–50) and Richardson number (0.1–100) at time τ = 1 using the finite-element method (FEM). Temperature, mass, and velocity distribution are expressed graphically as heatlines, masslines, and stream function, respectively. Nusselt and Sherwood numbers are used to demonstrate heat and mass transfer graphically. Better heat and mass transfer were found for case I than case II.

Effect of buoyancy ratio on unsteady thermosolutal combined convection in a lid driven trapezoidal enclosure in the presence of magnetic field

In this paper we concentrate to investigate the double diffusive unsteady mixed convection flow in a trapezoidal enclosure in presence of magnetic field. The bottom wall of the enclosure is heated and concentrated uniformly (case-I) and non-uniformly (case-II) while the top wall is cooled and moved uniformly with a constant velocity. Both side walls are adiabatic and impermeable. The coupled governing equations for this phenomenon is solved numerically using weighted residual based Galerkin technique of finite element method (FEM) for Richardson’s number (Ri=0.1–100) and Buoyancy ratio (Br=−10 to 10) at time τ=1.0. Reynolds number, Prandtl number and Lewis number are fixed at 100, 0.71 and 10 respectively. Streamlines, isotherm lines and iso-concentration lines are used to show the result graphically for velocity, temperature and mass distribution respectively. Nusselt and Sherwood number values are presented graphically to show the heat and mass transfer rate from the bottom surface of the cavity.

A Peclet Number Based Analysis of Mixed Convection for Lid-Driven Porous Trapezoidal Enclosure

Mixed convection flows in a lid-driven trapezoidal enclosure filled with porous medium are studied numerically using our recently proposed higher order compact (HOC) scheme presented in [1]. The top wall of the enclosure is allowed to move in its own plane at a constant speed, the bottom wall is heated uniformly while all other walls maintained at constant cold temperature. The relevant parameters in the present study are Darcy number (Da) (10–5 ≤ Da ≤ 10–3), Grashof number (Gr) = 105, Prandtl number (Pr) (0.026 ≤ Pr ≤ 10)) and Reynolds number (Re) (1 ≤ Re ≤ 100). The influence of convection is analyzed with Peclet number (Pe = Re.Pr). The flow distribution affects significantly temperature distributions at high Pe irrespective of Da. Effect of Peclet numbers has been further investigated for both natural convection and forced convection dominant regimes at high Da. Strong coupling between flow fields and temperature are observed at high Pe.

Natural Convection Heat Transfer In Trapezoidal Enclosure with Baffles Attached to Heated Wall

A two-dimensional solution of natural convection heat transfer in a trapezoidal enclosure using baffles attached to hot wall has been analyzed numerically. The vertical and inclined walls of the enclosure are isothermal while the bottom and top horizontal walls are insulated and the temperature of the vertical wall is higher than the temperature of the inclined wall. Governing equations are solved using the finite difference technique. The study included three cases: one baffle at position 0.5, two baffles at positions 0.2 and 0.5, and three baffles at positions 0.2, 0.4 and 0.6, in addition to Rayleigh number 10 3 , 10 4 and 10 5 and baffle length of 0.2, 0.3 and 0.4 used as governing parameters that are effective on heat transfer and fluid flow. Results for the mean Nusselt number, and contour maps of the streamlines and isotherms are presented. It is found that Nusselt number is an increasing with increasing in Rayleigh number while decreasing with increasing in the baffle length and number of baffles. Key words : Natural convection, Trapezoidal enclosure , Heat transfer , baffles

Transient Buoyancy- Driven Laminar Convection in an Inclined Three- Dimensional Trapezoidal Enclosure

Numerical analysis of transient laminar threedimensional buoyancy-driven convection in an inclined threedimensional trapezoidal air-filled enclosure was investigated in this paper. The right and left sidewalls of the enclosure are kept at constant cold temperatures. The bottom wall is maintained at a constant hot temperature , while the top wall is considered adiabatic. Numerical investigation is performed for Rayleigh numbers varied as 103 ≤ Ra ≤ 105 , while the trapezoidal enclosure inclination angle is varied as 0° ≤  ≤ 180°. Prandtl number is considered constant at Pr = 0.71. Flow and thermal fields are presented in both two and threedimensional pattern. Also, both local and average Nusselt numbers are calculated and discussed. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. The minimum average Nusselt number inside the trapezoidal cavity corresponds to the highest inclination angle [i.e., 180 ].While, the average Nusselt number reaches its maximum value at    30 . Moreover, when the Rayleigh number increases the average Nusselt number increases as expected.

Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures

This paper analyzes probable steady state flow structures and temperature patterns that may evolve during mixed convection within a lid-driven trapezoidal enclosure with cold top wall and hot bottom wall as the speed of moving lid varies with respect to the intensity of imposed temperature gradients. In this regard, a Grashof (Gr)–Reynolds (Re)–Prandtl (Pr) number formulation has been used to induce varying contributions from moving lid compared to that from imposed thermal gradients, where Grashof number has been varied from 103 to 105 at Re=1 and 100 for three different fluids of Pr=0.015, 0.7 and 10. Simulations have been performed for two different scenarios of isothermal (case 1) and non-isothermal (case 2) bottom wall with inclination angle of the side wall being kept at 45o. It has been found that non-isothermal bottom wall (case 2) leads to multiple steady states in either natural convection dominated regime (Gr/Re2≫1) or mixed convection regime (Gr/Re2∼O(1)) in convection dominated heat transport regime (Pr×Re≳1). Number of steady states are observed to be more in natural convection dominated regime at Re=1. The flow structures of various steady states are found to be crucial to achieve higher heat transfer rates for non-isothermal bottom wall.

Heatlines for Visualization of Heat Transport for Natural Convection within Porous Trapezoidal Enclosures with Various Wall Heating

A detailed study on natural convection heat transfer within porous trapezoidal enclosures has been carried out for two different cases. The effect of linearly heated side walls on flow pattern is investigated in case 1; whereas, the effect of linearly heated left wall and cold right wall is studied in case 2. In both cases, the bottom wall of the cavity is uniformly heated and the upper wall is adiabatic. The results are analyzed for a wide range of parameters such as Rayleigh number, Ra(103 ≤ Ra ≤ 106), Prandtl number, Pr(0.015 ≤Pr ≤ 988.24), and Darcy number, Da(10−5 ≤ Da ≤ 10−3).

Finite Element Analysis of MHD Free Convection within Trapezoidal Enclosures with Uniformly Heated Side Walls

A numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within trapezoidal enclosures. A finite element analysis is performed to investigate the effects of unifor heating and is also used for solving the Navier-Stokes and Energybalance equations.In this study, cold bottom walls, uniformly heated left and right (side) walls and insulated top walls with inclination angles (ф) are considered in a trapezoidal enclosure. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters, Prandtl numbers, (Pr = 0.026 - 0.7), and Rayleigh numbers (Ra = 10 3 - 10 5 ), Hartmann number (Ha = 50) with various tilt angles Ф = 45 0 , 30 0 and 0 0 (square).Numerical results are presented in terms of streamlines, isotherms, heat

Steady Natural Convection of Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure

Numerical investigation of free convection heat transfer in a differentially heated trapezoidal cavity filled with non-Newtonian Power-law fluid has been performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is maintained as uniformly cooled. The top and bottom surfaces are kept adiabatic with initially quiescent fluid inside the enclosure. Finite-volume-based commercial software FLUENT 14.5 is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number (Ra) ranging from 105 to 107, Prandtl number (Pr) from 100 to 10,000, and power-law index ( n) from 0.6 to 1.4. Outcomes have been reported in terms of isotherms, streamlines, and local Nusselt number for various Ra, Pr, n, and inclined angles. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and were in good agreement.

Natural Convection in a Trapezoidal Enclosure with Wavy Top Surface

The effects of various parameters, Rayleigh number (Ra), Darcy number (Da), and wave amplitude (a), on natural convection inside a trapezoidal enclosure with wavy top surface are studied. The enclosure is filled with seawater having Prandtl number (Pr) of 7.2 and uniformly heated on bottom and partially heated on inclined boundaries. The flow field and temperature distribution are observed when interested parameters are chosen for Ra = 104, 105, and 106, Da = 10−5, 10−4, and 10−3, anda=0.9, 1, and 1.1. FlexPDE, a finite element model builder, is used to solve the governing equations to obtain the numerical results displayed by streamlines and isotherms. From the study results, convection motion is affected by different parameters in which the increase in flow intensity and temperature distribution can be seen at higher Rayleigh and Darcy numbers. The wavy top surface has small influence on the flow field and temperature distribution compared to the influence of Rayleigh and Darcy numbers.

MHD natural convection and entropy generation in a trapezoidal enclosure using Cu–water nanofluid

The present work investigates the entropy generation and enhancement of heat transfer in natural convection flow and heat transfer using Copper (Cu)–water nanofluid in the presence of a constant magnetic field. The analysis uses a two dimensional trapezoidal enclosure with the left vertical wall and inclined walls kept in a low constant temperature and a heat source with constant heat flux placed on the bottom wall of the enclosure. The governing equations were discretized by the control volume method and solved numerically by SIMPLE algorithm. The computations were carried out for a wide range of the Rayleigh number (104⩽Ra⩽107), Hartman number (0⩽Ha⩽100) and solid volume fraction (0⩽ϕ⩽0.05). The results show that at Ra=104 and 105 the enhancement of the Nusselt number due to presence of nanoparticles increases with the Hartman number, but at higher Rayleigh number, a reduction has been observed. In addition it was observed that the entropy generation is decreased when the nanoparticles are present, while the magnetic field generally increases the magnitude of the entropy generation.

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.