Numerical solution of mixed convection in a lid-driven cavity with arc-shaped moving wall

2017 ◽  
Vol 34 (3) ◽  
pp. 869-891 ◽  
Author(s):  
Muneer A. Ismael
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Numerical Solution ◽  
Rotational Speed ◽  
Uniform Mesh ◽  
Content Type ◽  
Driven Cavity ◽  
Moving Wall ◽  
Mesh Grid ◽  
Rayleigh Numbers

Purpose This paper investigates a numerical treatment to steady mixed convection in a lid-driven square cavity with arc-shaped moving wall or lid. The horizontal walls are thermally insulated. The vertical left wall is kept isothermally at high temperature, while the right arc-shaped moving wall is kept isothermally at low temperature. Design/methodology/approach Finite difference method in Cartesian coordinates with the upwind scheme is used in numerical solution. The irregular curved boundary has been treated by invoking non-uniform mesh grid with the ability to generate boundary fitted nodes. Jensen’s formulas of Neumann’s boundary condition have derived for the non-uniform mesh grid. The arc-shaped moving wall is considered as a segment of a rotating cylinder; thus, the studied pertinent parameters are the rotational speed of the arc-shaped wall in both aiding and opposing directions ω = −1,000-1,000, the arc-wall radius Ro = 0.5099-1.534 which is governed by its center (X0, Y0) = (1.1, 0.5)-(2.45, 0.5) and the Rayleigh number Ra = 103 − 106. Findings The results have shown that for low Rayleigh numbers, the rotational speed enhances heat transfer irrespective to the direction of rotation, while for high Rayleigh numbers, the aiding anticlockwise rotation (negative ω) enhances the heat transfer, while the opposing clockwise rotation (positive ω) manifests a retardation effect on the heat transfer. For a motionless arc-wall, its radius is ineffective for aiding heat transfer, while for non-zero arc-shaped wall speed, the heat transfer is an increasing function of its radius. Originality/value The arc-shaped moving wall has never been investigated until now. Therefore, the originality of this paper is due to studying the mixed convection in a lid-driven cavity with moving arc-shaped wall and inspecting the effect of its curvature and rotational speed in both directions on the flow and thermal fields.

Numerical simulation of water/alumina nanofluid mixed convection in square lid-driven cavity

2019 ◽  
Vol 30 (5) ◽  
pp. 2781-2807
Author(s):  
Davood Toghraie ◽  
Ehsan Shirani
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Richardson Number ◽  
Hartmann Number ◽  
Two Phase ◽  
Content Type ◽  
Driven Cavity

Purpose The purpose of this paper is to investigate the mixed convection of a two-phase water–aluminum oxide nanofluid in a cavity under a uniform magnetic field. Design/methodology/approach The upper wall of the cavity is cold and the lower wall is warm. The effects of different values of Richardson number, Hartmann number, cavitation length and solid nanoparticles concentration on the flow and temperature field and heat transfer rate were evaluated. In this paper, the heat flux was assumed to be constant of 10 (W/m2) and the Reynolds number was assumed to be constant of 300 and the Hartmann number and the volume fraction of solid nanoparticles varied from 0 to 60 and 0 to 0.06, respectively. The Richardson number was considered to be 0.1, 1 and 5. Aspect ratios were 1, 1.5 and 2. Findings Comparison of the results of this paper with the results of the numerical and experimental studies of other researchers showed a good correlation. The results were presented in the form of velocity and temperature profiles, stream and isotherm lines and Nusselt numbers. The results showed that by increasing the Hartmann number, the heat transfer rate decreases. An increase from 0 to 20 in Hartmann number results in a 20 per cent decrease in Nusselt numbers, and by increasing the Hartmann number from 20 to 40, a 16 per cent decrease is observed in Nusselt number. Accordingly, it is inferred that by increasing the Hartmann number, the reduction in the Nusselt number is decreased. As the Richardson number increased, the heat transfer rate and, consequently, the Nusselt number increased. Therefore, an increase in the Richardson number results in an increase of the Nusselt number, that is, an increase in Richardson number from 0.1 to 1 and from 1 to 5 results in 37 and 47 per cent increase in Nusselt number, respectively. Originality/value Even though there have been numerous investigations conducted on convection in cavities under various configurations and boundary conditions, relatively few studies are conducted for the case of nanofluid mixed convection in square lid-driven cavity under the effect of magnetic field using two-phase model.

Upward and downward conjugate mixed convection heat transfer in a partially porous cavity

2016 ◽  
Vol 26 (1) ◽  
pp. 159-188 ◽  
Author(s):  
Abderrahim Bourouis ◽  
Abdeslam Omara ◽  
Said Abboudi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mixed Convection ◽  
Transfer Rate ◽  
Vertical Wall ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Content Type ◽  
Moving Wall ◽  
The Right

Purpose – The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer. The effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10) and thermal conductivity ratio (Rk=0.1, 1, 10, 100) are investigated. Design/methodology/approach – The studied system is a two dimensional lid-driven enclosure with thick vertical porous layer. The left vertical wall of the enclosure is allowed to move in its own plane at a constant velocity. The enclosure is heated from the right vertical wall isothermally. The left and the right vertical walls are isothermal but temperature of the outside of the right vertical wall is higher than that of the left vertical wall. Horizontal walls are insulated. The governing equations are solved by finite volume method and the SIMPLE algorithm. Findings – From the finding results, it is observed that: for the two studied cases, heat transfer rate along the hot wall is a decreasing function of thermal conductivity ratio irrespective of Richardson numbers contrary to the heat transfer rate along the fluid-porous layer interface which is an increasing function of thermal conductivity ratio. At forced convection dominant regime, the difference between heat transfer rate for upward and downward moving wall is insensitive to the thermal conductivity ratio. For downward moving wall, average Nusselt number is higher than that of upward moving wall. Practical implications – Some applications: building applications, furnace design, nuclear reactors, air solar collectors. Originality/value – From the bibliographic work and the authors’ knowledge, the conjugate mixed convection in lid-driven partially porous enclosures has not yet been investigated which motivates the present work that represent a continuation of the preceding investigations.

Effects of magnetic field and viscous dissipation on entropy generation of mixed convection in porous lid-driven cavity with corner heater

2016 ◽  
Vol 26 (5) ◽  
pp. 1548-1566 ◽  
Author(s):  
Sameh E Ahmed ◽  
Hakan F. Öztop ◽  
Khaled Al-Salem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Heat Transfer Fluid ◽  
Content Type ◽  
Driven Cavity ◽  
Corner Heater

Purpose – The purpose of this paper is to investigate the effects of magnetic field and viscous dissipation on mixed convection heat transfer, fluid flow and entropy generation in a porous media filled square enclosure heated with corner isothermal heater. Design/methodology/approach – Finite volume method has been used to solve governing equations. A code is developed by FORTRAN and entropy generation is calculated from the obtained results of velocities and temperature. Results are presented via streamlines, isotherms, local and mean Nusselt number for different values of Richardson number (0.001=Ri=100), Hartmann number (0.001=Ha=100), Darcy number (0.001=Da=0.1), length of heaters (0.25=hx=hy=0.75) and viscous dissipation factors (10−4=ε=10−6). Findings – It is observed that entropy is generated mostly due to lid-driven wall and right side of the heater. Entropy generation decreases with increasing of Hartmann number and heat transfer increases with decreasing of viscous parameter. Originality/value – The originality of this work is to application of magnetic field and viscous dissipation on entropy generation in a lid-driven cavity with corner heater. Here, both corner heater and the external forces are original parameters.

Effects of two-phase nanofluid model on convection in a double lid-driven cavity in the presence of a magnetic field

2019 ◽  
Vol 29 (4) ◽  
pp. 1272-1299 ◽  
Author(s):  
Ammar I. Alsabery ◽  
Taher Armaghani ◽  
Ali J. Chamkha ◽  
Muhammad Adil Sadiq ◽  
Ishak Hashim
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Square Cavity ◽  
Two Phase ◽  
Content Type ◽  
Driven Cavity ◽  
Horizontal Wall

Purpose The aim of this study is to investigate the effects of two-phase nanofluid model on mixed convection in a double lid-driven square cavity in the presence of a magnetic field. The authors believe that this work is a good contribution for improving the thermal performance and the heat transfer enhancement in some engineering instruments. Design/methodology/approach The current work investigates the problem of mixed convection heat transfer in a double lid-driven square cavity in the presence of magnetic field. The used cavity is filled with water-Al2O3 nanofluid based on Buongiorno’s two-phase model. The bottom horizontal wall is maintained at a constant high temperature and moves to the left/right, while the top horizontal wall is maintained at a constant low temperature and moves to the right/left. The left and right vertical walls are thermally insulated. The dimensionless governing equations are solved numerically using the Galerkin weighted residual finite element method. Findings The obtained results show that the heat transfer rate enhances with an increment of Reynolds number or a reduction of Hartmann number. In addition, effects of thermophoresis and Brownian motion play a significant role in the growth of convection heat transfer. Originality/value According to above-mentioned studies and to the authors’ best knowledge, there has no study reported the MHD mixed convection heat transfer in a double lid-driven cavity using the two-phase nanofluid model. Thus, the authors of the present study believe that this work is valuable. Therefore, the aim of this comprehensive numerical study is to investigate the effects of two-phase nanofluid model on mixed convection in a double lid-driven square cavity in the presence of a magnetic field. The authors believe that this work is a good contribution for improving the thermal performance and the heat transfer enhancement in some engineering instruments.

scholarly journals Conjugate heat transfer performance of stepped lid-driven cavity with Al2O3/water nanofluid under forced and mixed convection

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Naveen Janjanam ◽  
Rajesh Nimmagadda ◽  
Lazarus Godson Asirvatham ◽  
R. Harish ◽  
Somchai Wongwises
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mixed Convection ◽  
Conjugate Heat Transfer ◽  
Heat Transfer Performance ◽  
Pure Water ◽  
Interface Temperature ◽  
Transfer Model ◽  
Transfer Performance ◽  
Driven Cavity

AbstractTwo-dimensional conjugate heat transfer performance of stepped lid-driven cavity was numerically investigated in the present study under forced and mixed convection in laminar regime. Pure water and Aluminium oxide (Al2O3)/water nanofluid with three different nanoparticle volume concentrations were considered. All the numerical simulations were performed in ANSYS FLUENT using homogeneous heat transfer model for Reynolds number, Re = 100 to 500 and Grashof number, Gr = 5000, 13,000 and 20,000. Effective thermal conductivity of the Al2O3/water nanofluid was evaluated by considering the Brownian motion of nanoparticles which results in 20.56% higher value for 3 vol.% Al2O3/water nanofluid in comparison with the lowest thermal conductivity value obtained in the present study. A solid region made up of silicon is present underneath the fluid region of the cavity in three geometrical configurations (forward step, backward step and no step) which results in conjugate heat transfer. For higher Re values (Re = 500), no much difference in the average Nusselt number (Nuavg) is observed between forced and mixed convection. Whereas, for Re = 100 and Gr = 20,000, Nuavg value of mixed convection is 24% higher than that of forced convection. Out of all the three configurations, at Re = 100, forward step with mixed convection results in higher heat transfer performance as the obtained interface temperature is lower than all other cases. Moreover, at Re = 500, 3 vol.% Al2O3/water nanofluid enhances the heat transfer performance by 23.63% in comparison with pure water for mixed convection with Gr = 20,000 in forward step.

Effects of moving lid direction on mixed convection and entropy generation in a cubical cavity with longitudinal triangular fin insertion

2017 ◽  
Vol 27 (4) ◽  
pp. 839-860 ◽  
Author(s):  
Lioua Kolsi ◽  
Hakan F. Öztop ◽  
Nidal Abu-Hamdeh ◽  
Borjini Mohamad Naceur ◽  
Habib Ben Assia
Keyword(s):  
Mixed Convection ◽  
Entropy Generation ◽  
Three Dimensional ◽  
Thermal Conductivity Ratio ◽  
Governing Equations ◽  
Content Type ◽  
Driven Cavity ◽  
Triangular Fin ◽  
Cubical Cavity ◽  
3D Problem

Purpose The main purpose of this work is to arrive at a three-dimensional (3D) numerical solution on mixed convection in a cubic cavity with a longitudinally located triangular fin in different sides. Design/methodology/approach The 3D governing equations are solved via finite volume technique by writing a code in FORTRAN platform. The governing parameters are chosen as Richardson number, 0.01 ≤ Ri ≤ 10 and thermal conductivity ratio 0.01 ≤ Rc ≤ 100 for fixed parameters of Pr = 0.7 and Re = 100. Two cases are considered for a lid-driven wall from left to right (V+) and right to left (V−). Findings It is observed that entropy generation due to heat transfer becomes dominant onto entropy generation because of fluid friction. The most important parameter is the direction of the moving lid, and lower values are obtained when the lid moves from right to left. Originality The main originality of this work is to arrive at a solution of a 3D problem of mixed convection and entropy generation for lid-driven cavity with conductive triangular fin attachments.

scholarly journals A finite element analysis on combined convection and conduction in a channel with a thick walled cavity

2014 ◽  
Vol 24 (8) ◽  
pp. 1888-1905 ◽  
Author(s):  
M.M. Rahman ◽  
Hakan Oztop ◽  
S. Mekhilef ◽  
R. Saidur ◽  
A. Chamkha ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Mixed Convection ◽  
Conjugate Heat Transfer ◽  
Transfer Problem ◽  
Thick Wall ◽  
Thermal Conductivity Ratio ◽  
Element Analysis ◽  
Content Type ◽  
Combined Convection

Purpose – The purpose of this paper is to examine the effects of thick wall parameters of a cavity on combined convection in a channel. In other words, conjugate heat transfer is solved. Design/methodology/approach – Galerkin weighted residual finite element method is used to solve the governing equations of mixed convection. Findings – The streamlines, isotherms, local and average Nusselt numbers are obtained and presented for different parameters. It is found heat transfer is an increasing function of dimensionless thermal conductivity ratio. Originality/value – The literature does not have mixed convection and conjugate heat transfer problem in a channel with thick walled cavity.

Nanofluidic thermal-fluid transport in a split-driven porous system working under a magnetic environment

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Dipak Kumar Mandal ◽  
Milan Kumar Mondal ◽  
Nirmalendu Biswas ◽  
Nirmal K. Manna ◽  
Rama Subba Reddy Gorla ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous System ◽  
Nanoparticle Suspension ◽  
Porous Substance ◽  
Content Type ◽  
Driven Cavity ◽  
Flow Physics ◽  
Thermal Buoyancy ◽  
High Heat Transfer

Purpose This study aims to focus on a thermo-fluid flow in a partially driven cavity (PDC) using Cu-water nanoliquid, magnetic field and porous substance. The cooling and sliding motion are applied on the upper half of the vertical walls and the bottom wall is heated. Thermal characteristics are explored to understand magnetohydrodynamic convection in a nanoliquid filled porous system from a fundamental viewpoint. The governing parameters involved to cater to the moving speed of the sidewalls and partial translation direction are the relative strength of thermal buoyancy, porous substance permeability, magnetic field intensity, nanoparticle suspension and orientation of the cavity. Design/methodology/approach The coupled transport equations of the problem are solved using an in-house developed finite volume-based computing code. The staggered nonuniform grids along the x and y directions are used. The SIMPLE algorithm technique is considered for the iterative solution of the discretized equations with the convergence check of the continuity mass defect below 10–10. Findings The present study unveils that the heat transfer enhances at higher Ri with the increasing value of Re, irrespective of the presence of a porous substance or magnetic field or the concentration of nanofluid. Apart from different flow controlling parameters, the wall motions have a significant contribution to the formation of flow vortices and corresponding heat transfer. Orientation of the cavity significantly alters the transport process within the cavity. The upward wall velocity for both the sidewalls could be a better choice to enhance the high heat transfer (approximately 88.39% at Richardson and Reynolds numbers, respectively, 0.1 and 200). Research limitations/implications Considering other multi-physical scenarios like porous layers, conducting block, microorganisms and the present investigation could be further extended to analyze a problem of complex flow physics. Practical implications In this study, the concept of partially driven wall motion has been adopted under the Cu-water nanoliquid, magnetic field, porous substance and oblique enclosure. All the involved flow-controlling parameters have been experimented with under a wide parametric range and associated thermo-flow physics are analyzed in detail. This outcome of this study can be very significant for designing as well as controlling thermal devices. Originality/value The convective process in a partially driven cavity (PDC) with the porous medium has not been investigated in detail considering the multi-physical scenarios. Thus, the present effort is motivated to explore the thermal convection in such an oblique enclosure. The enclosure is heated at its bottom and has partially moving-wall cold walls. It consists of various multi-physical conditions like porous structure, magnetic field, Cu–H2O nanoliquid, etc. The system performance is addressed under different significant variables such as Richardson number, Reynolds number, Darcy number, Hartmann number, nanoliquid concentration and orientation of cavity.

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