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The main objective of the present numerical investigation is to understand the effect of partially active thermal zones and density inversion on the buoyancy-driven convection of cold water near its maximum density under the influence of uniform magnetic field inside a square cavity. The partially heated or cooled zones are placed along the vertical sidewalls of the cavity while the other inactive portions of the walls are considered to be adiabatic and thermally insulated. The length of the partially active thermal zones is measured to be equal to half the length of the cavity's height. When the locations of heating and cooling zones are placed in different positions, it provides a significant effect on flow pattern and the rate of heat transfer. To investigate this location effect, the thermally active zones are placed in a combination of five different relative positions along the vertical sidewalls. The modeled equations are solved using finite volume method with Semi-Implicit Method for Pressure Linked Equation algorithm. The numerical coding is done through the FORTRAN 95 programming for numerical simulation and the results attained are represented graphically in the form of flow field and temperature distribution for various values of density inversion parameter, Hartmann number, and for various positions of thermal zones. The results reveal that the heat transfer rate behaves nonlinearly on increasing the density inversion parameter values. The high transfer rate is perceived for the location middle–middle when T m < 0.5 and for top–bottom when T m ≥ 0.5 for all values of the Hartmann number. [ABSTRACT FROM AUTHOR]

The aim of the present numerical study is to analyze the effect of cooler location and aspect ratio and position of the hot solid body inside the enclosure on three-dimensional natural convection flow in a cubical enclosure. The cooler and heater positions and aspect ratio of the heater in a cavity are examined under different combinations of partially cooling vertical sidewalls and, hot solid body in the cubical cavity. That is, (i) different cooler locations with a fixed size of the hot solid body, and, (ii) centrally located hot solid body with different aspect ratio. The three-dimensional convective flow and thermal arrangements in the enclosure are analyzed using the distribution of streamlines, isosurfaces, and Nusselt number. It is found that the cooler location and aspect ratio of hot solid body play a key role on convective cooling and energy transport inside the enclosure. The unit aspect ratio of hot solid body provides higher energy transport inside the enclosure for all cooler positions. [ABSTRACT FROM AUTHOR]

The aim of the present study is to analyze the convective flow and heat transfer of nanofluid in an inclined cavity filled with heat generating porous medium using the local thermal non-equilibrium model. The horizontal bottom wall of the cavity is maintained at a constant higher temperature while the left and right vertical walls are maintained at a constant lower temperature. The top wall is to be kept as adiabatic. The Darcy model is adopted for flow through the porous medium and the Boussinesq approximation is taken into account. The pores are saturated by a water-based nanofluid consisting of Cu nanoparticles. The governing equations are solved iteratively by finite difference based Alternating Direction Implicit (ADI) method. The results are discussed by various combinations of parameters involved in the study. The average heat transfer rate decreases when increasing the values of nanoparticle volume fraction for the case of high Rayleigh numbers. The heat transfer rate is enhanced by increasing values of the modified conductivity ratio and the porosity of the media. The results have possible applications in the heat-storage nanofluid-saturated porous systems. [ABSTRACT FROM AUTHOR]

The present study analyzes natural convective flow and heat transfer in a wavy cavity saturated with porous medium. The sidewalls of the cavity are maintained at constant temperatures where higher temperature is applied on the vertical left wall while the wavy right wall is cooled at a lower temperature. The remaining top and bottom walls are taken to be adiabatic. The Darcy model is adopted for the fluid flow through the porous medium. The governing equations and boundary conditions are solved using the finite difference method over a range of cavity aspect ratios, wavy wall amplitudes, number of undulations and Darcy-Rayleigh numbers. The waviness of the cavity enhances the heat transfer inside the cavity, and the heat transfer rate is more enhanced when the aspect ratio of the cavity is close to 1. The study is applicable to the design of solar heating systems and geothermal reservoirs. [ABSTRACT FROM AUTHOR]

This paper examines numerically by using the finite difference method the laminar steady magneto-hydrodynamic natural convection in an inclined T-shaped enclosure filled with different types of nanofluids. A uniform heat source is embedded on a part of the upper wall of the enclosure. Both left and right sidewalls of the enclosure leg are maintained at a constant cold temperature, while the other portions of the enclosure walls are considered adiabatic. A magnetic field is applied vertically downward on the bottom wall of the enclosure. Based on the numerical results, the effects of the dominant parameters such as Rayleigh number, Hartmann number, inclination angle, solid volume fraction, location and length of the heat source and enclosure aspect ratio are examined. The numerical results are obtained for Hartmann number varying as 0 ⩽ Ha ⩽ 100, inclination angle varying as 0 ⩽ Φ ⩽ 90°, Rayleigh numbers varying as 10 3 ⩽ Ra ⩽ 10 6 , aspect ratio 0.3 ⩽ AR ⩽ 0.9, heat source length 0.2 ⩽ B ⩽ 0.8, heat source location 0.2 ⩽ D ⩽ 0.5 and the solid volume fractions varying as 0 ⩽ ϕ ⩽ 0.2. Comparison with previously published numerical work is performed and a good agreement between the results is observed. It is found that the mean Nusselt number increases with the increase of Rayleigh number, inclination angle, aspect ratio, heat source location and volume fraction of nanoparticles, while, it decreases when the Hartmann number and heat source length increase. [ABSTRACT FROM AUTHOR]

Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work. The vertical right and left sidewalls of the cavity are maintained at constant cold temperatures. The lower wall is subjected to a constant hot temperature, while the upper one is considered insulated. Computations are performed for Rayleigh numbers varied as 10 3 ⩽ Ra ⩽ 10 5 , while the trapezoidal cavity inclination angle is varied as 0° ⩽ Φ ⩽ 180°. Prandtl number is considered constant at Pr = 0.71. Second law of thermodynamics is applied to obtain thermodynamic losses inside the cavity due to both heat transfer and fluid friction irreversibilities. The variation of local and average Nusselt numbers is presented and discussed, while, streamlines, isotherms and entropy contours are presented in both two and three-dimensional pattern. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. Also, the inclination angle effect on the total entropy generation becomes insignificant when the Rayleigh number is low. Moreover, when the Rayleigh number increases the average Nusselt number increases. [ABSTRACT FROM AUTHOR]

A steady laminar two-dimensional magneto-hydrodynamics (MHD) natural convection flow in a square enclosure filled with an electrically conducting fluid is numerically investigated using Lattice Boltzmann Method (LBM). The left and right vertical sidewalls of the square enclosure are maintained at hot and cold temperatures respectively. The horizontal top and bottom walls are considered thermally insulated. An adiabatic square shaped body is located in the center of a square enclosure and an external magnetic field is applied parallel to the horizontal x -axis. In the present work, the following parametric ranges of the non-dimensional groups are utilized: Hartmann number is varied as 0 ⩽ Ha ⩽ 50, Rayleigh number is varied as 10 3 ⩽ Ra ⩽ 10 5 , Prandtl number is varied 0.05 ⩽ Pr ⩽ 5. It is found that the Hartmann number, Rayleigh number, and Prandtl number have an important role on the flow and thermal characteristics. It is found that when the Hartmann number increases the average Nusselt number decreases. The results also explain that the effect of magnetic field on flow field increases by increasing Prandtl number. However, the Prandtl number effect on the average Nusselt number with a magnetic field is less than the case without a magnetic field. Comparisons with previously published numerical works are performed and good agreements between the results are observed. [ABSTRACT FROM AUTHOR]

The present study analyzed convective heat transfer and fluid flow characteristics of nanofluid in a two-dimensional square cavity under different combinations of thermophysical models of nanofluids. The right vertical wall temperature is varying linearly with height and the left wall is maintained at low temperature whereas the horizontal walls are adiabatic. Finite volume method is used to solve the governing equations. Two models are considered to calculate the effective thermal conductivity of the nanofluid and four models are considered to calculate the effective viscosity of the nanofluid. Numerical solutions are carried out for different combinations of effective viscosity and effective thermal conductivity models with different volume fractions of nanoparticles and Rayleigh numbers. It is found that the heat transfer rate increases for Models M1 and M3 on increasing the volume fraction of the nanofluid, whereas heat transfer rate decreases for Model M4 on increasing the volume fraction of the nanoparticle. The difference among the effective dynamic viscosity models of nanofluid plays an important role here such that the average Nusselt number demonstrates an increasing or decreasing trend with the concentration of nanoparticle. [ABSTRACT FROM AUTHOR]

A numerical study is performed to investigate the effects of amplitude and phase deviation of sinusoidal temperature distribution on the convective flow and heat transfer of nanofluids in a square cavity. The horizontal walls of the cavity are adiabatic. The governing equations are solved by the finite volume method with the SIMPLE algorithm. The results are discussed for different combinations of phase deviation, amplitude ratio, volume fraction of nanoparticles, and Rayleigh numbers. It is observed that the heat transfer rate is increased when increasing the amplitude ratio and volume fraction of nanoparticles. The heat transfer rate behaves nonlinearly with the Rayleigh number and the phase deviation, attaining the maximum at 3π/4. [ABSTRACT FROM AUTHOR]

A numerical study has been performed on buoyancy-induced convection in a square porous cavity. The vertical sidewalls of the cavity are maintained with sinusoidal temperature distribution. The finite volume method is used to numerically solve the nondimensional governing equations. The Brinkman Forchheimer extended Darcy model is used in the present study. The results are analyzed over a range of the amplitude ratio, phase deviation, porosity, and Grashof and Darcy numbers. It is found that the heat transfer rate is increased when increasing the amplitude ratio, porosity, and Darcy number. The nonuniform heating on both sidewalls provides higher heat transfer rate than the nonuniform heating of one wall. [ABSTRACT FROM AUTHOR]

We deal with the effect of an adiabatic partition and magnetic field on magneto-hydrodynamic natural convection flow and heat transfer in a partitioned enclosure. The horizontal walls of the enclosure are adiabatic and the vertical walls are isothermal. The adiabatic partition is attached to either the bottom adiabatic wall or hot isothermal wall of the enclosure. The governing equations are discretized by the finite-volume method and are solved by iteration. We discuss transient and steady-state cases for different combinations of parameters in the study. The results are obtained for different values of the Hartmann, Grashof and Prandtl numbers and different positions of the partition, and presented graphically. The heat transfer and fluid flow characteristics inside the enclosure are affected by the partition and magnetic field. We find that the heat transfer rate is enhanced when the partition is attached to the adiabatic wall. The heat transfer rate is suppressed when the Hartmann number is increased. In the presence of the magnetic force, the heat transfer rate is increased by 1 and 2% when the Prandtl number is increased from 0.015 to 0.054 for the vertical and horizontal partition cases, respectively. [ABSTRACT FROM AUTHOR]

In the present study, a numerical analysis is performed to understand the mixed convection flow, and heat and mass transfer with Soret effect in a two-sided lid-driven square cavity. The horizontal walls of the cavity are adiabatic and impermeable, while vertical walls are kept at constant but different temperatures and concentrations. The vertical walls move in a constant velocity. According to the direction of the movement of walls, three cases have been studied for different combinations of parameters involved in the study. The governing unsteady equations are solved numerically by the finite volume method with the SIMPLE algorithm. The results are presented graphically in the form of streamlines, isotherms, and velocity profiles. Heat and mass transfer rates are reduced if both walls are moving the in same direction, while heat and mass transfer rates are enhanced if the walls are moving in the opposite direction. [ABSTRACT FROM AUTHOR]

The main objective of this article is to study the effect of discrete heating on free convection heat transfer in a rectangular porous enclosure containing a heat-generating substance. The left wall of the enclosure has two discrete heat sources and the right wall is isothermally cooled at a lower temperature. The top and bottom walls, and the unheated portions of the left wall are adiabatic. The vorticity-stream function formulation of the governing equations is numerically solved using an implicit finite difference method. The effects of aspect ratio, Darcy number, heat source length, and modified Rayleigh number on the flow and heat transfer are analyzed. The numerical results reveal that the rate of heat transfer increases as the modified Rayleigh number and the Darcy number increases, but decreases on increasing the aspect ratio. The average heat transfer rate is found to be higher at the bottom heater than at the top heater in almost all considered parameter cases except for ε = 0.5. Also, the maximum temperature takes place generally at the top heater except for the case ε = 0.5, where the maximum temperature is found at the bottom heater. Further, the numerical results reveal that the maximum temperature decreases with the modified Rayleigh number and increases with the aspect ratio. [ABSTRACT FROM AUTHOR]

Abstract: Natural convection of water near its density maximum in the presence of magnetic field in a cavity with temperature dependent properties is studied numerically. The viscosity and thermal conductivity of the water is varied with reference temperature and calculated by cubic polynomial. The finite volume method is used to solve the governing equations. The results are presented graphically in the form of streamlines, isotherms and velocity vectors and are discussed for various combinations of reference temperature parameter, Rayleigh number, density inversion parameter and Hartmann number. It is observed that flow and temperature field are affected significantly by changing the reference temperature parameter for temperature dependent thermal conductivity and both temperature dependent viscosity and thermal conductivity cases. There is no significant effect on fluid flow and temperature distributions for temperature dependent viscosity case when changing the values of reference temperature parameter. The average heat transfer rate considering temperature-dependent viscosity are higher than considering temperature-dependent thermal conductivity and both temperature-dependent viscosity and thermal conductivity. The average Nusselt number decreases with an increase of Hartmann number. It is observed that the density inversion of water leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. The heat transfer rate behaves non-linearly with density inversion parameter. The direction of external magnetic field also affect the fluid flow and heat transfer. [Copyright &y& Elsevier]

Abstract: Transient natural convection of cold water around its density maximum in a square cavity is studied numerically. Nine different positions of the active zones are considered. The governing equations are solved using Control volume method with power low scheme. The results obtained for various values of parameters are presented graphically in the form of streamlines and isotherms. It is found that the average Nusselt number behaves non-linearly as a function of Grashof number. The heat transfer rate is decreased in the density maximum regions. [Copyright &y& Elsevier]

Abstract: The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study. [Copyright &y& Elsevier]

Abstract: This study reports a numerical investigation of the convective flow and heat transfer in a square porous cavity with partially active thermal walls. Five different heating and cooling zones are considered along the vertical walls while the remaining portions of the side walls as well as the top and bottom of the cavity are adiabatic. The Brinkman Forchheimer extended Darcy model is used in the present study and the resulting governing equations are solved by finite volume method with SIMPLE algorithm. The computations are carried out for a wide range of parameters and the results are presented graphically. The results reveal that the location of heating and cooling zones has a significant influence on the flow pattern and the corresponding heat transfer in the enclosure. The location of partial heating has different effect on velocity and heat transfer, and the heat transfer rate approaches to a constant value for very low values of the Darcy number. [Copyright &y& Elsevier]

Highlights: [•] Convection very strong when Ra is high and Ha =0. [•] Isotherms smooth when Ra is low and Ha is high. [•] Maximum stream function increases by adding nano-particle. [•] Flow circulation decreases when magnetic orientation angle increases. [•] Nusselt number ratio increases when Ra increases. [ABSTRACT FROM AUTHOR]

Highlights: [•] Ha decelerates the flow field. [•] Ha enhances conduction. [•] Magnetic field orientation is important. [•] Radiation parameter important. [•] Nu decreases as Ha increases. [ABSTRACT FROM AUTHOR]