Mixed convection in a lid-driven triangular enclosure filled with nanofluids

This paper presents the results of a numerical study on the mixed convection in a lid-driven triangular enclosure filled with a water–Al₂O₃ nanofluid. A comparison study between two different scenarios of upward and downward left sliding walls is presented. The effects of parameters such as Richardson number, solid volume fraction and the direction of the sliding wall motion on the flow and temperature fields as well as the heat transfer rate are examined. The results show that the addition of Al₂O₃ nanoparticles enhances the heat transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the downward sliding wall motion results in a stronger flow circulation within the enclosure and hence, a higher heat transfer rate.     

Mixed convection in a square vented enclosure filled with a porous medium

Steady mixed convection flow in a vented enclosure with an isothermal vertical wall and filled with a fluid-saturated porous medium is investigated numerically. The forced flow conditions are imposed by providing an inlet at the bottom surface, and a vent at the top, facing the inlet. The nature and the basic characteristics of the mixed aiding as well as mixed opposing flows that arise are investigated using the Darcy law model. The governing parameters are the Rayleigh number, Péclet number, and the width of the inlet as a fraction of the height of the square enclosure. These parameters are varied over wide ranges and their effect on the heat transfer characteristics is studied in detail.     

On the effects of viscous dissipation and pressure work in free convection loops

The effects of viscous dissipation and pressure work are examined theoretically for laminar free convection loops. The appropriate governing equations are derived. Whereas previous work has considered only dissipation effects, the present paper shows that dissipation and pressure work effects are of comparable magnitude and must be considered together. Analytical solutions are presented for several open and closed loops. Both constant flux and constant temperature heating conditions are examined. Viscous dissipation and pressure work effects are found to have opposing influences on the flow in a loop. The former can enhance a flow for certain heating orientations, but the latter is usually dominant and retards a flow.     

Effect of pressure stress work and viscous dissipation in some natural convection flows

A regular two-parameter perturbation analysis is presented here to study the effects of both viscous dissipation and pressure stress on natural convection flows. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall-plume. For high gravity levels, stress work effects may be important for gases at very low temperatures, and for high Prandtl number liquids. Significant changes in heat transfer and flow quantities are observed even at moderate values of the perturbation parameters. For the entire range of Prandtl number values considered, the viscous dissipation term is seen to inhibit heat transfer from the surface for heated upward flows. The pressure term enhances heat transfer from the surface for lower Prandtl numbers. However, this effect is seen to reverse at Pr = 100, for both the isothermal and uniform flux surfaces. It is observed that viscous dissipation effects on heat transfer are much smaller than those due to the pressure stress, for many practical circumstances.     

Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall

Conjugate heat transfer by mixed convection and conduction in lid-driven enclosures with thick bottom wall has been studied by a numerical method. The enclosure is heated from the bottom wall isothermally. Temperature of the top moving wall, which has constant flow speed, is lower than that of the outside of bottom wall. Vertical walls of the enclosure are adiabatic. Governing parameters are solved for a wide range of Richardson numbers (0.1 ≤ Ri ≤ 10), ratio of height of bottom wall to enclosure height (0.1 ≤ h/H ≤ 0.5) and thermal conductivity ratio (0.01 ≤ λ_f/λ_s ≤ 10). Obtained results showed that heat transfer decreases with increasing of λ_f/λ_s ratio, Richardson number and thickness ratio of the wall. Flow strength is affected for only higher values of λ_f/λ_s ratio.     

Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure

A computational work has been done to investigate the effects of mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure. Finite difference method is used to solve governing equations of mixed convection for different parameters as Hartmann number, Richardson number, nanoparticle volume rate in partially heated and wavy walled enclosure. It is found that the rate of heat transfer decreases with increasing the Hartmann number. The rate of heat transfer can be enhanced or reduced by increasing the volume fraction of nanoparticles based on Hartmann and Richardson numbers.     

Natural convection in a square enclosure with a hot source

The aim of this paper is to analyse the convective heat transfer generated by a source with three different heights (ζ). This strip is located in the middle of a square enclosure. In detail the experimental analysis was carried out using holographic interferometry, to study the effect of the heat transfer, and a 2D-PIV system, to analyse the dynamic behaviour of the phenomenon. The comparison is based both on the evaluation of the Nusselt numbers at different Rayleigh numbers and on the study of the velocity fields at the same Rayleigh numbers in different configurations. During the experimental analysis we can see how the height of the strip influences the distribution of the velocity fields and consequently the heat transfer efficiency. Three different heights are analysed: ζ = 0, ζ = 0.25 and ζ = 0.5. The study shows how the natural convective heat transfer worsens with the increase in the source height. This can clearly be seen by analysing the upper side of the strip, which was studied for each geometrical configuration, and is also confirmed by the results on the lateral sides, analysed only for ζ = 0.25 and ζ = 0.5.Finally the experimental data are compared with the results obtained through a numerical simulation performed using the volume finite software, Fluent 6.3.26. The aim of this comparison is to validate the numerical procedure, which is useful for enlarging the Rayleigh number range.     

Effect of viscous dissipation and pressure stress work in natural convection along a vertical isothermal plate. New results

The steady laminar boundary layer flow along a vertical stationary isothermal plate is studied taking into account the viscous dissipation and pressure stress work of the fluid. The results are obtained with the direct numerical solution of the boundary layer equations without any approximation. It was found that the variation of wall heat transfer and wall shear stress along the plate is quite different compared to that given by the approximate perturbation method.     

Combined convection heat transfer in a porous lid-driven enclosure due to heater with finite length

A numerical work is performed to analyze combined convection heat transfer and fluid flow in a partially heated porous lid-driven enclosure. The top wall of enclosure moves from left to right with constant velocity and temperature. Heater with finite length is located on the fixed wall where its center of location changes along the walls. The finite volume-based finite-difference method is applied for numerical experiments. Parameters effective on flow and thermal fields are Richardson number, Darcy number, center of heater and heater length. The results are shown that the best heat transfer is formed when the heater is located on the left vertical wall.     

Mixed convection of nanofluid in a square enclosure with a hot bottom wall and a conductive half-immersed rotating circular cylinder

In this study. The mixed convection in a square enclosure with a hot bottom wall and a conductive half-immersed rotating cylinder from its top wall is investigated numerically. The enclosure is filled with a copper-water nanofluid. The upper half of the cylinder is cooled by the surrounding air, whereas its solid lower half is exposed to the nanofluid. The two left and right sidewalls of the enclosure, together with the remaining regions of its top wall, are assumed to be adiabatic. The dimensionless governing equations are expressed for the velocity and the temperature formulation, and they are modeled by using COMSOL code based on the Galerkin finite element method. In the present work, the geometrical aspect ratio is considered to be varied as (0.2 ≤ R/L ≤ 0.5), the thermal conductivity ratio is considered to be varied as 1 ≤ K_r ≤ 10, the angular rotational velocity is considered to be varied as 0 ≤ $\mathrm{\Omega }$ ≤ 1000, and the ambient convection heat transfer coefficient is considered to be varied as 5 ≤ h ≤ 20. However, the solid volume fraction (ϕ), the Prandtl number (Pr), and the Rayleigh number (Ra) are considered to be fixed at ϕ = 0.02, Pr = 6.2, and Ra = 10⁵. It was found that the convection effect becomes more pronounced when the angular rotational velocity increases, whereas a reverse behavior is observed with an increase in the geometrical aspect ratio. Also, it was observed that the heat explorer depth begins to decrease as the angular rotational velocity increases until the increases of angular rotational velocity effect is diminishing therefore it may be the main target of the present research. This observation is seen for both considered values of the thermal conductivity ratio and the geometrical aspect ratio. Moreover, it was observed that both the local and the average Nusselt numbers increase as the geometrical aspect ratio increases. A comparison with a previously published numerical work is performed, and a good agreement between the results is observed.     

Two-dimensional natural convection in a porous triangular enclosure with a square body

A two-dimensional numerical solution for steady-state buoyancy induced convection in a right-triangular enclosure with a square body is obtained using finite difference technique. The solid body is located far from the origin with the distance of 0.3 in both directions. It is considered that the temperature of the bottom wall of triangular enclosure is higher than that of inclined wall while the vertical wall is insulated. To obtain the effects of the presence of a square body on heat transfer and fluid flow inside the enclosure, four different temperature boundary conditions were applied for the body as heated, cooled, neutral and adiabatic at different Ra numbers. It is observed that fluid flow and temperature fields strongly depend on thermal boundary conditions of the body.     

Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder

Mixed convection heat transfer in a lid-driven cavity with a rotating cylinder was analyzed numerically for two important parameters - Richardson number, the non-dimensional angular velocity of the cylinder, and the direction of rotation using the commercial software, ADINA. The results from these simulations were validated using an open-source spectral element code, Nek5000. The results of this investigation were presented in terms of streamlines, isotherms, and average and local Nusselt numbers. The present results illustrated that the average Nusselt number was found to depend on the direction of the angular velocity. The average Nusselt number increased with an increase in the clockwise angular velocity of the cylinder for various Richardson numbers. However, it decreased with an increase in the counterclockwise until reached a critical velocity where average Nusselt number increased with an increase in the angular velocity. This study illustrated that the maximum heat transfer can be achieved when placing a rotating cylinder inside a cavity compared with non-rotating cylinder.     

Laminar convection in a vertical channel with viscous dissipation and buoyancy effects

The fully developed and laminar convection in a parallel-plate vertical channel is investigated by taking into account both viscous dissipation and buoyancy. Uniform and symmetric temperatures are prescribed at the channel walls. The velocity field is considered as parallel. A perturbation method is employed to solve the momentum balance equation and the energy balance equation. A comparison with the velocity and temperature profiles in the case of laminar forced convection with viscous dissipation is performed in order to point out the effect of buoyancy. The case of convective boundary conditions is also discussed.     

Thermodynamics of natural convection in enclosures with viscous dissipation

Consideration of the viscous dissipation effects in natural and mixed convection heat transfer must be taken carefully, both in what concerns the thermodynamics of the problem and the relevance of the dissipation term. This applies equally to external or internal natural and mixed convection, and to spaces filled with a single fluid or to spaces filled with fluid-saturated porous media. The main question is related to the fact that, in natural convection, the work done by the pressure forces must equal the energy dissipated by viscous effects, which is the unique situation compatible with the First Law of Thermodynamics, the net energy generation in the overall domain being zero. If only the (positive) viscous dissipation term is considered in the energy conservation equation, the domain behaves like a heat multiplier, the heat output being higher than the heat input. If this is not taken into consideration, erroneous conclusions about flow and temperature fields and heat transfer results are obtained. In mixed convection problems, part of the viscous dissipation term is equally due to the work of pressure forces. Attention is given mainly to the natural convection problem in a square enclosure, the main conclusions applying for general natural or mixed convection heat transfer problems.     

Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10⁴, 10⁵, 10⁶, of Darcy number effect Da = 10^?5, 10^?4, 10^?3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k_2,1 = 3.7 × 10^?2, 5.7 × 10^?4, 6.8 × 10^?5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

Numerical simulation of double-diffusive mixed convection and entropy generation in a lid-driven trapezoidal enclosure with a heat source

In this study, entropy generation of double-diffusive mixed convection is investigated inside a right-angled trapezoidal cavity with a partially heated and salted bottom wall. Similar to the approach that assigns color to streamlines, a new coloring scheme is employed to visualize heatlines and masslines in a more meaningful manner. In addition, various consequential parameters, namely the Lewis and Richardson numbers, the buoyancy ratio, the direction of lid movement, and the heat source location, have been analyzed. According to the results, as the Lewis number increases, the average Nusselt number declines, while the total entropy generation augments. Furthermore, for Le?=?0.1, the conduction mass transfer dominates the mass transfer field; hence, the masslines are virtually perpendicular to the isoconcentration lines.     

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

Heat and mass transfer under MHD mixed convection in a four-sided lid-driven square cavity

This paper investigates the heat and mass transfer under magnetohydrodynamic mixed convection flow of a binary gas mixture in a four-sided lid-driven square cavity. The enclosure's left wall is sinusoidally heated and acts as a source term, while the right wall functions as a sink. The cavity's horizontal walls are adiabatic and impermeable to mass transfer. The governing equations under Boussinesq approximation and stream function-vorticity formulation are solved using the alternating-direction-implicit scheme, a finite-difference method. The numerical scheme's consistency and stability are demonstrated using the matrix method. The MATLAB code is written, validated against some existing studies, and used to perform numerical simulations. The numerical solutions are graphically examined by visualizing the streamline, isotherm, and concentration contours for nondimensional parameters, such as Hartmann number $\left(0\le Ha\le 100\right)$, heat absorption or generation coefficient $\left(-2\le \varphi \le 2\right)$, Richardson number $\left(0.01\le Ri\le 100\right)$, and buoyancy ratio $\left(-6\le N\le 6\right)$. The magnetic field modifies the temperature and concentration distribution in the cavity, depending on the convection mode. The magnetic field forces the fluid to stagnate in different regions of the cavity, depending on the mode of convection. It was found that the difference between the maximum and minimum temperature and concentration at the cavity's midpoint increases up to 13 and 10 times, respectively, in the natural convection compared with the forced convection. The average Nusselt number on the vertical walls of the cavity is maximum in natural convection in the absence of a magnetic field but reaches a minimum value at $Ha=100$ in forced and mixed convection. The average Sherwood number on the cavity's vertical walls decreases with the magnetic field in mixed and natural convection.