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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.

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.

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.

Some applications: building applications, furnace design, nuclear reactors, air solar collectors.

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.

This study aims to numerically analyse the impact of an inclined magnetic field and Joule heating on the conjugate heat transfer because of the mixed convection of an Al₂O₃–water nanofluid in a thick wall enclosure.

A horizontal temperature gradient together with the shear-driven Flow creates the mixed convection inside the enclosure. The nonhomogeneous model, in which the nanoparticles have a slip velocity because of thermophoresis and Brownian diffusion, is adopted in the present study. The thermal performance is evaluated by determining the entropy generation, which includes the contribution because of magnetic field. A control volume method over a staggered grid arrangement is adopted to compute the governing equations.

The Lorentz force created by the applied magnetic field has an adverse effect on the flow and thermal field, and consequently, the heat transfer and entropy generation attenuate because of the presence of magnetic force. The Joule heating enhances the fluid temperature but attenuates the heat transfer. The impact of the magnetic field diminishes as the angle of inclination of the magnetic field is increased, and it manifests as the volume fraction of nanoparticles is increased. Addition of nanoparticles enhances both the heat transfer and entropy generation compared to the clear fluid with enhancement in entropy generation higher than the rate by which the heat transfer augments. The average Bejan number and mixing-cup temperature are evaluated to analyse the thermodynamic characteristics of the nanofluid.

This literature survey suggests that the impact of an inclined magnetic field and Joule heating on conjugate heat transfer based on a two-phase model has not been addressed before. The impact of the relative slip velocity of nanoparticles diminishes as the magnetic field becomes stronger.

This study aims to investigate numerically the problem of conjugate conduction and mixed convection heat transfer of a nanofluid in a rotational/stationary circular enclosure using a two-phase mixture model.

Hot and cold surfaces on the wall or inside the enclosure (heater and cooler) are maintained at constant temperature of T_h and T_c, respectively, whereas other parts are thermally insulated. To examine the effects of various parameters such as Richardson number (0.01 = Ri =100), thermal conductivity ratio of solid to base fluid (1 = K_r = 100), volume fraction of nanoparticle (0 = φ = 0.05), insertion of conductive covers (C.Cs) around the heater in a different shape (triangular, circular or square), segmentation and arrangement of the conductive blocks (C.Bs) and rotation direction of the enclosure on the flow structure and heat transfer rate, two-dimensional equations of mass, momentum and energy conservation, as well as volume fraction, are solved using finite volume method and Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm.

The results show that inserting C.C around heater can increase or decrease heat transfer rate, and it depends on thermal conductivity ratio of solid to pure fluid. Also, it is found that by the division of C.B and location of its portions in a horizontal configuration, heat transfer rate reduces. Moreover, it is observed that external heating and cooling of the enclosure causes enhancement of heat transfer relative to that of internal heating and cooling. Finally, results illustrate that under the condition that cylinders rotate in the same direction, the heat transfer rate increases as compared to those that rotate in the opposite direction. Hence rotation direction of cylinders can be used as a desired parameter for controlling heat transfer rate.

A comprehensive report of results for the problem of conjugate conduction and mixed convection heat transfer in a circular cylinder containing different shapes of C.C, conducting obstacle and heater and cooler has been presented. An efficient numerical technique has been developed to solve this problem. The achievements of this paper are purely original, and the numerical results were never published by any researcher.

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.

Galerkin weighted residual finite element method is used to solve the governing equations of mixed convection.

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.

The literature does not have mixed convection and conjugate heat transfer problem in a channel with thick walled cavity.

This paper deals with numerical studies into combined conduction, convection and radiation from a heated vertical electronic board are provided here.

Here three inbuilt heaters with decrease in their heights were placed in the vertical electronic board. With respect to the non-heat portions, two configurations were studied. The first considers the non-heat portions to be adiabatic, while in the second, they are non-adiabatic. The heat that is produced in three heaters is conducted along the board and is dissipated either from the heater portions alone or from the whole board by convection and radiation. Air is considered as working medium, while the equations of heat transfer and flow of fluid are handled without boundary layer approximations. These equations were further solved using finite volume method with Gauss–Seidel iteration method.

Results of various comparative studies were discussed to bring out the relevance of thermal conductivity, modified Richardson number and surface emissivity on different heat transfer and flow results concerning this problem.

The optimum values of surface emissivity, thermal conductivity and modified Richardson number have also been notionally explored.

The purpose of this paper is to analyze the thermal and fluid dynamic behaviors of mixed convection in air because of the interaction between a buoyancy flow and a moving plate induced flow in a horizontal no parallel-plates channel to investigate the effects of the minimum channel spacing, wall heat flux, moving plate velocity and converging angle.

The horizontal channel is made up of an upper inclined plate heated at uniform wall heat flux and a lower adiabatic moving surface (belt). The belt moves from the minimum channel spacing section to the maximum channel spacing section at a constant velocity so that its effect interferes with the buoyancy effect. The numerical analysis is accomplished by means of the finite volume method, using the commercial code Fluent.

Results in terms of heated upper plate and moving lower plate temperatures and stream function fields are presented. The paper underlines the thermal and fluid dynamic differences when natural convection or mixed convection takes place, varying minimum channel spacing, wall heat flux, moving plate velocity and converging angle.

The hypotheses on which the present analysis is based are two-dimensional, laminar and steady state flow and constant thermo physical properties with the Boussinesq approximation. The minimum distance between the upper heated plate of the channel and its lower adiabatic moving plate is 10 and 20 mm. The moving plate velocity varies in the range 0-1 m/s; the belt moves from the right reservoir to the left one. Three values of the uniform wall heat flux are considered, 30, 60 and 120 W/m², whereas the inclination angle of the upper plate θ is 2° and 10°.

Mixed convection because of moving surfaces in channels is present in many industrial applications; examples of processes include continuous casting, extrusion of plastics and other polymeric materials, bonding, annealing and tempering, cooling and/or drying of paper and textiles, chemical catalytic reactors, nuclear waste repositories, petroleum reservoirs, composite materials manufacturing and many others. The investigated configuration is used in applications such as re-heating of billets in furnaces for hot rolling process, continuous extrusion of materials and chemical vapor deposition, and it could also be used in thermal control of electronic systems.

This paper evaluates the thermal and velocity fields to detect the maximum temperature location and the presence of fluid recirculation. The paper is useful to thermal designers.

A comprehensive investigation on the outlet air position effects on the thermal comfort and air quality has been achieved. In addition, airflow and temperature distributions in ventilated cavities filled with an air-CO₂ mixture with mixed convection are predicted. The airflow enters from the cavity through an opening in the lower side of the left vertical wall and exits through the opening in one wall of the cavity. This paper aims to investigate the outlet location effect, four different placement configurations of output ports are considered. Three of them are placed on the upper side and the fourth on top of the opposite side of the inlet opening. A uniform heat and CO₂ contaminant source are applied on the left vertical wall, while the remaining walls are impermeable and adiabatic to heat and solute. The cooling efficiency inside the enclosure and the average fluid temperature are computed for different Reynolds and Rayleigh numbers to find the most suitable fluid outlet position that ensures indoor comfortable conditions while effectively removing heat and the contaminant. This is demonstrated by three relevant indices, namely, the effectiveness for heat removal, the contaminant removal and the index of indoor air quality.

The simulations were performed via the finite-volume scSTREAM CFD solver V11. Three different values of CO₂ amount are considered, namely, 10³, 2 × 10³ and 3 × 10³ ppm, the Reynolds number being in the range 100 ≤ Re ≤ 800.

Based on the findings obtained, it is the configuration whose air outlet is placed near the heat source and the contaminant, which provides a better air distribution and a ventilation efficiency compared to the others ventilation strategies.

The studies on heat and mass transfers by natural and forced convection in ventilated cavities remain a fruitful research topic. Thereby, such a study deals with different ventilation strategies through cavities containing an air-CO₂ mixture subjected to a mixed regime. In particular, the air inlet velocity and contaminant sources’ effects on thermal comfort and air quality have been investigated.

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

The authors believe that the presented results are original and have not been published elsewhere.

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.