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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.

It is well known that the mixed convection process is the combined effect of the presence of both the forced and the free convection processes. In several applications such as environmental chambers, IC engines, etc. the forced convection is brought in by multiple suction/injection (S/I) effect. Study of mixed convection in a vertical square fluid saturated porous cavity with multiple S/I effect greatly contributes to such an understanding. So far, not much research work has reported in this direction. Hence, the purpose of this paper is to investigate such a mixed convection process in a fluid saturated vertical porous square cavity.

In this study, the authors numerically solved the couple partial differential equations governing the mixed convection process in a fluid saturated vertical square porous cavity by finite element method. The study is parametric in nature wherein the authors cover a large range of values for different parameters arising the mathematical model governing the problem under consideration.

The influence of multiple S/I effects on mixed convection is analyzed for a wide range of controlling parameters such as S/I flow velocities (a), S/I window size (D/H) and Rayleigh number (Ra). Both the flow and temperature fields are highly sensitive to magnitude of S/I velocity, S/I window slit size and “Ra”. While heat fluxes along the isothermal left vertical wall decrease with increasing S/I velocities they are formed to increase with increasing “(D/H)” and “Ra”. Nusselt numbers increase with increasing “Ra” and increasing size of S/I window slit size. Multi‐cellular circulation pattern and thermal boundary layers are seen to manifest in flow and temperature fields, respectively.

The study is based on 2D model, but the model is generic in nature; also it is fully numerical in nature. Due to lack of apt literature no experimental support is provided. The mathematical model used in the study is based on certain assumptions such as isotropic porous medium, fluid is viscous in nature and follows Newtonian laws and the porous structure is saturated with fluid, etc. Regarding future work, 3D modelling and simulation is in progress and attempts are also being made to collaborate with experimental groups on the problem under investigation.

The results from the work are relevant to the context of heat and fluid flow studies in IC engines, influence of mixed convection process on bacterial growth process in environmental chambers and cooling of electronic devices, etc.

The paper describes a mathematical model, especially the boundary treatment, for describing the influence of multiple S/I effects on mixed convection flow in a vertical square enclosure filled with a Darcian fluid saturated homogeneous porous medium. To understand the physics behind the mixed convection process in the proposed configuration, extensive numerical simulations have been carried out for the first time for different values of the important governing parameters arising from the model.

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.

This paper's aim is to examine flow and heat transfer through vertical channels between parallel plates, which is of prime importance in the design of cooling systems for electronic equipment such as that of finned cold plates in general, plate‐and‐frame heat exchangers, etc.

Numerical and analytical solutions are presented to investigate the heat transfer enhancement and the pressure drop reduction due to buoyancy effects (for buoyancy‐aided flow) for the developing laminar mixed convection in vertical channel between parallel plates in the vicinity of the critical values of the buoyancy parameter (Gr/Re)crt that are obtained analytically. The numerical solutions are presented for a wide range of the buoyancy parameters Gr/Re that cover both of buoyancy‐opposed and buoyancy‐aided flow situations under each of the isothermal boundary conditions under investigation.

Buoyancy parameters greater than the critical values result in building‐up the pressure downstream of the entrance such that the vertical channel might act as a thermal diffuser with possible incipient flow reversal. Locations at which the pressure gradient vanishes and the locations at which the pressure‐buildup starts have been numerically obtained and presented for all the investigated cases.

The study is limited to the laminar flow situation.

The results clearly show that for buoyancy‐aided flow, the increase of the buoyancy parameter enhances the heat transfer and reduces the pressure drop across the vertical channel. These findings are very useful for cooling channel or chimney designs.

The study is original and presents new findings, since none of the previous studies reported the conditions for which pressure buildup might take place due to mixed convection in vertical channels between parallel plates.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

The purpose of this paper is to investigate numerically mixed convection of Al₂O₃-water nanofluids flowing through a horizontal ventilated cavity heated from below by a temperature varying sinusoidally along its lower wall. The simulations focus on the effects of different key parameters, such as Reynolds number (200 ≤ Re ≤ 5,000), nanoparticles’ concentration (0 ≤ ϕ ≤ 0.1) and phase shift of the heating temperature (0 ≤ γ ≤ π), on flow and thermal patterns and heat transfer performances.

The Navier–Stokes equations describing the nanofluid flow were discretized using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over-relaxation method.

The simulations were performed for two modes of imposed external flow (injection and suction). The main findings are that the dynamical and thermal fields are affected by the parameters Re, ϕ, γ and the applied ventilation mode; the addition of nanoparticles leads to an improvement of heat transfer rate and an increase of mean temperature inside the enclosure; the heat exchange performance and the better cooling are more pronounced in suction mode; the phase shift of the heating temperature may lead to periodic solutions for weaker values of Re and contributes to an increase or a decrease of heat transfer depending on the value of ϕ and the convection regime.

To the best of the authors’ knowledge, the problem of mixed convection of a nanofluid inside a vented cavity using the injection or suction technics and submitted to non-uniform heating conditions has not been treated so far.

An analysis of steady laminar mixed convection boundary layer flow along a vertical cone of constant wall temperature is presented. A mixed convection parameter ξ, as proposed by Lin and Chen, is used to serve as a controlling parameter that determines the relative importance of the forced and the free convection flows. New coordinates and dependent variables are then defined in terms of ξ, so that the transformed non‐similar boundary layer equations give computationally efficient numerical solutions which are valid over the entire range of mixed convection flow from the forced convection limit to the free convection limit for fluids of any Prandtl number. The effects of the mixed convection parameter ξ and the Prandtl number Pr on the velocity and temperature profiles as well as on the skin friction and heat transfer coefficients are shown for both cases of buoyancy assisting and buoyancy opposing flow conditions.

The purpose of this study is the identification of the best method to apply the body force in the lattice Boltzmann method (LBM). In the simulation of mixed convection, especially for large Richardson number flows in a square cavity.

First, three methods for applying the body force were compared to each other in the LBM. Then, an LBM-based code was written in the FORTRAN language using these three methods. Next, that code was used to simulate natural/mixed convection in a two-dimensional cavity to evaluate the methods for applying the body force. Finally, the optimum way for applying the body force was used for the simulation of free convection heat transfer in a concentric annulus with Rayleigh number in a range of 1,000 to 50,000, and mixed convection heat transfer in a concentric annulus with Rayleigh number in a range of 10,000 to 50,000 and Reynolds number in a range of 100 to 400.

Mixed convection heat transfer was simulated in a two-dimensional cavity with Richardson number in a range of 0.0001 to 100. The results which were obtained in low Richardson number flows have shown good adaptation to the available data. However, the results of large Richardson number flows, for example, Ri = 100, have shown a significant difference to the available data. Investigations revealed that this difference was due to the method of applying the body force. Therefore, the choice of the best way to apply the body force was investigated. Finally, for the large Richardson number flows, the best method to apply the body force has been identified among the several techniques.

To the authors’ knowledge, the effects of methods for applying the body force were not investigated in the cavities mixed convection, even though there are numerous investigations conducted on mixed convection with the LBM. In this study, the effects of techniques to apply the body force were investigated in large Richardson number flows. Finally, the best method to apply the body force is distinguished between several techniques for the large Richardson number mixed convection flows.

This paper seeks to increase our understanding on the fluid mechanics and heat transfer in a transitional mixed convection flow between two vertical plates. Direct numerical simulation by the spectral method, with a weak formulation, is used to solve the transient 3–D Navier‐Stokes equations and energy equation. Initial disturbances consist of the finite‐amplitude 2–D Tollmien‐Schlichting wave and two 3–D oblique waves. The transition phenomena in a mixed‐convection flow can be significantly different from the isothermal flow. Disturbance competitions among different modes are also found to be different from those known for an isothermal flow. In a mixed‐convection flow, there exist thresholds for the low‐mode Fourier waves. The intensified vortices are concentrated left of the central surface between the two plates. Hairpin vortices are formed with high Ri. Based on the flow visualization, the λ vortices are found to be staggered on the surfaces parallel to the plates. The Ri number seems to be the main parameter governing the transition mechanism. The Nu number is found to increase during transition.

The purpose of this study is to determine interfacial convective heat transfer coefficient numerically, for a porous media consisting of square blocks in inline arrangement under mixed convection heat transfer.

The continuity, momentum and energy equations are solved in dimensionless form for a representative elementary volume of porous media, numerically. The velocity and temperature fields for different values of porosity, Ri and Re numbers are obtained. The study is performed for the range of Ri number from 0.01 to 10, Re number from 100 to 500 and porosity value from 0.51 to 0.96. Based on the obtained results, the value of the interfacial convective heat transfer coefficient is calculated by using volume average method.

It was found that at low porosities (such as 0.51), the interfacial Nusselt number does not considerably change with Ri and Re numbers. However, for porous media with high Ri number and porosity (such as 10 and 0.51, respectively), secondary flows occur in the middle of the channel between rods improving heat transfer between solid and fluid, considerably. It is shown that the available correlations of interfacial heat transfer coefficient suggested for forced convection can be used for mixed convection for the porous media with low porosity (such as 0.51) or for the flow with low Ri number (such as 0.01).

To the best of the authors’ knowledge, there is no study on determination of interfacial convective heat transfer coefficient for mixed convection in porous media in literature. The present study might be the first study providing an accurate idea on the range of this important parameter, which will be useful particularly for researchers who study on mixed convection heat transfer in porous media, macroscopically.