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The purpose of this paper is to simulate flow inside differentially heated rotating cavity using two different formulations; one using Navier‐Stokes (NS) equations derived in non‐inertial (rotating) frame of reference and the other using NS equations in inertial frame of reference. Then to compare the results obtained from these formulations to find their merits and demerits.

The NS equations for both non‐inertial and inertial formulations are written in artificial compressibility form before discretizing them by a high resolution finite volume method. The dual time steeping approach of Jameson is used for time accuracy in both the formulations. Arbitrary Lagrangian Eulerian (ALE) approach is used for taking care of moving boundary problem arising in the inertial formulation. A newly developed HLLC‐AC Riemann solver for discretizing convective fluxes and central differencing for discretizing viscous fluxes are used in the finite volume approach. Results for both the formulations are first validated with test cases reported in literature. Then the results of the two formulations are compared among themselves.

Results of the non‐inertial formulation obtained by the proposed method are found to match well with those reported in literature. The results of both the formulations match well for low rotational speeds of the cavity. The discrepancies between the results of the two formulations progressively increase with the increase in rotational speed. Implicit treatment of the source term is found to reduce the discrepancies.

The present approach is useful for accurate prediction of flow feature and heat transfer characteristic in case of applications such as manufacturing of single wafer crystal for semiconductor and in numerous metallurgical processes.

The ALE formulation is used for the first time to simulate a differentially heated rotating cavity problem. The attempt to compare non‐inertial and inertial formulations is also reported for the first time. Implicit treatment of the source term leading to change in solution accuracy is one of the important findings of the present investigation.

A heated rotating cavity with an axial throughflow of cooling air is used as a model for the flow in the cylindrical cavities between adjacent discs of a high‐pressure gas‐turbine compressor. In an engine the flow is expected to be turbulent, the limitations of this laminar study are fully realised but it is considered an essential step to understand the fundamental nature of the flow. The three‐dimensional, time‐dependent governing equations are solved using a code based on the finite volume technique and a multigrid algorithm. The computed flow structure shows that flow enters the cavity in one or more radial arms and then forms regions of cyclonic and anticyclonic circulation. This basic flow structure is consistent with existing experimental evidence obtained from flow visualization. The flow structure also undergoes cyclic changes with time. For example, a single radial arm, and pair of recirculation regions can commute to two radial arms and two pairs of recirculation regions and then revert back to one. The flow structure inside the cavity is found to be heavily influenced by the radial distribution of surface temperature imposed on the discs. As the radial location of the maximum disc temperature moves radially outward, this appears to increase the number of radial arms and pairs of recirculation regions (from one to three for the distributions considered here). If the peripheral shroud is also heated there appear to be many radial arms which exchange fluid with a strong cyclonic flow adjacent to the shroud. One surface temperature distribution is studied in detail and profiles of the relative tangential and radial velocities are presented. The disc heat transfer is also found to be influenced by the disc surface temperature distribution. It is also found that the computed Nusselt numbers are in reasonable accord over most of the disc surface with a correlation found from previous experimental measurements.

The purpose of this study is to apply an incompressible smoothed particle hydrodynamics (ISPH) method to simulate the Magnetohydrodynamic (MHD) free convection flow of a nanofluid in a porous cavity containing rotating hexagonal and two circular cylinders under the impacts of Soret and Dufour numbers.

The inner shapes are rotating around a cavity center by a uniform circular motion at angular rate ω. An inner hexagonal shape has higher temperature T_h and concentration C_h than the inner two circular cylinders in which the temperature is T_c and concentration is C_c. The performed numerical simulations are presented in terms of the streamlines, isotherms and isoconcentration as well as the profiles of average Nusselt and Sherwood numbers.

The results indicated that the uniform motions of inner shapes are changing the characteristics of the fluid flow, temperature and concentration inside a cavity. An augmentation on a Hartman parameter slows down the flow speed and an inclination angle of a magnetic field raises the flow speed. A rise in the Soret number accompanied by a reduction in the Dufour number lead to a growth in the concentration distribution in a cavity.

ISPH method is used to simulate the double-diffusive convection of novel rotating shapes in a porous cavity. The inner novel shapes are rotating hexagonal and two circular cylinders.

Rotating flows are very important because they are found in industrial and domestic applications. For a good performance, it is important to dimension correctly the energy efficiency and the lifespan of the apparatuses while studying, for example, the influence of their physical and geometrical characteristics on the various hydrodynamic constraints, thermal and mechanics which they will support. The purpose of this paper is to describe experiments and a numerical study of the inter‐disc space effects on the mean and the turbulent characteristics of a Von Karman isotherm steady flow between counter‐rotating disks.

Experimental results are obtained by the laser Doppler anemometer technique performed at IRPHE (Institute of Research on the Phenomena out Equilibrium) in Marseille, France. The numerical predictions are based on one‐point statistical modeling using a low Reynolds number second‐order full stress transport closure (RSM model).

It was found that the level of radial velocity increases with the aspect ratio near to the axis of rotation but this phenomenon is reversed far from this zone; the level of tangential velocity, of turbulence kinetic energy and of the torsion are definitely higher for the largest aspect ratio. The best contribution of this work is, at the same time, the new experimental and numerical database giving the effect of the aspect ratio of the cavity on the intensity of turbulence for Von Karman flow between two counter rotating disks.

The limitation of this work is that it concerns rotating flows with very high speeds because the phenomena of instability appear and the application of this model for cavities of forms is not obvious.

This work is of technological interest; it can be exploited by industrialists to optimize the operation of certain machines using this kind of flow. It can be exploited in the teaching of certain units of Masters courses: gathering experimental techniques; numerical methods; and theoretical knowledge.

This work can also have a social interest where this kind of simulation can be generalized with other types of flows responsible for certain phenomena of society, such as the phenomenon of pollution. This work can have a direct impact on everyday life by the exploitation of the rotary flows, such as being a very clean and very economic means to separate the undesirable components present in certain fluid effluents.

The best contribution of this work is the new experimental and numerical database giving the effect of the aspect ratio of the cavity on the intensity of turbulence for Von Karman flow between two counter rotating disks.

This paper aims to study numerically the simulation of convective–radiative heat transfer under an effect of variable thermally generating source in a rotating square chamber. The performed analysis deals with a development of passive cooling system for the electronic devices.

The domain of interest of size H rotating at a fixed angular velocity has heat-conducting solid walls with a constant cooling temperature for the outer boundaries of the vertical walls and with thermal insulation for the outer borders of the horizontal walls. The chamber has a heater on the bottom wall with a time-dependent volumetric heat generation. The internal surfaces of the walls and the energy element are both grey diffusive emitters and reflectors. The fluid is transparent to radiation. Computational model has been written using non-dimensional parameters and worked out by the finite difference technique. The effect of the angular velocity, volumetric heat generation frequency and surface emissivity has been studied and described in detail.

The results show that growth of the surface emissivity leads to a diminution of the mean heater temperature, while a weak rotation can improve the energy transport for low volumetric thermal generation frequency.

An efficient computational approach has been used to work out this problem. The originality of this work is to analyze complex (conductive–convective–radiative) energy transport in a rotating system with a local element of time-dependent volumetric heat generation. To the best of the authors’ knowledge, an interaction of major heat transfer mechanisms in a rotating system with a heat-generating element is scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of complex heat transfer in rotating enclosures with internal heat-generating units, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

The purpose of this study is to use the incompressible smoothed particle hydrodynamics method to examine the influences of a magnetic field on the double-diffusive convection caused by a rotating circular cylinder with paddles within a square cavity filled by a nanofluid.

The cavity is saturated by two wavy layers of non-Darcy porous media with a variable amplitude parameter. The embedded circular cylinder with paddles carrying T_h and C_h is rotating around the cavity center by a uniform circular velocity.

The lineaments of nanofluid velocity and convective flow, as well as the mean of Nusselt and Sherwood numbers, are represented below the variations on the frequency parameter, amplitude parameter of the wavy porous layers, Darcy parameter, nanoparticles parameter, Hartmann number and Ryleigh number. The performed simulations showed the role of paddles mounted on circular cylinders for enhancing the transmission of heat and mass within a cavity. The wavy porous layers at the lower Darcy parameter are playing as a blockage for the nanofluid flow within the porous area. Increasing the concentration of the nanoparticles to 6% reduces the maximum flow speed by 8.97% and maximum streamlines |ψ|_max by 10.76%. Increasing Hartmann number to 100 reduces the maximum flow speed by 65.83% and |ψ|_max by 75.54%.

The novelty of this work is to examine the effects of an inclined magnetic field and rotating novel shape of a circular cylinder with paddles on the transmission of heat/mass in the interior of a nanofluid-filled cavity saturated by undulating porous medium layers.

The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method.

The cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method.

The major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity.

The originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

Presents three non‐isothermal, time dependent, three dimensional examples having cylindrical geometries to show the significant effort of numerical precision and dissipation on rotating flow predictions. The examples are relevant to turbomachinery design and geophysical studies. Discusses the relationship between numerical precision, numerical dissipation and co‐ordinate system angular velocity. Compares predictions made in stationary and rotating co‐ordinate systems, using contour plots of dimensionless stream function and temperature. Shows that wrong, axisymmetric solutions are predicted if the co‐ordinate system is not selected to minimize relative tangential velocities/Peclet numbers, thereby increasing numerical precision and reducing dissipation.

This study aims to numerically examine mixed convection of CuO-water nanofluid in a three-dimensional (3D) vented cavity with inlet and outlet ports under the influence of an inner rotating circular cylinder, homogeneous magnetic field and surface corrugation effects. In practical applications, it is possible to encounter some of the considered configurations in a vented cavity such as magnetic field, rotating cylinder and it is also possible to specially add some of the active and passive control means to control the convection inside the cavity such as adding nanoparticles, corrugating the surfaces. The complicated physics with nanofluid under the effects of magnetic field and inclusion of complex 3D geometry make it possible to use the results of this numerical investigation for the design, control and optimization of many thermal engineering systems as mentioned above.

The bottom surface is corrugated with a rectangular wave shape, and the rotating cylinder surface and cavity bottom surface were kept at constant hot temperatures while the cold fluid enters the inlet port with uniform velocity. The complicated interaction between the forced convection and buoyancy-driven convection coupled with corrugated and rotating surfaces in 3D configuration with magnetic field, which covers a wide range of thermal engineering applications, are numerically simulated with finite element method. Effects of various pertinent parameters such as Richardson number (between 0.01 and 100), Hartmann number (between 0 and 1,000), angular rotational speed of the cylinder (between −30 and 30), solid nanoparticle volume fraction (between 0 and 0.04), corrugation height (between 0 and 0.18H) and number (between 1 and 20) on the convective heat transfer performance are numerically analyzed.

It was observed that the magnetic field suppresses the recirculation zone obtained in the lower part of the inlet port and enhances the average heat transfer rate, which is 10.77 per cent for water and 6.86 per cent for nanofluid at the highest strength. Due to the thermal and electrical conductivity enhancement of nanofluid, there is 5 per cent discrepancy in the Nusselt number augmentation with the nanoadditive inclusion in the absence and presence of magnetic field. The average heat transfer rate of the corrugated surface enhances by about 9.5 per cent for counter-clockwise rotation at angular rotational speed of 30 rad/s as compared to motionless cylinder case. Convective heat transfer characteristics are influenced by introducing the corrugation waves. As compared to number of waves, the height of the corrugation has a slight effect on the heat transfer variation. When the number of rectangular waves increases from N = 1 to N = 20, approximately 59 per cent of the average heat transfer reduction is achieved.

In this study, mixed convection of CuO-water nanofluid in a 3D vented cavity with inlet and outlet ports is numerically examined under the influence of an inner rotating circular cylinder, homogeneous magnetic field and surface corrugation effects. To the best of authors knowledge such a study has never been performed. In practical applications, it is possible to encounter some of the considered configurations in a vented cavity such as magnetic field, rotating cylinder and it is also possible to specially add some of the active and passive control means to control the convection inside the cavity such as adding nanoparticles, corrugating the surfaces. The complicated physics with nanofluid under the effects of magnetic field and inclusion of complex 3D geometry make it possible to use the results of this numerical investigation for the design, control and optimization of many thermal engineering systems as mentioned above.

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.