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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.

This paper aims to present a possible complete set of dimensionless parameters to describe the process of selective laser melting (SLM). This makes it possible to compare the similarity between different experiments, a sine‐qua‐non for a correct comparison of the results.

The paper describes the application of dimensional analysis to SLM.

Although the idea of dimensionless numbers is far from new, it has apparently never been applied rigorously to rapid prototyping and rapid manufacturing technologies. The technique is important, since it reduces the number of factors and makes it possible to compare results of different research groups. Furthermore, some more fundamental insights about the process can be gained.

This work is a first step towards a manageable system to control very difficult processes.

The purpose of this paper is to investigate the hydromagnetic third-grade non-Newtonian fluid flow and heat transfer between two coaxial pipes with a variable radius ratio.

To solve the approximate nonlinear and linear problems with variable coefficients, a trial function was applied. Methods include collocation, least square and Galerkin that can be applied for obtaining these coefficients.

It is revealed that an increase of the non-Newtonian parameter, Hartmann number, and radius ratio leads to an augmentation of the absolute value of the dimensionless velocity, temperature, velocity gradient, and temperature gradient of about 10-60%. Further, the augmentation of Bi₁ reduces the absolute value of the dimensionless temperature profile and dimensionless temperature gradient about three to four times; hence, the dimensionless heat transfer rate reduces. However, the growth of Bi₂ has a contrary impact. Besides, the increase of Pr and Ec leads to an increase in the dimensionless temperature profile and dimensionless temperature gradient; therefore, the dimensionless heat transfer rate increases.

The convection heat transfer on the walls of the pipes is considered, and the nonlinear coupled momentum and energy equations are solved using the least squared method and collocation methods, respectively.

This study aims to utilize the equations of flow equilibrium to determine the variations of film thickness or worktable displacement with respect to the recess pressure for both open‐ and closed‐type hydrostatic flat bearings. The static stiffness can be not only presented directly by these variations but also determined by the differentiation of flow equilibrium equations.

The single‐action variable compensations of three types including cylindrical‐spool, conical‐spool and membrane restrictors are taken into consideration in this study. Specifically, this study presents that membrane restrictor and both spool restrictors with or without preload whilst considering initial opening.

Consequently, the usage range of recess pressure and optimal parameters of appropriate compensation type can be obtained from maximum stiffness and also according to smallest gradient in variations of worktable displacement or film thickness.

This article studies the influences of single‐action variable compensations for its design varieties. The determination of stiffness comes from the differentiating recess pressure with respect to worktable displacement. The large and small positive stiffness correspond to a negative slope in steep and plain gradient, respectively; the negative stiffness and infinite stiffness are obtained by positive gradient and zero gradient, respectively, in the variations of film thickness. The finding results can be expressed further in the relationship between the static stiffness and the static load.

Unsteady natural convection of water-based nanofluid within a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno is presented. The paper aims to discuss these issues.

The left vertical and right inclined walls of the enclosure are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and to nanoparticles. In order to study the behavior of the nanofluid, a non-homogeneous Buongiorno’s mathematical model is taken into account. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite difference scheme the dimensionless governing equations are numerically solved.

The governing parameters are the Rayleigh, Hartmann and Lewis numbers along with the inclination angle of the magnetic field relative to the gravity vector, the aspect ratio and the dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall, as well as on the developments of streamlines, isotherms and isoconcentrations are analyzed. The results show that key parameters have substantial effects on the flow, heat and mass transfer characteristics.

The present results are new and original for the heat transfer and fluid flow in a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The results would benefit scientists and engineers to become familiar with the flow behavior of such nanofluids, and the way to predict the properties of this flow for possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

The purpose of this paper is to apply the numerical methods to study the heap leaching process in a bed of porous and spherical ore particles. This study is performed in two stages: first, modeling the leaching process of a soluble mineral from a spherical and porous ore particle to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the particles (the particle model), and second, modeling the heap leaching of the mineral from a porous bed consisting of spherical and porous ore particles to obtain the distribution of mineral concentrations, leaching solvent concentration and dissolved mineral in the bed (the bed model).

The governing equations are derived for the particle model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised on a uniform spherical grid fitted to the particle using finite difference method. The resulting algebraic equations are solved using Tri‐Diagonal Matrix Algorithm, and the governing equations are derived for the bed model, and then converted into non‐dimensional form using reference quantities. The non‐dimensional equations are discretised explicitly on a one‐dimensional and uniform grid fitted to the bed. The unknown quantities are evaluated using the corresponding values at the previous time interval.

The results obtained from numerical modeling show that, when the particle has a low diffusion resistance or a high chemical resistance, the reaction takes place slowly and homogeneously throughout the ore particle. On the other hand, when the bed has a low convection resistance, the reaction takes place homogeneously throughout the bed. As the convection resistance increases, the non‐homogeneous (local) behavior predominates. It is also noticed that, when the chemical reaction resistance is high, the reaction takes place homogeneously throughout the bed.

The dynamic diffusion and movement of solution in the ore particles and ore bed are not modeled and volumetric ratio of solution in the particles and the bed and also vertical velocity of solution in the bed are assumed to be fixed constants.

This study shows that the reaction takes place homogeneously throughout the bed when the convection resistance is low, the diffusion resistance is high, the concentration resistance is low, and the chemical reaction resistance is high.

Homogeneous reaction conditions being suitable for heap leaching operations are identified. Thus, it is recommended to approach the above conditions when preparing ore heaps and designing the relevant operation.

The paper aims to investigate the effect of the electromagnetic field on the convective events which occur when electrically conducting fluid is squeezed between two parallel disks.

The effects of the current occurring due to the direct voltage power supply at the thin electrical conducting fluid layer squeezed between the parallel disks, the magnetic field inducted by this current, and Ohmic heating on the squeezing process and heat convection are considered. Both approximate analytical and numerical solutions of the problem are obtained and a good agreement is observed between them.

The effects of the basic parameters such as Hartmann number, Reynolds number, the ratio of the distance between the disks to the radius of the disks, Prandtl number, Eckert number, heat conduction, and electric current on the squeezing event, and load capacity of the fluid between two parallel disks are able to be determined from the solutions. These solutions also enable the effects of the basic parameters such as Hartmann number, Reynolds number, the ratio of the distance between the disks to the radius of the disks, Prandtl number, Eckert number, heat conduction, and electric current on the squeezing event and load capacity of the fluid between two parallel disks to be determined.

Some important results and comparisons are presented graphically.

The effect of a transverse magnetic field on the squeeze film behaviors between two parallel annular disks lubricated within an electrically conducting fluid is studied. The modified Reynolds equation governing the squeeze film pressure is derived by using the continuity equation and the magneto‐hydrodynamic (MHD) motion equations. According to the results obtained, the influence of magnetic fields signifies an enhancement in the squeeze film pressure. On the whole, the magnetic field effect characterized by the Hartmann number provides an increase in value of the load‐carrying capacity and the response time as compared to the classical non‐conducting lubricant case. It improves the MHD squeeze film characteristics of the system.

The dynamic stability of nano-tubes is an important issue in engineering applications. Dynamic stability of anti-symmetric coupled-carbon nanotubes (C-CNTs)-systems in thermal environment is presented in this paper. In this system, the top and bottom CNTs are subjected to axial harmonic load and action of the viscous fluid, respectively.

The coupling and surrounding mediums of the CNTs are simulated by visco-Pasternak foundation containing the spring, shear and damper coefficients. Based on the Timoshenko beam theory and Hamilton’s principle, the coupled motion equations are derived considering size effects using Eringen’s nonlocal theory. Using the exact solution in conjunction with Bolotin’s method, the dynamic instability region (DIR) of the coupled structure is obtained. The effects of various parameters such as small scale parameter, Knudsen number, fluid velocity, static load factor, temperature change, surrounding medium and nanotubes aspect ratio are shown on the DIR of the coupled system.

Results indicate that considering parameters such as small scale effects, static load factor, Knudsen number and fluid velocity shifts the DIR of C-CNTs to a lower frequency zone.

To the best of our knowledge, analyses of anti-symmetric coupled CNTs have not received enough attentions so far. In order to optimize the nanostructures designing, the main purpose of the present paper is to investigate nonlocal dynamic stability of CNTs subjected to axial harmonic load coupled with CNTs conveying fluid.

The paper aims to determine whether the type selection and parameters determination of the compensation are most important for yielding the acceptable or optimized characteristics in design of hydrostatic bearings.

This paper utilizes the equations of flow equilibrium to determine the film thickness or displacement of worktable with respect to the recess pressure.

The stiffness due to compensation of constant‐flow pump increases monotonically as recess pressure increases. Also, the paper considers which is larger than that due to orifice compensation and capillary compensation at the same recess pressure ratio.

The findings show that the usage range of recess pressure and compensation parameters can be selected to correspond to the smallest gradient in variations of worktable displacement or film thickness.