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Unsteady simulation of forced convection of two heated horizontal cylinders confined in a 2D squared enclosure. The paper aims to discuss this issue.

The finite-volume method is used to solve the transient heat transfer problem by employing quadrilateral mesh type. To solve the governing equations (conservations of mass, momentum and energy) on unstructured control volumes, a second-order quadratic upwind interpolation of convective kinematics scheme for the convection terms and the semi-implicit method for pressure-linked equations pressure correction algorithm were used.

The results indicate that the variation of the area-averaged Nusselt number strongly depends on the Reynolds number. On the contrary, the effect of cylinders’ space on heat transfer was found to be nearly negligible for Re < 460. It is also observed that steady state flow and heat transfer shift to periodical oscillation, and ultimately chaotic oscillation in non-dimensional cylinders distance of 0.1; however the sequence of appearing this route is completely different for higher cylinder spaces.

Reynolds numbers between 380 and 550 and dimensionless horizontal distances of cylinders 0.1, 0.2 and 0.3.

Comprehensive knowledge of the effect of tube arrays flow regime on each other and in turn, heat transfer among them. Better understanding of convective heat transfer around an array of horizontal cylinders compared with from those around a single cylinder because of the mutual interaction of the buoyant plumes generated by the cylinders. Time-dependent phenomena of the problem including periodical oscillation or chaotic features.

The purpose of this paper is to discuss, with numerical simulations, magnetohydrodynamic (MHD) natural convection laminar flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature.

The governing boundary layer equations are transformed into a non‐dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form, which are solved numerically by two very efficient methods: implicit finite difference method together with Keller box scheme; and direct numerical scheme.

Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin‐friction coefficient and the local Nusselt number for a wide range of MHD parameter, viscosity‐variation parameter and viscous dissipation parameter.

MHD flow in this geometry with temperature dependent viscosity is absent in the literature. IN this paper, the results obtained from the numerical simulations have been verified by two methodologies.

The laminar mixed convection boundary‐layer flow of a micropolar fluid past a horizontal circular cylinder in a stream flowing vertically upwards has been studied in both cases of a heated and cooled cylinder. The solutions for the flow and heat transfer characteristics are evaluated numerically for different parameters, such as the mixed convection parameter λ, the material parameter K (vortex viscosity parameter) and the Prandtl number Pr=1 and 6.8, respectively. It is found, as for the case of a Newtonian fluid considered for Pr=1, that heating the cylinder delays separation and can, if the cylinder is warm enough, suppress it completely. Cooling the cylinder, on the other side, brings the separation point nearer to the lower stagnation point and for sufficiently cold cylinder there will not be a boundary‐layer on the cylinder. This model problem may solve industrial problems with processing of polymeric liquids, lubricants and molten plastics.

This paper aims to investigate numerically buoyancy-induced convection from a pair of differentially heated horizontal circular cylinders set side by side in a nanofluid-filled adiabatic square enclosure, inclined with respect to gravity so that the heated cylinder is located below the cooled one, using a two-phase model based on the double-diffusive approach assuming that the Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase.

The system of the governing equations of continuity, momentum and energy for the nanofluid, and continuity for the nanoparticles, is solved by a computational code based on the SIMPLE-C algorithm. Numerical simulations are performed for Al₂O₃ + H₂O nanofluids using the average volume fraction of the suspended solid phase, the tilting angle of the enclosure, the nanoparticle size, the average nanofluid temperature and the inter-cylinder spacing, as independent variables.

The main results obtained may be summarized as follows: at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid has a peak at an optimal tilting angle of the enclosure; the relative heat transfer performance of the nanofluid increases notably as the average temperature is increased, and just moderately as inter-cylinder spacing is increased and the nanoparticle size is decreased.

The two-phase computational code used in the present study incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of literature experimental data.

The purpose of this paper is to study the steady mixed convection boundary layer flow of a nanofluid past a horizontal circular cylinder in a stream flowing vertically upwards for both cases of a heated and cooled cylinder.

The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite‐difference scheme known as the Keller‐box method. This method is very efficient for solving boundary layer problems.

The solutions for the flow and heat transfer characteristics are evaluated numerically for various values of the parameters, namely the nanoparticle volume fraction φ and the mixed convection parameter λ at Prandtl number Pr=1 and 6.2. Three different types of nanoparticles considered are Cu, Al₂O₃ and TiO₂ by using water‐based fluid with Pr=6.2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the skin friction coefficient and heat transfer rate at the surface also increase, and it also leads to the increment of the value of mixed convection parameter λ which first gives no separation.

The results of this paper are valid only up to the value of λ=λ₀ (<0) below which a boundary layer solution does not exist.

The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro‐channel heat sinks. Nanofluids usually contain the nanoparticles such as metals, oxides, or carbon nanotubes, whereby these nanoparticles have unique chemical and physical properties.

The results of this paper are important for the researchers working in the area of nanofluids. The paper is well prepared and presented. The results are original, new and important from both theoretical and application point of views.

A numerical study has been conducted for natural convection heat transfer for air around two vertically separated horizontal heated cylinders placed inside an isothermal rectangular enclosure having finite wall conductances. The interaction between convection in the fluid filled cavity and conduction in the walls surrounding the cavity is investigated. Results have been obtained for Rayleigh numbers (Ra) between 10³ and 10⁶, dimensionless wall thickness (W) between 0.5 and 1.375 and dimensionless wall‐fluid thermal conductivity ratio (α) between 0.01 and 5.0. The results indicate that wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer. The overall heat transfer coefficient for both cylinders is correlated with CRaⁿ for different W and α.

The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM).

Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM.

The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number.

A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

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.

Laminar natural convection of nanofluids in a square cooled cavity enclosing a heated horizontal cylinder is studied numerically. This paper aims to investigate in what measure the nanoparticle size and average volume fraction, the cavity width, the cylinder diameter and position, the average temperature of the nanofluid and the temperature difference imposed between the cylinder and the cavity walls, affects the basic heat and fluid flow features, as well as the thermal performance of the nanofluid relative to that of the base liquid.

The four-equation system of the mass, momentum and energy transfer governing equations has been solved using a computational code incorporating three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of experimental data available in the literature. The SIMPLE-C algorithm has been used to handle the pressure-velocity coupling. Simulations have been performed using Al₂O₃ + H₂O, for different values of the average volume fraction of the suspended solid phase in the range 0-0.04, the diameter of the nanoparticles in the range 25-75 nm, the temperature difference imposed between the cylinder and the cavity walls in the range 5-20 K, the average nanofluid temperature in the range 300-330 K, the ratio between the cylinder diameter and the cavity width in the range 0.1-0.5 m, the ratio between the distance of the cylinder axis from the bottom wall and the cavity width in the range 0.2-0.8 and the ratio between the distance of the cylinder axis from the left sidewall and the cavity width in the range 0.2-0.5.

The main results obtained may be summarized as follows: the overall solid phase migration from hot to cold results in a cooperating solutal buoyancy force which tends to compensate the friction increase consequent to the viscosity growth due to the dispersion of the nanoparticles into the base fluid; the effect of the increased thermal conductivity consequent to the nanoparticle dispersion into the base fluid plays the major role in determining the heat transfer enhancement of the nanofluid, at least in the upper range of the investigated average temperatures; at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures, it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid increases notably with increasing the average temperature, and just moderately as the imposed temperature difference, the width of the cavity and the distance of the cylinder from the bottom of the cavity, are increased; the relative heat transfer performance of the nanofluid increases as the nanoparticle size, the cylinder diameter and the distance of the cylinder from the sidewall, are decreased; as a consequence of the local competition between the thermal and the solutal buoyancy forces, a periodic flow arises when the cylinder is located in the vicinity of one of the cooled walls of the enclosure.

Framed in this general background, a comprehensive numerical study on buoyancy-driven convection of alumina-water nanofluids inside a cooled square cavity containing a heated circular cylinder is executed by the way of a two-phase model based on the double-diffusive approach accounting for the effects of the Brownian diffusion and thermophoresis.

The purpose of this paper is to study the effects of natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic circular cylinder. The fluid in the enclosure is Cu-water nanofluid. The main emphasis is to find the numerical treatment for the said mathematical model. The effects of Rayleigh number, inclined angle of elliptic inner cylinder, effective of thermal conductivity and viscosity of nanofluid, volume fraction of nanoparticles on the flow and heat transfer characteristics have been examined.

A very effective and higher order numerical scheme Control Volume-based Finite Element Method (CVFEM) is used to solve the resulting coupled equations. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and inclined angle of elliptic inner cylinder. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively.

The results reveal that Nusselt number increases with an increase of nanoparticle volume fraction, Rayleigh numbers and inclination angle. Also it can be found that increasing Rayleigh number leads to a decrease in heat transfer enhancement. For high Rayleigh number the minimum heat transfer enhancement ratio occurs at.

To the best of the authors’ knowledge, no such analysis is available in the literature which can describe the natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder by means of CVFEM.