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The main purpose of this study is to investigate the natural convection of micropolar fluid in a square cavity with two orthogonal heaters placed inside. The study of natural convection in a two-dimensional enclosure determines the effect of non-uniform heated plate on certain micropolar fluid flows which are found in many engineering applications. Therefore, because of its practical interest in the engineering fields such as building design, cooling of electronic components, melting and solidification process, solar energy systems, solar collectors, liquid crystals, animal blood, colloidal fluids and polymeric fluids, the topic needs to be further explored.

The dimensionless governing equations have been solved by finite volume method of the second-order central difference and upwind scheme.

The effects of the Rayleigh number, nonuniformity parameter and vortex viscosity parameter on fluid flow and heat transfer have been analyzed. The rate of heat transfer increases with an increase in the aspect ratio of the heated plates for all the values of Rayleigh number and vortex viscosity parameter. The heat transfer rate is reduced with an increase in the vortex viscosity parameter. It is predicted that the non-uniform of the baffle gives better heat transfer than uniform heating.

The present numerical results were tested against the experimental work. The present results have an excellent agreement with the results obtained by the previous experimental work.

The purpose of this paper is to investigate the nanofluid flow and heat transfer induced by two co- axially rotating disks using Buongiorno’s model. This model took into account the Brownian diffusion and thermophoresis effects due to the presence of nanoparticles.

The governing partial differential equation was transformed into a set of nonlinear ordinary differential equations by using similarity transformation and solved numerically using shooting techniques.

The present work is a comparison study of Maxwell-Garnett model and modified Maxwell model for the effective thermal conductivity of nanofluids. The effects of different involved parameters on velocity and temperature profile are examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and studied.

It is found that the results of azimuthal velocity profile are an increasing function of upper disk stretching parameter. The radial and axial velocity profile is enlarged for a large value of lower stretching parameter. Fluid temperature decays for large values Reynolds number and lower disk stretching parameter.

This paper aims to present a study on stability analysis of Jeffrey fluids in the presence of emergent chemical gradients within microbial systems of anisotropic porous media.

This study uses an effective method that combines non-dimensionalization, normal mode analysis and linear stability analysis to examine the stability of Jeffrey fluids in the presence of emergent chemical gradients inside microbial systems in anisotropic porous media. The study focuses on determining critical values and understanding how temperature gradients, concentration gradients and chemical reactions influence the onset of bioconvection patterns. Mathematical transformations and analytical approaches are used to investigate the system’s complicated dynamics and the interaction of numerous characteristics that influence stability.

The analysis is performed using the Jeffrey-Darcy type and Boussinesq estimation. The process involves using non-dimensionalization, using the normal mode approach and conducting linear stability analysis to convert the field equations into ordinary differential equations. The conventional thermal Rayleigh Darcy number RDa,c is derived as a comprehensive function of various parameters, and it remains unaffected by the bio convection Lewis number Łe. Indeed, elevating the values of ζ and γ′ in the interval of 0 to 1 has been noted to expedite the formation of bioconvection patterns while concurrently expanding the dimensions of convective cells. The purpose of this investigation is to learn how the temperature gradient affects the concentration gradient and, in turn, the stability and initiation of bioconvection by taking the Soret effect into the equation. The results provide insightful understandings of the intricate dynamics of fluid systems affected by chemical and biological elements, providing possibilities for possible industrial and biological process applications. The findings illustrate that augmenting both microbe concentration and the bioconvection Péclet number results in an unstable system. In this study, the experimental Rayleigh number RDa,c was determined to be 4π2at the critical wave number ( δcˇ) of π.

The study’s novelty originated from its investigation of a novel and complicated system incorporating Jeffrey fluids, emergent chemical gradients and anisotropic porous media, as well as the use of mathematical and analytical approaches to explore the system’s stability and dynamics.

The purpose of this study is to numerically study the heat transfer of free convection of a magnetizable micropolar nanofluid inside a semicircular enclosure.

The flow domain is under simultaneous influences of two non-uniform magnetic fields generated by current carrying wires. The directions of the currents are the same. Although the geometry is symmetric, it is physically asymmetric. The impacts of key parameters, including Rayleigh number Ra = 10³-10⁶, Hartman number Ha = 0-50, vortex viscosity parameter Δ = 0-4, nanoparticles volume fraction φ = 0-0.04 and magnetic number Mn_f = 0-1000, on the macro- and micro-scales flows, temperature and heat transfer rate are studied.

The outcomes show that dispersing of the nanoparticles in the host fluid increases the strength of macro- and micro-scale flows. When Mn_f = 0, the increment of the vortex viscosity parameter increases the strength of the particles micro-rotations, while this characteristic is decreased by growing Δ for Mn_f ≠ 0. The increment of Δ and Ha decreases the rate of heat transfer. The increment of Ha decreases the enhancement percentage of heat transfer rate because of dispersing nanoparticles, known as En parameter. In addition, the value of Δ has no effect on En. Moreover, the average Nusselt number Nu_avg and En remain constant by increasing the magnetic number Mn_f for different volume fraction values.

The authors believe that all of the results, both numerical and asymptotic, are original and have not been published elsewhere yet.

The boundary layer flow of immiscible fluids plays a crucial role across various industries, influencing advancements in industrial processes, environmental systems, healthcare and more. This study explores the thermally radiative boundary layer flow of a shear-driven Ree–Eyring fluid over a nanofluid. The investigation offers valuable insights into the intricate dynamics and heat transfer behavior that arise when a nanofluid, affected by thermal radiation, interacts with a non-Newtonian Ree–Eyring fluid. This analysis contributes to a deeper understanding of the complex interactions governing such systems, which is essential for enhancing efficiency and innovation in multiple applications.

The simulation investigates the convergence of boundary layers under varying shear strengths. A comparative analysis is conducted using γAl2O3 and Al₂O₃ nanoparticles, with water as the base fluid. The model’s numerical outcomes are derived using the bvp4c method through the application of appropriate similarity transformations. The resulting numerical data are then used to produce graphical representations, offering valuable insights into the influence of key parameters on flow behavior and patterns.

The temperature of the Al₂O₃ nanoparticles is always higher than the γAl2O3 nanoparticles, and hence, Al₂O₃ nanoparticles become more significant in the cooling process then γAl2O3 nanoparticles. It is also observed that the fluid velocity for both regions is enhanced by increasing values of the Ree–Eyring fluid parameter.

The results stated are original and new with the thermal radiative boundary layer flow of two immiscible Ree–Eyring fluid and Al₂O₃/γAl2O3 nanofluid.

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.

Flow induced by rotating disks is of great practical importance in several engineering applications such as rotating heat exchangers, turbine disks, pumps and many more. The present research has been freshly displayed regarding the implementation of an engine oil-based Casson tri-hybrid nanofluid across a rotating disk in mass and heat transferal developments. The purpose of this study is to contemplate the attributes of the flowing tri-hybrid nanofluid by incorporating porosity effects and magnetization and velocity slip effects, viscous dissipation, radiating flux, temperature slip, chemical reaction and activation energy.

The articulated fluid flow is described by a set of partial differential equations which are converted into one set of higher-order ordinary differential equations (ODEs) by using convenient conversions. The numerical solution of this transformed set of ODEs has been spearheaded by using the effectual bvp4c scheme.

The acquired results show that the heat transmission rate for the Casson tri-hybrid nanofluid is intensified by, respectively, 9.54% and 11.93% when compared to the Casson hybrid nanofluid and Casson nanofluid. Also, the mass transmission rate for the Casson tri-hybrid nanofluid is augmented by 1.09% and 2.14%, respectively, when compared to the Casson hybrid nanofluid and Casson nanofluid.

The current investigation presents an educative response on how the flow profiles vary with changes in the inevitable flow parameters. As per authors’ knowledge, no such scrutinization has been carried out previously; therefore, our results are novel and unique.

The purpose of this paper is to investigate the impact of thermal radiation interaction with Hall current, buoyancy force, and oscillatory surface temperature on hydromagnetic-mixed convective heat exchange stream of an electrically conducting nanofluid past a moving permeable plate in a porous medium within a rotating system.

Analytical closed-form solutions are obtained for both the momentum and the energy equations using the perturbation method.

The effects of various important parameters on velocity and temperature fields within the boundary layer are discussed for three different water-based nanofluids containing copper (Cu), aluminum oxide (Al₂O₃), and titanium dioxide (TiO₂) as nanoparticles. Local skin friction and Nusselt number are illustrated graphically and discussed quantitatively. The results show that Hall current significantly affects the flow system. Results for some special cases of the present analysis are in good agreement with the existing literature.

The problem is relatively original to study the hydromagnetic-oscillatory flow of a nanofluid with Hall effect and thermal radiation past a vertical plate in a rotating porous medium.

Steady-state free convection heat transfer and fluid flow of Cu-water nanofluid is investigated within a porous tilted right-angle triangular enclosure. The paper aims to discuss these issues.

The flush mounted heater with finite size is placed on one right-angle wall. The temperature of the inclined wall is lower than the heater, and the rest of walls are adiabatic. The governing equations are obtained based on the Darcy's law, and the nanofluid model adopted is that by Tiwari and Das. The transformed dimensionless governing equations were solved numerically by finite difference method, and the solution for algebraic equations was obtained through successive under relaxation method.

Investigations were made as the tilted angle of the cavity varies within under different values of Rayleigh number for a porous medium with and solid volume fraction parameter of Cu-water nanofluid with. It is found that the maximum value of the average Nusselt number is achieved with the highest Rayleigh number when the tilted angle of the cavity is 150°, while the minimum value of the average Nusselt number is obtained with the lowest Rayleigh number when the tilted angle of the cavity locates at 240°. As soon as the flow convection in the cavity is not significant, increasing can improve the value of, but opposite effects appear when flow convection becomes stronger.

The present results are new and original for the heat transfer and fluid flow in a porous tilted triangle enclosure filled by Cu-water nanofluid. The results would benefit scientists and engineers to become familiar with the flow behaviour 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 theoretically investigate the steady two‐dimensional boundary‐layer flow past a moving semi‐infinite flat plate in a water‐based nanofluid containing three different types of nanoparticles: copper (cuprum) Cu, alumina (aluminium oxide) Al₂O₃, and titania (titanium dioxide) TiO₂. The effects of moving parameter λ as well as solid volume fraction parameter φ on the flow and heat transfer characteristics are studied. Taking into account the rising demands of modern technology, including chemical production, power stations and microelectronics, there is a need to develop new types of fluids that will be more effective in terms of heat exchange performance.

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.

There is a region of unique solutions for λ>0, however, multiple (dual) solutions exist for λ_c<λ≤0 and no solutions for λ<λ_c<0. A reverse flow is formed when λ<0.

The solutions can be obtained up to a certain value of the moving parameter (critical value or turning point). The boundary layer separates from the plate beyond the turning point hence it is not possible to get the solution based on the boundary‐layer approximations after this point. To obtain further solutions, the full Navier‐Stokes equations have to be solved.

The present results are original and new for the boundary‐layer flow and heat transfer of a moving flat plate in a nanofluid. Therefore, this study would be important for the scientists and engineers in order to become familiar with the flow behaviour and properties of such nanofluids, and the way to predict the properties of this flow for the process equipments.