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The effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.

The thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained.

The conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number T_a is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number T_a leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.

This research paper is new and original.

The aim of the present study is to examine the ferrohydrodynamic laminar boundary layer flow of electrically non-conducting magnetic fluid on a uniformly heated and radially stretchable disk with or without rotation in the presence of an externally applied magnetic field.

Governing equations give rise to highly non-linear coupled partial differential equations which are reduced to a set of ordinary differential equations in dimensionless form by the means of conventional similarity transformation. These equations are further discretized using central finite difference scheme. And, the solution is obtained in MATLAB environment by finding the missing boundary conditions using shooting method.

The effects of magnetic field dependent viscosity and rotation strength parameter on velocity and temperature profiles are investigated. Besides, the other significant physical quantities such as radial and tangential skin frictions, rate of heat transfer and boundary layer displacement thickness are also computed. The obtained results are discussed quantitatively and qualitatively.

Heat transfer in ferrofluid flow over a radially stretchable and uniformly heated rotating disk has not been investigated yet.

Thermoconvective instability with Soret effect in multi-component fluids has wide range of applications in heat and mass transfer. This work deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on Soret-driven ferrothermohaline convection heated and salted from below in an anisotropic porous medium subjected to a transverse uniform magnetic field. The resulting eigen value problem is solved using Brinkman model. An exact solution is obtained for the case of two free boundaries and the stationary and oscillatory instabilities are investigated by using linear stability analysis and normal mode technique for the vertical of anisotropic porous medium. The analysis has been made for different parameters like porosity, anisotropy, ratio of heat transport to mass transport, buoyancy magnetization, non-buoyancy magnetization, Soret parameter and Salinity Rayleigh number. The effect of MFD viscosity is assumed to be isotropy. It is found that the presence of MFD viscosity has a stabilizing effect, whereas magnetization has a destabilizing effect.

The purpose of this paper is to examine the effect of magnetic field on ferrofluid convective mode with radiation.

Viscosity of Fe₃O₄ ferrofluid is considered as a function of magnetic field. Solutions of the governing equations are obtained by a powerful numerical method, namely, control volume finite element method (CVFEM). Roles of radiation parameter (Rd), number of undulations (N), Fe₃O₄–water volume fraction (ϕ), Hartmann (Ha) and Rayleigh numbers are illustrated graphically. A correlation for Nu_ave is extracted.

The inner wall temperature decreases with increasing buoyancy forces, but increases with increasing Rd and Ha. Also increasing Rd results in increasing nanofluid motion. This influence is more evident when convection flow is dominant. As nanofluid temperature increases, the nanofluid begins moving from the warm surface to the outer one and dropping along the circular cylinder. At low Rayleigh number, conduction is more significant than convection. |Ψ_max| increases as buoyancy force increases and it decreases as the Lorentz force increases. As Hartmann number increases, the center of the vortices moves to x = 0. As Ra increases, convection becomes stronger. Thus, |Ψ_max| and temperature gradient increase with increasing Ra. As N increases, the distortion of isotherms reduces and vortices become weaker. Increasing Hartmann number results in a reduction in the thermal plume and the heat transfer mechanism changes from convection to conduction. Nusselt number decreases with increasing N ⋅ Nu decreases with increasing Lorentz force. At N = 5 , increasing the Lorentz force causes the main vortices to convert into three smaller ones. As the Lorentz force increases, the two upper vortices merge together and the thermal plume vanishes. The number of extrema in the Nu_loc profile matches the existence of the thermal plume and the number of undulations. Nu_ave increases with increasing Rd. As buoyancy forces increase, the temperature decreases and in turn Nu_ave increases with increasing Ra.

Nanofluids are an innovative way to enhance radiation heat. In this paper, MHD Fe₃O₄–water nanofluid natural convection with radiation source term is examined. Magnetic field-dependent (MFD) viscosity is considered. Using the CVFEM, numerical simulations are carried out for various values of the radiation parameter (Rd = 0 to 0.8), volume fraction of Fe₃O₄–water (ϕ = 0 to 0.04), Rayleigh number (Ra = 10³, 10⁴ and 10⁵), number of undulations (N = 3,4 and 5) and Hartmann number (Ha = 0 to 40).

The purpose of this research is to describe the importance of the Cattaneo–Christov theory of heat conduction in a triangular enclosure with a semi-circular heater. Analysis subjected to Fe₃O₄-H₂O nanofluid is reported. Viscosity dependent on magnetic field is taken into consideration to simulate ferrofluid viscosity. Besides, heat generation and shape factor of nanoparticles are also considered.

The well-known control volume finite element method is used for simulations.

The outcomes reveal that the magnetic field can be introduced to the system as a controlling element.

No such analysis exists in the literature.

Nanofluid flow which is squeezed between parallel plates is studied using differential transformation method (DTM). The fluid in the enclosure is water containing different types of nanoparticles: Al₂O₃ and CuO. The effective thermal conductivity and viscosity of nanofluid are calculated by Koo–Kleinstreuer–Li (KKL) correlation. The comparison between the results from DTM and numerical method are in well agreement which proofs the capability of this method for solving such problems. Effects of the squeeze number and nanofluid volume fraction on flow and heat transfer are examined. Results indicate that Nusselt number augment with increase of the nanoparticle volume fraction. Also, it can be found that heat transfer enhancement of CuO is higher than Al₂O₃.

The problem of nanofluid flow which is squeezed between parallel plates is investigated analytically using DTM. The fluid in the enclosure is water containing different types of nanoparticles: Al₂O₃ and CuO. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL correlation. In this model, effect of Brownian motion on the effective thermal conductivity is considered. The comparison between the results from DTM and numerical method are in well agreement which proves the capability of this method for solving such problems. The effect of the squeeze number and the nanofluid volume fraction on flow and heat transfer is investigated. The results show that Nusselt number increase with increase of the nanoparticle volume fraction. Also, it can be found that heat transfer enhancement of CuO is higher than Al₂O₃.

The effect of the squeeze number and the nanofluid volume fraction on flow and heat transfer is investigated. The results show that Nusselt number increase with increase of the nanoparticle volume fraction. Also, it can be found that heat transfer enhancement of CuO is higher than Al₂O₃.

This paper is original.

The effect of a magnetic field on nanofluid natural convection in a porous annulus is simulated. Control volume-based finite element method (CVFEM) is applied to find the influence of tilted angle and Darcy, Rayleigh and Hartmann numbers on nanofluid hydrothermal behavior. Vorticity stream function formulation is taken into account. Also, Brownian motion effect on nanofluid thermal conductivity is considered. Results reveal that Hartmann number and tilted angle make changes in nanofluid flow style. Nusselt number enhances with augment of Darcy number and buoyancy forces but reduces with rise of tilted angle and Hartmann number.

The influence of adding CuO nanoparticles in water on the velocity and temperature distribution in an inclined half-annulus was studied considering constant heat flux. CVFEM is applied to the simulation procedure.

Influences of CuO volume fraction, inclination angle and Rayleigh number on hydrothermal manners are presented.

Results indicate that inclination angle makes changes in flow style. The temperature gradient enhances with rise of buoyancy forces, whereas it reduces with augment of inclination angle.

This paper aims to investigate non-Darcy magnetohydrodynamic nanofluid flow in a uniformly porous medium. It is assumed that viscosity of nanofluid (Fe₃O₄-water) is a function of external magnetic field. Roles of Darcy number, inclination angle, volume fraction of nanofluid, Hartmann and Rayleigh numbers are demonstrated graphically.

The problem is modeled, and simulation has been done by means of control volume base finite element method.

Results proved that Nusselt number enhances with augment of buoyancy forces and Darcy number while it decreases with the increase of Lorentz forces. Isotherms become denser near the inner cylinder with increase of inclination angle and the Darcy number.

As per the authors’ knowledge, this problem is new and not been published before.

This study comprehensively examines entropy generation and thermosolutal performance of a ternary hybrid nanofluid in a partially active porous cabinet. The purpose of this study is to comprehend the intricate phenomena of double diffusion by investigating the dispersion behavior of Al₂O₃, CuO, and Ag nanoparticles in water.

The cabinet design consists of two horizontal walls and two curved walls with the lower border divided into a heated and concentrated region of length b and the remaining sections are adiabatic. The vertical borders are cold and low concentration, while the upper border is adiabatic. Two cavity configurations such as convex and concave are considered. A uniform porous medium is taken within the ternary hybrid nanofluid. This has been characterized by the Brinkman-extended Darcy model. Thermosolutal phenomena are governed by the Navier-Stokes equations and are solved by adopting a higher-order compact scheme.

The present study focuses on exploring the influence of several well-defined parameters, including Rayleigh number, Darcy number, Lewis number, Buoyancy ratio number, nanoparticle volume concentration and heater size. The results indicate that the ternary hybrid nanofluid outperforms both the mono and hybrid nanofluids in all considered aspects.

This study brings forth a significant contribution by uncovering novel flow features that have previously remained unexplored. By addressing a well-defined problem, the work provides valuable insights into the enhancement of thermal transport, with direct implications for diverse engineering devices such as solar collectors, heat exchangers and microelectronics.

In this paper the effects of viscous dissipation and ohmic heating on the fluid flow and resulting heat and mass transfer caused by vertically moving rotating disk are explored with magnetic field acting perpendicular to disk rotation. The flow regime is also under the influence of Dufour and Soret effects.

An approach of similarity transformation is used to transform the governing set of equations into non-linear ordinary differential equations. Numerical simulations are carried out in Maple software to study the influence of incorporated non-dimensional parameters viz. disk movement parameter (−0.3 < S < 0.2), magnetic parameter (0.1 < M < 0.4), Eckert number (0.1 < Ec < 1), Schmidt number (0.1 < Sc < 1), Soret parameter (0.1 < Sr < 1) and Dufour number (0.1 < Du < 1) on velocity, temperature and concentration profiles.

The upward/downward motion of the disk along with rotation set up a three-dimensional flow over the disk surface and exerts the same effects as injection/suction through the wall. It is also observed that incorporated parameters along with disk movement greatly affect the flow regime and associated heat and mass transfer.

The present study examines the heat and mass transfer characteristics of incompressible Newtonian fluid over an impermeable rotating disk moving vertically. The effect of viscous dissipation and ohmic heating is considered. To the best of the authors’ knowledge, such consideration is yet to be published in the literature.