This computational study examines the electrophoretic and thermophoretic particle deposition, as well as the mass and heat transfer, of a dissipative and radiative Fe3O4 aqueous nanofluid flow in a porous, inclined annular medium under the influence of a magnetic field. The modelling of the current problem resulted in a complex, non-linear system of partial differential equations. These equations are solved by adopting a finite difference approach. The computed results are in exceptional agreement with those of existing results. This study demonstrates that for the normal incidence of inclination , hydrostatic pressure plays a major role in the axial velocity and also when the annulus is horizontal maximum axial velocity moves downward. Adjusting the radiation parameter improves thermal efficiency and homogeneity in nanofluid-based heating systems. As the values of the electrophoretic particle deposition parameter increase, the concentration of the nanofluid enhances, whereas the concentration diminishes with a rise in the thermophoretic particle deposition parameter. Higher values of radiation parameters increase the nanofluid's heat transfer rate and the increased values of the viscous dissipation diminish the heat transfer rate.
The research on heat and flow in porous annular regions offers substantial benefits by enhancing thermal efficiency, improving fluid management, and providing insights into complex flow behaviors, making it a critical area of research in engineering and environmental sciences. Recently, Nield and Simmons presented a mathematical representation to show the heat transport behaviour in a porous medium. In their study of Rogers-Horton-Lapwood issue with significant anisotropy and heterogeneity, Nield and Kuznetsov looked at a straightforward scenario in which two isotropic and homogeneous layers in a horizontal plane produced heterogeneity. The authors first developed and statistically computed the eigenvalue issue by deriving a novel hydrodynamic boundary value at the point of interaction between two different porous media. Nield and Bejan have presented a chapter to express the first law of thermodynamics in a permeable region. The authors have considered an isotropic medium with negligible radiation, heat dissipation, and work done through pressure variations. The effects of solid boundaries and momentum forces on mass transport in a permeable medium have been investigated numerically and experimentally by Vafai and Tien. The authors used the local volume-averaging approach to solve the model while considering the mass transport via the permeable medium close to an impermeable border. Heat transmission and liquid flow in the interface zone created between two distinct porous media were analyzed by Vafai and Thiyagaraja. The authors studied the interface area between a permeable and an impermeable region, as well as three kinds of interface regions between a liquid region and a permeable medium. Vafai and Tien explored the inertial forces and a solid border effect on heat transmission in a porous domain. The authors focused on analyzing the flow via a porous media near a non-permeable boundary. The TNE model and the internal heat production effect were considered by Rani et al. while analyzing the heat and fluid flow via an internally heated porous layer. The authors estimated the field variables using the ANN model and the finite element approach (FEA). Leela et al. considered the impact of three different viscous dissipation models on heat transfer and addressed the problem using the FEA and ANN-based models.
Double-diffusive natural convection (DDNC) refers to natural convection that occurs when temperature and concentration gradients interact. The phenomena of DDNC in fluid-saturated porous material have been widely studied because of their significance in many applications. Examples include flow through packed beds, dispersion of chemicals in water-saturated soil, moisture migration in fiber insulation and grain storage, energy extraction from geothermal reservoirs, and chemical reactors used to separate or purify mixes.
DDNC fluxes in porous media have applications in geophysics, electrochemistry, metallurgy, and other domains. These characteristics have prompted theoretical, experimental, and numerical research on this phenomenon. Using the implicit finite difference approach, Hossain and Rees have examined the impact of buoyant forces on mass and heat diffusion via natural convective flow from an upward wavy surface. The authors concentrated on surface shear stress, heat transmission rate, and surface concentration gradient changes as a function of the governing variable. Shilpa and Leela have examined heat and solute transport in an inclined annulus, considering double diffusive convection, heat generation/absorption, and a distinct order of chemical reaction rates. The authors have addressed the coupled nonlinear system of PDEs by considering the implicit FDM approach. Using an implicit FDM, Hossain et al. evaluated the temperature-reliant viscosity influence on the free convection of a viscous fluid from a vertical undulating surface. Shilpa et al. examined the DDC of a couple-stress fluid in porous channels considering the linearly varying wall temperature boundary conditions. The authors have used the FEM to solve the modelled nonlinear coupled system of DEs of the model.
In recent years, the study of nanofluid magnetohydrodynamics (MHD) in permeable media has become a novel field of study. In such a situation, the imposed magnetic field reduces flow velocities and degrades heat exchange, but the high surface area of the porous medium and the suitable thermophysical characteristics of the nanofluid tend to increase heat transmission. Here are a few recent works on the topic. Khaled Al-Farhany et al. have investigated the quantitative dynamics of a Fe3O4-aqueous fluid in an inclined curvilinear lid-driven space under the influence of an angled magnetic field. The authors demonstrated that while the average Nu and Sh drop with rising Hartmann numbers, they rise with enhancing Re, nanoparticle volume fraction, and fin length. The impact of a magnetic field and a distinct thermo-solutal source on stable DDC in a dual-sided cavity containing liquid potassium alloy has been investigated numerically by Gnanasekaran and Satheesh using the finite volume approach. According to the authors, the Reynolds number causes the heat and mass transmission to rise, whereas the Hartmann number causes them to fall. Using the Soret and Dufour effect in complex regions, Mohammadi and Gandjalikhan investigated the effect of radiation on DDC.
Numerous studies have focused on heat transmission analysis of nanofluids within enclosures. Due to density and temperature gradients, natural heat transfer takes place inside enclosures and is frequently employed in industrial and technological settings. This phenomenon affects thermal insulating systems in buildings, solar collectors, commercial heat exchangers, fiber insulation, nuclear cooling elements, grain storage regions, and room air conditioners. Due to its significance, recent numerical and experimental research has focused on free convection. FeO nanoliquid packed in an enclosure between a rhombus and a wavy circular cylinder has been the subject of interest by Dogonchi and Hashim on free convection heat transport. Using a 2D nanofluid model, the authors have examined the effects of heat radiation and magnetic fields (MF) on three distinct forms of FeO-water nanofluids. Also, Hosseinzadeh et al. experimentally reviewed the impact of a magnetic field on the friction factor and heat transfer enhancement of FeO/water nanofluid. The calculations were done at various Reynolds number values and MF intensities in a device that contained a horizontal circular tube. The free convective flow and temperature efficiency characteristics of an inclined, partially warmed rectangular permeable cavity filled with an electroconductive ternary nanofluid were examined by Thirumalaisamy et al. with viscous dissipation and a tilted magnetic field, and they used the Marker and Cell approach to obtain the solution. By taking non-uniform heat source/sink effects, Shilpa and Leela explored the HMT of three distinct nanofluids in a vertical annulus. The authors have determined that the Jeffrey fluid performs better than the Oldroyd-B and Maxwell fluids concerning heat transport. Suneetha et al. have analyzed the hybrid nanofluid flow HMT in a stretching sheet by considering irreversibility effect. Revathi et al. have explored the hybrid nanofluid flow and heat transmission in a microchannel considering activation energy and distinct heat sources. Also, Revathi et al. have investigated the nanofluid flow HMT in a porous medium considering thermal radiation and activation energy effect.
Thermal radiation plays a major role in many technical advances, including propulsion equipment for space vehicles, satellites, airplanes, nuclear power systems, and gas turbines. Consequently, several studies exist to illustrate the effects of radiative thermal transfer in nanofluids. In the boundary layer of a shifting magneto nanofluid, Sedki investigated the chemical processes, solar radiation, and Brownian movement effects on mixed convection HMT caused by a porous stretched surface that generates heat through a porous medium. Irfan et al. used a thermal non-equilibrium model to numerically assess heat transport by all three modes in a saturated permeable square cavity. The authors used the FEM to solve the governing PDEs, assuming that the flow complies with Darcy's law.
As an energy source, viscous dissipation (VD) modifies temperature distributions and affects the heat transmission rate. The significance of VD is dependent on whether the plate is frozen or warmed. Exact examples of real-world applications where the final output of desired features depends on the freezing pace and stretching process include the ejection of heat towards the creation of materials, the production of paper, the freezing of electronic chips, and so on. VD is a prime instance of this phenomenon. Fand and Buckner and Fand et al. investigated the VD influences on free convection in a flat cylinder immersed in porous media. Their analysis indicated that VD should not be overlooked. Saeid and Pop examined the effect of VD on free convection in a permeable cavity and noticed that increasing the VD parameter affects the heat transport in the hot region. Israel-Cookey et al. evaluated the impact of VD and radiative unsteady MHD convective flow across a permeable vertical plate. They found that increasing VD results in an augmentation in the thermal profile. Leela et al. explored the effect of three distinct VD models on heat with flow in a microporous channel by considering the induced magnetic field effect. Irfan et al. analyzed heat transport with the impact of radiation and VD in a square porous cavity. The authors presented the Nu at warm and cold walls of the cavity for distinct values of VD with radiation parameters. Also, Irfan et al. have explored the VD and radiation effect on convective flow in a permeable annular medium. The authors observed a reduction in the mean Nu at the hot surface and an enhancement in the mean Nu at the cold region for the increased values of the VD parameter.
According to a recent study, the mechanisms of gravity, convection, Brownian diffusion, electrophoresis, and thermophoresis are accountable for aerosol particle deposition. The distribution and rate of particle deposition on an annular surface will be examined in this work using thermophoresis and electrophoresis. A temperature gradient that pushes fluid from high to low temperatures and causes particles to travel from high to lower temperatures is known as the thermophoresis effect. Electrophoresis occurs when charged particles move and come in touch with one another. The electric field applied to particles, whether positively or negatively charged, affects their deposition rate differently. When particles are less than a micron, then the effects of electrophoresis and thermophoresis are substantial. As particle sizes increase, gravity and inertia become more important.
The connection between particle deposition and thermophoresis has been provided by many authors. The most often used connection was given by Tablot et al.. The impact of thermophoresis on particle accumulation in laminar flow systems has been the subject of much research in the last few years. Batchelor and Shen discussed the effects of TPD in flow across flat surfaces, cylinders, and spinning objects using a similarity technique. Goren found that the thermophoretic energy is inclined to pull the particle away from the surface when the heat of the object's surface is greater than the flow field. Tsai and Liang investigated the phenomena using thermophoresis when the region heat was lower than the fluid heat. In 2007, Postelnicu investigated the TPD effect on a horizontal permeable flat plate in a free convectional flow environment. In 2024, Shilpa et al. numerically examined the TPD effect on heat and solute transport of nanolubricants and tri hybrid nanofluids in stretching sheet and inclined annular geometry, considering radiation and non-linear heat source/sink effects. Particle deposition is influenced by thermophoresis, electrophoresis, and gravitational forces. Cooper et al. used convection-diffusion speed and electrophoretic velocity to estimate the deposition of particle rates in an axially symmetric and stagnant viscous flow model. A mathematical representation of the accumulation of particles in a 2D stationary flow field that takes electrophoresis, convection, diffusion, and gravity into consideration was presented by Turner et al.. The governing equation was further developed using the similarity approach, which could be solved using the FDM, by Hwang and Daily, who finished their analytical and empirical studies on silicon particle accumulation under the influence of an electric field in 1995. Tsai and Huang concentrated on the impact of electrophoretic and thermophoretic deposition in 2010. Chamkha and Pop have analysed the HMT past a vertical flat plate by considering the thermophoretic particle deposition effect. Theories of CCHF and generalised Fick's relations were employed by Gangadhar et al. to examine the modern aspects of HMT. Salma et al. have explored the thermal conductivity variations of alumina nanofluid in an annulus.
The synergistic effects of electrophoretic and thermophoretic particle deposition, in conjunction with viscous dissipation and radiative heat transfer, on the thermo-hydrodynamic behavior of a FeO₄-water nanofluid in a porous inclined annular configuration are also investigated in this work. To the best of the author's knowledge, no prior open literature report has included such a thorough investigation -- integrating these concurrent transport mechanisms. The work meticulously clarifies the interaction between the previously described physical influences on heat and mass transport properties by using a robust finite difference approach. A deeper understanding of the underlying transport physics is provided by the graphical analysis of the temperature, concentration, and velocity fields, as well as the variation of Nusselt and Sherwood numbers.
Crucially, this study establishes the foundation for contemporary practical applications like the following while also enhancing the theoretical framework of nanofluid dynamics in porous structures: