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The purpose of this paper is to study the effects of Soret and Dufour effects on convective heat and mass transfer flow through a porous medium in a rectangular duct in the presence of inclined magnetic field.

Using the non-dimensional variables, the governing equations have been transformed into a set of differential equations, which are non-linear and cannot be solved analytically, therefore finite element method has been used for solving the governing equations.

The influence of thermo-diffusion, diffusion thermo, radiation, dissipation, heat sources and the inclined magnetic field on all the flow, heat and mass transfer characteristics has been found to be significant.

The problem is relatively original as it combines many effects as Soret and Dufour effects and chemical reaction under inclined magnetic field.

The purpose of this study is to investigate the effects of entropy generation of some embedded thermophysical properties on heat and mass transfer of pulsatile flow of non-Newtonian nanofluid flows between two porous parallel plates in the presence of Lorentz force are taken into account in this research.

The governing partial differential equations (PDEs) were nondimensionalized using suitable nondimensional quantities to transform the PDEs into a system of coupled nonlinear PDEs. The resulting equations are solved using the spectral relaxation method due to the effectiveness and accuracy of the method. The obtained velocity and temperature profiles are used to compute the entropy generation rate and Bejan number. The influence of various flow parameters on the velocity, temperature, entropy generation rate and Bejan number are discussed graphically.

The results indicate that the energy losses can be minimized in the system by choosing appropriate values for pertinent parameters; when thermal conductivity is increasing, this leads to the depreciation of entropy generation, and while this increment in thermal conductivity appreciates the Bejan number, the Eckert number on entropy generation and Bejan number, the graph shows that each time of increase in Eckert will lead to rising of entropy generation while this increase shows a reduction in Bejan number. To shed more light, these results were further demonstrated graphically. The current research was very well supported by prior literature works.

All results are presented graphically, and the results in this article are anticipated to be helpful in the area of engineering.

This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe₃O₄ and MoS₂-Fe₃O₄.

The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios.

Results obtained show that the Cu-Fe₃O₄hybrid nanofluid exhibits higher entropy generation than the MoS₂-Fe₃O₄ hybrid nanofluid when comparing them at a Rayleigh number of 10⁶ and a Darcy number of 10^–1. The MoS₂ hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10^–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 10⁴are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS₂ nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 10⁵ and a Darcy number of 10^–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature.

The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

The purpose of this paper is to analyze the thermal-diffusion and diffusion-thermo effects on magnetohydrodynamics (MHD) natural convective flow through porous medium in a rotating system with ramped temperature.

Using the non-dimensional variables, the flow governing equations along with corresponding initial and boundary conditions have been transformed into non-dimensional form. These non-dimensional partial differential equations are solved by using finite element method. This method is powerful and stable. It provides excellent convergence and flexibility in providing solutions.

The effects of Soret number, Dufour number, rotation parameter, magnetic parameter, Hall current parameter, permeability parameter, thermal Grashof number, solutal Grashof number, Prandtl number, thermal radiation parameter, heat absorption parameter, Schmidt number, chemical reaction parameter and time on the fluid velocities, temperature and concentration are represented graphically in a significant way and the influence of pertinent flow governing parameters on the skin frictions and Nusselt number are presented in tabular form. On the other hand, a comparison for validation of the numerical code with previously published work is performed, and an excellent agreement is observed for the limited case existing literature.

A very useful source of information for researchers on the subject of MHD flow through porous medium in a rotating system with ramped temperature.

The problem is moderately original, as it contains many effects like thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects and chemical reaction.

The analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities.

The cavity inclination angle is fixed ω = 0 in case (I) and ω=π4 in case (II). The traditional fluid is water, and Fe3O4+MWCNT+Cu/H2O is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions.

The average heat transfer rate is computed for four combinations of ternary nanofluids: Fe3O4(25%)+MWCNT(25%)+Cu(50%),Fe3O4(50%)+MWCNT(25%)+Cu(25%),Fe3O4(33.3%)+MWCNT(33.3%)+Cu(33.3%) and Fe3O4(25%)+MWCNT(50%)+Cu(25%) under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations.

The purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications.

The current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells.

To the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective Fe3O4+MWCNT+Cu/H2O ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.

This paper aims to focus on the mathematical modeling of magnetohydrodynamic natural convective boundary layer flow of nanofluids past a stationary and moving inclined porous plate considering temperature and concentration gradients with suction effects.

The transformed non-dimensional and coupled governing partial differential equations are solved numerically using the finite element method.

The obtained numerical results for physical governing parameters on the velocity, temperature and concentration distributions are exemplified graphically and presented quantitatively. The boundary layer thickness increased with the increasing values of Soret, Dufour and Grashof numbers, while the thickness of boundary layer decreased with increasing values of suction for both stationary and moving plate cases. The primary and secondary velocity profiles are decreasing with an angle of inclination for moving plate and inclination has no significant effect for the stationary plate. An increase of the Soret number and Dufour number tend to increase the heat and mass transfer, while an increase of suction reduces the heat and mass transfer.

The problem is an important contribution to the field of nanofluid science and technology and is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids. This study is relatively original in nanofluids.

The purpose of this paper is to present age-based replacement models subject to shocks and failure rate in order to determine the optimal replacement cycle. As a result, according to system reliability, maintenance costs of the system are to be minimized.

First, the modeling with respect to assumptions and two major factors (shocks and failure rate) is done. Second, by using of MATLAB the optimal parameters are obtained. Finally, analysis of results and comparison of models are done.

Analysis of results shows all models provide optimal replacement cycle and at this time, cost rate of the system by considering the reliability rate is minimal. Also with an increase of one unit to two units, reliability rate increases much higher than the rate of cost.

This work provides models that in addition to considering the failure rate (internal factors), also shocks as an external factor have been considered. By considering these two factors more comprehensive and adaptable models have been proposed.

This paper aims to study the mathematical modeling of passive cooling systems for electronic devices. Improving heat transfer is facilitated by the correct choice of the working fluid and the geometric configuration of the engineering cavity; therefore, this work is devoted to the analysis of the influence of the position of the heat-generating element and the tilted angle of the electronic cabinet on the thermal convection of a non-Newtonian fluid.

The area of interest is a square cavity with two cold vertical walls, while the horizontal boundaries are adiabatic. An element of constant volumetric heat generation is placed on the lower wall of the chamber. The problem is described by Navier–Stokes partial differential equations using dimensionless stream function and vorticity. The numerical solution is based on the developed computational code using the finite difference technique and a uniform rectangular grid.

The key conclusions of this work are the results of a detailed analysis of streamlines and isotherms, the average Nusselt number and profiles of the average heater temperature. It was found that more intensive cooling of the heat-generating element occurs when the cavity is filled with a pseudoplastic fluid (n < 1) and not inclined (α = 0). The Rayleigh number of Ra = 10⁵ and the thermal conductivity ratio of k = 100 are characterized by the most positive effect.

The originality of the research lies in both the study of thermal convection in a square chamber filled with power-law fluid under the influence of a volumetric heat production element and the analysis of the influence of geometric and thermophysical parameters characterizing the considered process.

The purpose of this paper is to investigate the convective heat transfer of magnetic nanofluid (MNF) inside a square enclosure under uniform magnetic fields considering nonlinearity of magnetic field-dependent thermal conductivity.

The properties of the MNF (Fe₃O₄+kerosene) were described by polynomial functions of magnetic field-dependent thermal conductivity. The effect of the transverse magnetic field (0 < H < 10⁵), Hartmann Number (0 < Ha < 60), Rayleigh number (10 <Ra <10⁵) and the solid volume fraction (0 < φ < 4.7%) on the heat transfer performance inside the enclosed space was examined. Continuity, momentum and energy equations were solved using the finite element method.

The results show that the Nusselt number increases when the Rayleigh number increases. In contrast, the convective heat transfer rate decreases when the Hartmann number increases due to the strong magnetic field which suppresses the buoyancy force. Also, a significant improvement in the heat transfer rate is observed when the magnetic field is applied and φ = 4.7% (I = 11.90%, I = 16.73%, I = 10.07% and I = 12.70%).

The present numerical study was carried out for a steady, laminar and two-dimensional flow inside the square enclosure. Also, properties of the MNF are assumed to be constant (except thermal conductivity) under magnetic field.

The results can be used in thermal storage and cooling of electronic devices such as lithium-ion batteries during charging and discharging processes.

The accuracy of results and heat transfer enhancement having magnetic field-field-dependent thermal conductivity are noticeable. The results can be used for different applications to improve the heat transfer rate and enhance the efficiency of a system.