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The present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.

The governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (T_h) left wall and a cold (T_c) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (10⁴ ≤ Ra ≤ 10⁵) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θ_f = 0.5) and volume fraction (ϕ = 0.04).

The findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 10⁴ to 10⁵, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.

This research is for two-dimensioal laminar flow only.

PCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.

As per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid.

The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles.

Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios.

The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.

The purpose of this study is to analyze the free convection phenomena arising from a temperature disparity between a cold circular cylinder and a heated corrugated cylinder.

Numerical simulations were used to analyze the convection patterns. The inner cylinder, made of a thermally conductive solid material, was heated through its inner surface, while the space between the cylinders was filled with air. The governing equations for velocity, pressure and temperature were solved using a Galerkin finite element method-based solver for partial differential equations.

The study explored various parameters affecting the dynamic and thermal structure of the flow, including the Rayleigh number (10³ ≤ Ra ≤ 10⁶), the number of corrugations of the inner cylinder (3 ≤ N ≤ 18), the thermal conductivity of the hollow cylinder (1 ≤ K ≤ 200) and the angle of inclination of the inner cylinder (0° ≤ φ ≤ 90°). Results indicated a notable sensitivity of flow intensity to changes in the Rayleigh number and the inner cylinder’s inclination angle φ. Particularly, for Ra = 10⁶, the average heat transfer rate increased by 203% with a K ratio increment from 1 to 100 but decreased by 16.3% as the number of corrugations increased from 3 to 18.

This research contributes to understanding the complex interplay between geometry, thermal properties and flow dynamics in natural convection systems involving cylindrical geometries. The findings offer useful insights for improving the transfer of heat procedures in real-world situations.

This study aims to investigate magnetohydrodynamic (MHD) conjugate pure mixed convection considering interior heat production and resistive heating inside a square closed/open cavity featuring a rotating cylinder for aiding (clockwise) and opposing (counterclockwise) flow configurations. Moreover, the impacts of altering cylinder size and conductivity on the system’s overall performance to determine optimum conditions are examined in this investigation.

The closed chamber is differentially heated by keeping high and low temperatures at the vertical boundaries. In contrast, the open cavity has a heated left wall and an open right boundary. The Galerkin finite element method is used to solve the Navier–Stokes and the thermal energy equations, which construct the present study’s mathematical framework. Numerical simulations are conducted for the specified ranges of several controlling parameters: Reynolds (31.62 ≤ Re ≤ 1000), Grashof (10³ ≤ Gr ≤ 10⁶) and Hartmann numbers (0 ≤ Ha ≤ 31.62), and volumetric heat generation coefficient (Δ = 0, 3).

When Gr, Re and Ha simultaneously increase, the average Nusselt number along the warmed boundary rises accordingly. Conversely, interior heat production lowers heat transmission within the computational domain, which is also monitored regarding mean fluid temperature, overall entropy production and thermal performance criterion. Finally, the open cavity confirms better thermal performance than the closed cavity.

Comprehending the impacts of the magnetic field, Joule heating, internal heat generation and enclosed or open boundary on pure MHD combined free-forced convective flow offers valuable understandings of temperature fluctuations, velocity propagations, heat transport and irretrievable energy loss in numerous engineering applications.

This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid’s non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations.

Following the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles.

Remarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena.

Available studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap.

The purpose of this paper is to analyze the mechanism of nanofluid enhanced heat transfer in microchannels and promote the application of nanofluids in industrial processes such as solar collectors, electronic cooling and automotive batteries.

The two-phase lattice Boltzmann method was used to calculate the flow and heat transfer characteristics of Al₂O₃ nanofluids in a microchannel at Re = 50. By comparing the simulation results of pure water, nanofluids without calculated nanoparticle-fluid interaction forces and nanofluids with calculated nanoparticle-fluid interaction forces, the effects of physical properties improvement and interaction forces on flow and heat transfer are quantified.

The findings show that the nanofluid (φ = 3%, R = 10 nm) increases the average Nusselt number by 22.40% at Re = 50. In particular, 16.16% of the improvement relates to nanoparticles optimizing the thermophysical parameters of the base fluid. The remaining 6.24% relates to the disturbance of the thermal boundary layer caused by the interaction between nanoparticles and the base fluid. Moreover, the nanoparticle has a negligible effect on the average Fanning friction factor. Ultimately, we conclude that the nanofluid is an excellent heat transfer working medium based on its performance evaluation criterion, PEC = 1.225.

To the best of the authors' knowledge, this research quantifies for the first time the contribution of nanoparticle-liquid interactions and nanofluids physical properties to enhanced heat transfer, advancing the knowledge of the nanoparticle's behavior in liquid systems.

The main purpose of this study is to analyze the heat transfer phenomena in a dynamically bulging enclosure filled with Cu-water nanofluid. This study examines the convective heat transfer process induced by a bulging area considered a heat source, with the enclosure's side walls having a low temperature and top and bottom walls being treated as adiabatic. Various factors, such as the Rayleigh number (Ra), nanoparticle volume fraction, Darcy effects, Hartmann number (Ha) and effects of magnetic inclination, are analyzed for their impact on the flow behavior and temperature distribution.

The finite element method (FEM) is employed for simulating variations in flow and temperature after validating the results. Solving the non-linear partial differential equations while incorporating the modified Darcy number (10⁻³ ≤ Da ≤ 10⁻¹), Ra (10³ ≤ Ra ≤ 10⁵) and Ha (0 ≤ Ha ≤ 100) as the dimensionless operational parameters.

This study demonstrates that in enclosures with dynamically positioned bulges filled with Cu-water nanofluid, heat transfer is significantly influenced by the bulge location and nanoparticle volume fraction, which alter flow and heat patterns. The varying impact of magnetic fields on heat transfer depends on the Rayleigh and Has.

The geometry configurations employed in this research have broad applications in various engineering disciplines, including heat exchangers, energy storage, biomedical systems and food processing.

This research provides insights into how different shapes of the heated bulging area impact the hydromagnetic convection of Cu-water nanofluid flow in a dynamically bulging-shaped porous system, encompassing curved surfaces and various multi-physical conditions.

The performance of solid fins inside a differentially heated cubical cavity is numerically studied in this paper. The main purpose of the study is to make an optimization to reach the maximum heat transfer in the enclosure having the solid fins with studied parameters.

The considered domain of interest is a differentially heated cube having heat-conducting solid fins placed on the heated wall while an opposite wall is a cooled one. Other walls are adiabatic. Governing equations describing natural convection in the fluid filled cube and heat conduction in solid fins have been written using non-dimensional variables such velocity and vorticity taking into account the Boussinesq approximation for the buoyancy force and ideal solid/fluid interfaces between solid fins and fluid. The formulated equations with appropriate initial and boundary conditions have been solved by the finite difference method of the second of accuracy. The developed in-house computational code has been validated using the mesh sensitivity analysis and numerical data of other authors. Analysis has been performed in a wide range of key parameters such as Rayleigh number (Ra = 10⁴–10⁶), non-dimensional fins length (l = 0.2–0.8), non-dimensional location of fins (d = 0.2–0.6) and number of fins (n = 1–3).

From numerical methods point of view the used non-primitive variables allows to perform numerical simulation of convective heat transfer in three-dimensional (3D) regions with two advantages, namely, excluding difficulties that can be found using vector potential functions and reducing the computational time compared to primitive variables and SIMPLE-like algorithms. From a physical point of view, it has been shown that using solid fins can intensify the heat transfer performance compared to cavities without any fins. Fins located close to the bottom wall of the cavity have a better heat transfer rate than those placed close to the upper cavity surface. At high Rayleigh numbers, increasing the fins length beyond 0.6 leads to a reduction of the average Nusselt number, and one solid fin can be used to intensify the heat transfer.

The present numerical study is based on hybrid approach for numerical analysis of convective heat transfer using velocity and vorticity that has some mentioned advantages. Obtained results allow intensifying the heat transfer using solid fins in 3D chambers with appropriate location and length.

The purpose of this study is to develop a new numerical algorithm to simulate the phase-field model.

First, the derivative of the temporal direction is discretized by a second-order linearized finite difference scheme where it conserves the energy stability of the mathematical model. Then, the isogeometric collocation (IGC) method is used to approximate the derivative of spacial direction. The IGC procedure can be applied on irregular physical domains. The IGC method is constructed based upon the nonuniform rational B-splines (NURBS). Each curve and surface can be approximated by the NURBS. Also, a map will be defined to project the physical domain to a simple computational domain. In this procedure, the partial derivatives will be transformed to the new domain by the Jacobian and Hessian matrices. According to the mentioned procedure, the first- and second-order differential matrices are built. Furthermore, the pseudo-spectral algorithm is used to derive the first- and second-order nodal differential matrices. In the end, the Greville Abscissae points are used to the collocation method.

In the numerical experiments, the efficiency and accuracy of the proposed method are assessed through two examples, demonstrating its performance on both rectangular and nonrectangular domains.

This research work introduces the IGC method as a simulation technique for the phase-field crystal model.

This study aims to examine the cilia-driven flow of magnetohydrodynamics (MHD) non-Newtonian fluid through a porous medium. The Jeffrey fluid model is taken into account. The fluid motion in a two-dimensional symmetric channel emphasizes the dominance of viscous properties over inertial properties in the context of long wavelength and low Reynolds number approximations.

An integrated numerical and analytic results are obtained by hybrid approach. A statistical method analysis of variance along with response surface methodology is used. Sensitivity analysis is used to validate the accuracy of nondimensional numbers.

The impact of various flow parameters is presented graphically and in numerical tables. It is noted that the velocity slip parameter is the most sensitive flow parameter in velocity and relaxation to retardation time ratio in temperature.

A model on cilia-generated flow of MHD non-Newtonian Jeffrey fluid is proposed.