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This study incorporates the impact of shape factor and slip conditions on a radiative hybrid magnetic nanofluid over slanted sheet being convectively heated within a porous medium, providing valuable insights for enhancing thermal management systems in manufacturing techniques such as the extrusion of plastic films, cooling of metallic plates, and the drawing of polymer fibers. The effect of viscous dissipation, thermal radiation, aligned magnetic field, velocity slip, heat generation, buoyancy force, porosity, and thermal slip on the dynamics of fluid movement are comprehensively discussed. The governing equations were simplified into nonlinear ordinary differential equations through similarity variables and Bvp4c solver in MATLAB was utilized to observe the effects of pertinent parameters on temperature and velocity profiles, alongside the local Nusselt number and skin friction coefficient. It was determined that the hybrid nanofluid’s effective thermal conductivity was most significantly enhanced by blade-shaped nanoparticles. The local Nusselt number enhanced with upsurge of thermal radiation parameter and Biot number whereas opposite trend was observed with incrementation in other parameters. The augmentation in thermal slip and velocity slip resulted in lowering local skin friction coefficient. This research highlights the complex interplay between various physical factors and their influence on the dynamics of hybrid nanofluids, offering potential strategies for optimizing performance of thermal systems comprising hybrid nanofluids.

The performance of a unit-load warehouse depends on numerous parameters such as storage area, layout, aisle configuration, width-to-depth ratio, the number and locations of dock doors, storage policy, etc. These parameters typically relate to the layout configuration, which can be either traditional (rectangle-shaped) or non-traditional (contour-line-shaped). In this paper, we analyze the performance of rectangle-shaped and contour-line-shaped storage areas within a unit-load warehouse having multiple dock doors. Expected distances traveled in rectangle-shaped storage areas are compared with expected distances in their counterpart contour-line-based storage areas when an ABC class-based storage policy is used to assign unit-loads. For a single product class, the expected-distance for a rectangle-shaped storage area is at most 6.07% greater than it is for the corresponding contour-line-shaped storage area. Depending on the skewness of the ABC curve or storage areas for multiple classes, the expected distance for rectangle-shaped storage areas can be no more than 0.59% greater than it is for the corresponding contour-line shaped storage areas when multiple dock doors are distributed with a specified distance between them.

Numerical simulation was offered for scrutinizing the freezing of water within the complex container. The container has elliptic left adiabatic wall while the right wall is sinusoidal wall and maintained at cold temperature. The drawback of water has been removed by adding alumina nanoparticles. For this modeling, different ranges of volume and shape factor of nanoparticles have been scrutinized by incorporating FEM. The configuration of grid alters with change of time and verification test has been presented which proved good accuracy. As bigger shape factor has been selected, the time of process decline less than 4% for cylinder shape and this percentage augments around 78.22% for blade shape. As nanoparticle fraction increases, the required time declines around 26.84%. The impact of blade shape in view of adding nanoparticles is 25.74% greater than that of cylinder shape.

Enhancement of heat transfer employing nanofluids, studied numerically, observed profound effects in thermophysical and theological properties used in various applications such as avionics, laser diode, rocket nozzels and microelectronics. In this paper, the influence of thermal radiations and hybrid nanoparticles on free convection flow and heat transfer of Casson hybrid nanofluid over vertical plate is investigated. A mixture of pure water and ethylene glycol has been considered as a base Casson fluid while Copper oxide ($\mathrm{\text{CuO}}$) as nanofluid (single kind) and, Copper oxide ($\mathrm{\text{CuO}}$) and Silicon dioxide ($\mathrm{\text{Si}}{\mathrm{\text{O}}}_2$) (double kind known as hybrid nanofluid) are disseminated in base Casson fluid mixture to be formed as hybrid nanofluid. The governing system of partial differential equations of the flow and heat transfer processes is converted to a system of well-posed coupled nonlinear ordinary differential equations by using the similarity transformations. The resulting system is solved using the Galerkin finite element (GFE) technique. The quadratic Lagrange polynomials are used as basis functions over the mesh of about 1000 to 2000 finite elements and the nonlinear system of order 6003 and upto 12003 is solved. The accuracy of developed numerical methods is confirmed by comparing their results with convection flow and heat transfer with nanoparticles. Thereafter, the said solutions are used to investigate the effects of thermal radiation, hybrid nanoparticle volume friction, Prandtl number, type of flow and heat transfer behavior. The innovative results of the present study reported higher velocities in suspensions with low sphericity particles and the radiation parameter is directly proportional to the temperature with the use of nano and hybrid nanoparticles. It has also been noted that the GFE method is a more stable numerical technique as compared with other existing analytic and semi-analytical methods.

Natural convection takes up the attention of researchers due to its expansive industrial and engineering utilizations i.e., heat exchangers and electronic cooling. In this work, free convection of Cu-H₂O nanoliquid flow and heat transfer (HT) in porous circular wavy domain under the internal heat generation has been perused by finite element method (FEM). The shape factor of nanomaterials is also considered. The influences of active factors like Rayleigh number Ra, nanofluid concentration, wavy wall’s contraction ratio A, number of undulations D, and shape factor of nanomaterials m are explored on flow and HT specifications. Moreover, the correlations for average Nusselt number Nu_ave have been attained with regard to impressive parameters of current study. Findings show that Nu_ave soars with soaring nanofluid concentration and nanoparticles’ shape factor. Further, the outcomes characterize that Nu_ave may lessen up to 15.11% and 9.95% by detracting A from 0.1 to 0.3 and by mounting D from 4 to 12, respectively.

A model is developed to account for the size-dependent melting temperature of pure metallic and bimetallic nanowires, where the effects of the contributions of all surface atoms to the surface area, lattice and surface packing factors and the cross-sectional shape of the nanowires are considered. As the size decreases, the melting temperature functions of pure metallic and bimetallic nanowires decrease almost with the same size-dependent trend. Due to the inclusion of the above effects, the present model can also be applied to investigate the melting temperature depression rate of different low-dimensional system, accurately. The validity of the model is verified by the data of experiments and molecular dynamics simulations.

The significance of hybrid nanofluid flow over a flat plate lies in its ability to enhance heat transfer, improve energy efficiency, enable temperature control, and provide surface protection. For instance, hybrid nanofluids can provide a protective coating on the surface of a flat plate due to the presence of nanoparticles. This coating can offer improved corrosion resistance, erosion resistance, and anti-fouling properties. Consequently, it can extend the lifespan of the flat plate and reduce maintenance requirements. In this study, we examined how several characteristics, such as variable viscosity, chemical reaction, thermal radiation and shape factor of nanoparticles, affect the flow of a hybrid nanofluid (H${}_2\mathrm{\text{O}}+\mathrm{\text{MWCNT}}+\mathrm{\text{CuO}}$) through a flat plate. The equations required to represent the problem have been turned into a system of nonlinear ordinary differential equations, and this system has been unraveled by means of the bvp4c solver. Outcomes are provided for three instances related to shape factor i.e. Platelet, Cylinder and Spherical. Using Multiple Linear Regression (MLR), we investigated how physical parameters of concern together with friction factor, are affected by a variety of parameters. It is remarked that the fluid’s velocity lessens as the variable viscosity parameter enhances. It is discovered that the temperature profile increases with the rise in exponential heat source parameter ($Qe$). It is discovered that when $0.1\le Qe\le 2.5$, the Nusselt number declines by 0.03588 (Platelet shape), 0.03562 (Cylinder shape), and 0.03489 (Spherical shape). It has been noted that magnetic field parameter (Mg) reduces the coefficient of skin friction. At $0\le \mathrm{\text{Mg}}\le 3$, the skin friction coefficient is seen to drop at a rate of 1.15018 (Platelet shape), 1.14871 (Cylinder shape), and 1.14476 (Spherical shape). There is an enhancement in the Sherwood number with the rise in Schmidt number (St) and chemical reaction parameter (Cr). At $0.1\le \mathrm{\text{Cr}}\le 1.3,$ the Sherwood number is seen to rise at a rate of 0.248303 (Platelet shape), 0.248344 (Cylinder shape), and 0.248447 (Spherical shape). Furthermore, it is detected that the fluid’s temperature rises as the thermal radiation parameter enhances and the entropy generation increases as the variable viscosity parameter increases.

In this paper, considering the structure of the shape factor and the rough element, combined with fractal geometry theory, the shape factor, the relative increase in the heat transfer between the rough surface and the smooth surface in a fractal unit, and the fractal analytical expression of the dimensionless equivalent thermal conductivity caused by convection thermal conductivity are derived. In addition, the relationship between the microstructure parameters of the rough surface and the shape factor, the relative increase in convective heat transfer and the dimensionless equivalent thermal conductivity are studied. It is found that the relative increment of the convective heat transfer and the shape factor are proportional to the ratio of the minimum height and maximum height of the rough element and the fractal dimension, and the dimensionless equivalent thermal conductivity model deduced in this paper is compared with the existing experimental data to verify the validity of the model.

Many scholars have studied the interporosity flow function (IFF) and shape factor. However, the existing research does not consider the complex microstructure of dual media and the influence of fluid types on interporosity flow. In this paper, the anisotropic IFF and shape factor model of power-law fluid in smooth and rough fracture dual media are established by using the rough capillary bundle model and considering the influence of the microstructure of dual media and the type of fluid. The relationship between IFF, shape factor, and relative roughness in dual media is studied. It is found that the relative roughness is inversely proportional to the IFF and inversely proportional to the shape factor. In addition, the model is compared with the existing research and experimental data to verify the rationality of the model.

The influence of different shapes of nanoparticles on peristaltic flow of Casson fluid in an asymmetric channel is studied in this paper. The suspension of Copper oxide nanoparticles of needle, platelet and lamina shapes is taken into account. The problem is modeled in partial differential equations with suitable slip boundary conditions. The standard nonlinear equations are solved by the Homotopy Analysis Method in Mathematica Software. The influences of different shapes of nanoparticles on concentration, velocity profile and temperature profile are analyzed through the graphs. It is observed that the different shape of nanoparticles has different thermal conductivity, but the lamina shaped nanoparticles have high thermal conductivity as compared to needle and platelet shaped nanoparticles.