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The current investigation aims to examine heat transfer as well as entropy generation analysis of Powell-Eyring nanofluid moving over a linearly expandable non-uniform medium. The nanofluid is investigated in terms of heat transport properties subjected to a convectively heated slippery surface. The effect of a magnetic field, porous medium, radiative flux, nanoparticle shapes, viscous dissipative flow, heat source, and Joule heating are also included in this analysis. The modeled equations regarding flow phenomenon are presented in the form of partial-differential equations (PDEs). Keller-box technique is utilized to detect the numerical solutions of modeled equations transformed into ordinary-differential equations (ODEs) via suitable similarity conversions. Two different nanofluids, Copper-methanol (Cu-MeOH) as well as Graphene oxide-methanol (GO-MeOH) have been taken for our study. Substantial results in terms of sundry variables against heat, frictional force, Nusselt number, and entropy production are elaborate graphically. This work’s noteworthy conclusion is that the thermal conductivity in Powell-Eyring phenomena steadily increases in contrast to classical liquid. The system’s entropy escalates in the case of volume fraction of nanoparticles, material parameters, and thermal radiation. The shape factor is more significant and it has a very clear effect on entropy rate in the case of GO-MeOH nanofluid than Cu-MeOH nanofluid.

Nowadays, with the advantages of nanotechnology and solar radiation, the research of Solar Water Pump (SWP) production has become a trend. In this article, Prandtl–Eyring hybrid nanofluid (P-EHNF) is chosen as a working fluid in the SWP model for the production of SWP in a parabolic trough surface collector (PTSC) is investigated for the case of numerous viscous dissipation, heat radiations, heat source, and the entropy generation analysis. By using a well-established numerical scheme the group of equations in terms of energy and momentum have been handled that is called the Keller-box method. The velocity, temperature, and shear stress are briefly explained and displayed in tables and figures. Nusselt number and surface drag coefficient are also being taken into reflection for illustrating the numerical results. The first finding is the improvement in SWP production is generated by amplification in thermal radiation and thermal conductivity variables. A single nanofluid and hybrid nanofluid is very crucial to provide us the efficient heat energy sources. Further, the thermal efficiency of MoS 2 –Cu/EO than Cu–EO is between 3.3 and 4.4% The second finding is the addition of entropy is due to the increasing level of radiative flow, nanoparticles size, and Prandtl–Eyring variable.

MHD Natural convection, which is one of the principal types of convective heat transfer in numerous research of heat exchangers and geothermal energy systems, as well as nanofluids and hybrid nanofluids. This work focuses on the investigation of Natural convective heat transfer evaluation inside a porous triangular cavity filled with silver-magnesium oxide/water hybrid nanofluid [H 2 O/Ag-MgO] hnf under a consistent magnetic field. The laminar and incompressible nanofluid flow is taken to account while Darcy–Forchheimer model takes account of the advection inertia effect in the porous sheet. Controlled equations of the work have been approached nondimensional and resolved by Galerkin finite element technique. The numerical analyses were carried out by varying the Darcy, Hartmann, and Rayleigh numbers, porosity, and characteristics of solid volume fraction and flow fields. Further, the findings are reported in streamlines, isotherms and Nusselt numbers. For this work, the parametric impact may be categorized into two groups. One of them has an effect on the structural factors such as triangular form and scale on the physical characteristics of the important outputs such as fluidity and thermal transfer rates. The significant findings are the parameters like Rayleigh and slightly supported by Hartmann along with Darcy number, minimally assists by solid-particle size and rotating factor as clockwise assists the cooler flow at the center and anticlockwise direction assists the warmer flow. Clear raise in heat transporting rate can be obtained for increasing solid-particle size.

Fluidity and thermal transport across the triangular aperture with lower lateral inlet and apply placed at the vertical outlet of the chamber which filled with efficient TiO 2 –SiO 2 /water hybrid nanofluid under the parametrical influence. Several parameters are tested like the numbers of Hartmann ( 0 ≤ H a ≤ 100 ), Richardson ( 0 ≤ R i ≤ 5 ), and Reynolds ( 10 ≤ R e ≤ 1000 ) were critiqued through streamlines, isotherms, and Nusselt number ( Nu ). Numerical model has to be developed and solved through the Galerkin finite element method (GFEM) by discretized with 13,569 triangular elements optimized through grid-independent analysis. The Hartmann number ( Ha ), exerts minimal impact over the flow and thermal aspects while the other parameters significantly manipulate the physical nature of the flowing and thermal aspects behaviors.

Heat transfer in a symmetrical cavity with two semi-cylinders was explored in this study. Several parameters, such as (103≤Ra≤106), (10−5≤Da≤10−2), (0.02≤ϕ≤0.08), (0.2≤ε≤0.8), and (0≤Ha≤100) were selected and evaluated in this research. The outcome of the magnetic field and the temperature gradient on the nanofluid flow is considered. The geometric model is therefore described using a symmetry technique. The flow issue for the governing equations has been solved using the Galerkin finite element method (G-FEM), and these solutions are presented in dimensionless form. The equations for energy, motion, and continuity were solved using the application of the COMSOL Multiphysics® software computer package. According to the results, there is a difference in the occurrence of the magnetic parameter and an increase in heat transmission when the right wall is recessed inward. The heat transmission is also significantly reduced when the right wall is exposed to the outside. The number of Nusselt grows directly proportional to the number of nanofluids in the environment. In contrast, all porous media with low Darcy and Hartmann numbers, high porosity, and low volume fraction have high Nusselt numbers. It is found that double streamlines for the hot side and single cooling for Darcy, Rayleigh, and Hartmann numbers. A cold isotherm at various physical parameters is needed in the top cavity. Rayleigh’s number and a solid volume fraction raise Darcy’s number, increasing heat transmission inside the cavity and thermal entropy determines entropy components.

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

In this present paper, we investigate a two dimensional magnetohydrodynamic (MHD) stagnation flow over shrinking sheet in the presence of thermal radiation. In this study, the effects of magnetic, heat generation or absorption, radiation and Prandtl number parameter are taken into consideration. An appropriate similarity transformation is introduced to transform the governing partial differential equations into a system of ordinary differential equations then solved using bvp4c in MATLAB. The effects of the involved parameters such as magnetic field, velocity, heat generation/absorption, Prandtl number as well as local Nusselt number are calculated numerically. Result on skin friction and temperature increased as the magnetic field increased. While, the temperature decreased as the radiation parameter increased as well as the Prandtl number.

A fluid’s moving class improves its heat transmission capability, as well as its rigidity, owing to multivariate molecule suspension. In this way, nanofluids are superior to common fluids. In this study, we evaluated the features of ease and heat transfer. Furthermore, we investigated permeable media, heat source, variable heat conductivity, and warm irradiation results. A mathematical technique known as the Galerkin finite element (G-FEM) approach was used to solve the supervising conditions. Third-grade nanofluid (TGNF), which consists of two types of nanoparticles (NPs), single-walled carbon nanotubes (SWCNT), and multi-walled carbon nanotubes (MWCNTs) distributed in a base liquid of carboxymethyl cellulose (CMC) water, was used for this examination. The main conclusion of this study is that MWCNT-CMC nanofluid has a higher heat transfer velocity than SWCNT-CMC nanofluid. The entropy of the framework can be increased by adjusting the thermal conductivity. Additionally, we found that increasing the main volume section decreases the speed but increases the dispersion of atomic energy. In order to separately account for the development properties of inertial forces and shallow heat dispersion forces, Reynolds and Brinkman values can be used to accelerate the entropy rate of the heating framework.

Modeling the boundary layer flow of ternary hybrid nanofluids is important for understanding and optimizing their thermal performance, particularly in applications where enhanced heat transfer and fluid dynamics are essential. This study numerically investigates the boundary layer flow of alumina-copper-silver/water nanofluid over a permeable stretching/shrinking sheet, incorporating both first and second-order velocity slip. The mathematical model is solved in MATLAB facilitated by the bvp4c function that employs the finite difference scheme and Lobatto IIIa formula. The solver successfully generates dual solutions for the model, and further analysis is conducted to assess their stability. The findings reported that only one of the solutions is stable. For the shrinking sheet case, increasing the first-order velocity slip delays boundary layer separation and enhances heat transfer, while, when the sheet is stretched, the second-order velocity slip accelerates separation and improves heat transfer. Boundary layer separation is most likely to occur when the sheet is shrinking; however, this can be controlled by adjusting the velocity slip with the inclusion of boundary layer suction.

Solar radiation, which is emitted by the sun, is required to properly operate photovoltaic cells and solar water pumps (SWP). A parabolic trough surface collector (PTSC) installation model was created to investigate the efficacy of SWP. The thermal transfer performance in SWP is evaluated thru the presence of warmth radiation and heat cause besides viscid dissipation. This evaluation is performed by measuring the thermal transmission proportion of the selected warmth transmission liquid in the PTSC, known as a hybrid nano-fluid. Entropy analysis of Oldroyd-B hybrid nano-fluid via modified Buongiorno's model was also tested. The functions of regulating parameters are quantitatively observed by using the Keller-box approach in MATLAB coding. Short terms define various parameters for tables in velocity, shear pressure and temperature, gravity, and Nusselt numbers. In the condition of thermal radiation and thermal conductivity at room temperature, the competence of SWP is proven to be enhanced. Unlike basic nano-fluids, hybrid nano-fluids are an excellent source of heat transfer. Additionally, with at least 22.56% and 35.01% magnitude, the thermal efficiency of AA7075-Ti-6Al-4 V/EO is higher than AA7075-EO.