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In heat transfer, fluids and nanoparticles can provide new innovative technologies with potential to adapt the heat transfer fluid’s thermal properties through control over particle size, shape and others. This paper aims to examine the effects of spherical and non-spherical (cylinder, disk, platelets, etc.) shapes of silver (Ag) nanoparticles on heat transfer enhancement and inherent irreversibility in hydromagnetic water base nanoliquid flow over a convectively heated stretching sheet with heat generation/absorption.

Applying suitable similarity constraints, the model partial differential equations are transformed into a set of nonlinear ordinary differential equations. Solutions are obtained analytically via optimal homotopy asymptotic method (OHAM) and numerically via shooting technique coupled with the Runge-Kutta-Fehlberg (RK-F) method.

The impact of Ag nanoparticle’s shape along with other germane factors, such as Biot number, magnetic field, solid volume fraction and heat source/sink on velocity and thermal profiles, Nusselt number, skin friction coefficient, heat transfer enhancement, rate of entropy generation and irreversibility ratio, are scrutinized via graphical simulations and discussed. This study revealed that cylindrical shape Ag nanoparticles generate high entropy and fluid friction irreversibility, whereas disk shape Ag nanoparticles exhibit high transfer enhancement rate. Moreover, a boost in magnetic field intensity, volume-fraction parameter and Biot number enhances the thermal boundary layer thickness.

The main objective of this work is to examine the different Ag nanoparticles shape effects on the heat transfer enhancement and inherent irreversibility owing to hydromagnetic nanoliquid flow past a convectively heated stretching sheet with heat source/sink, which has not been yet studied. It is hope that this study will bridge the gap in the present literature and serve as impetus to scholars, engineers and industries for more exploration in this direction. The intrinsic nonlinearity of the model equations precludes its exact solution; hence, OHAM and shooting technique coupled with the RK-F method have been used to numerically tackle the problem. Pertinent results are discussed quantitatively and displayed graphically and in tabular form.

The study aims to numerically examine the impact of nanoparticles on an unsteady flow of a Williamson fluid past a permeable convectively heated shrinking sheet.

In sort of the solution of the governing differential equations, suitable transformation variables are used to get the system of ODEs. The converted equations are then numerically solved via the shooting technique.

The impacts of such parameters on the velocity profile, temperature distribution and the concentration of nanoparticles are examined through graphs and tables. The results point out that multiple solutions are achieved for certain values of the suction parameter and for decelerating flow, while for accelerating flow, the solution is unique. Further, the non-Newtonian parameter reduces the fluid velocity and boosts the temperature distribution and concentration of nanoparticles in the first solution, while the reverse drift is noticed in the second solution.

The current results may be used in many applications such as biomedicine, industrial, electronics and solar energy.

The authors think that the current results are new and significant, which are used in many applications such as biomedicine, industrial, electronics and solar energy. The results have not been considered elsewhere.

In this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.

Infinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.

The impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (β_T, β_C), mixed convection parameter (α), Hartmann number (M²), Weissenberg number (We), nonlinear radiation parameter (N_R), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.

The velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

The purpose of this study is to examine the flow and heat transfer performance of titanium oxide/water and copper/water nanofluids with varying nanoparticle morphologies by considering magnetic, Joule heating and viscous dissipation effects. Furthermore, it studies the irreversibility caused by the flow of a hydromagnetic nanofluid past a radiated stretching sheet by considering different shapes of TiO₂ and Cu nanoparticles with water as the base fluid.

In this study, the authors investigated entropy production in an unsteady two-dimensional magneto-hydrodynamic nanofluid regime using water as the base fluid and five unique TiO₂ and Cu nanoparticle morphologies. Using appropriate similarity transformations, the controlling nonlinear system of partial differential equations is transformed into a system of ordinary differential equations. The shooting technique with Runge–Kutta method was then used to solve these equations quantitatively. The findings of this study are depicted graphically, and the skin friction corresponding to various nanoparticle geometries and physical parameter variations is tabulated.

To assess the reliability of the current findings, a tabular representation of the data was compared to that of previously published studies. It is noted that a reduction in thermal energy was detected as a result of the higher levels of Prandtl number (Pr). It is further analysed that the highest heat energy generation of TiO₂ nanoparticles was larger than that of Cu nanoparticles. The most important finding was that the sphere-shaped Cu/H₂O nanofluid had the lowest velocity and greatest temperature. Also, Cu nanoparticles in the shape of platelets generate the most entropy, while TiO₂ nanoparticles in the shape of spheres generate the least.

To the best of the knowledge of the authors, the attempt to investigate the previously unexplored shape effects of TiO₂ and Cu nanoparticles on the heat transfer enhancement and inherent irreversibility caused by hydromagnetic nanofluid flow past a radiated stretching sheet with magnetic, Joule heating and viscous dissipation effects. This study fills this gap in the existing literature and encourages scientists, engineers and businesses to do more research in this area. This model can be used to improve heat transfer in systems that use renewable energy, thermal management in industry and the processing of materials.

The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this paper is to investigate the entropy generation and homogeneous–heterogeneous reaction. Velocity and thermal slips are considered instead of no-slip conditions at the boundary.

Basic equations in form of partial differential equations are converted into a system of ordinary differential equations and then solved using the spectral quasi-linearization method (SQLM).

The validity of the model is established using error analysis. Variation of the velocity, temperature, concentration profiles and entropy generation against some of the governing parameters are presented graphically. It is to be noted that the increase in entropy generation due to increase in heterogeneous reaction parameter is due to the increase in heat transfer irreversibility. It is further noted that the Bejan number decreases with Brinkman number because increase in Brinkman number reduces the total entropy generation.

This paper acquires realistic numerical explanations for rapidly convergent temperature and concentration profiles using the SQLM. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The resulting equations are then integrated using the SQLM. The influence of emergent flow, heat and mass transfer parameters effects are shown graphically.

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation.

The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables.

Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile.

The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken.

Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

This work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al₂O₃), silicon dioxide (SiO₂) and titanium dioxide (TiO₂) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.

Through the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.

Numerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.

The fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

The purpose of this study is to present the magnetohydrodynamic (MHD) flow and heat transfer in an accelerating film of a non-Newtonian pseudo-plastic nanofluid along an inclined surface with viscous dissipation and Joule heating.

An incompressible and inelastic fluid is assumed to obey the Ostwald-de-Waele power law model and the action of viscous stresses is confined to the developing momentum boundary layer adjacent to the solid surface. Viscous dissipation and Joule heating on the flow of electrically conducting film in the presence of uniform transverse magnetic field is considered for the Carboxyl Methyl Cellulose (CMC) water-based nanofluid. The fluid is the CMC-water-based with concentration (0.1-0.4 per cent) containing three types of nano-solid particles Cu, Al₂O₃ and TiO₂. The modeled boundary layer conservation equations are transformed to dimensionless, coupled and highly non-linear system of differential equations, and then solved numerically by means of a local non-similarity approach with shooting technique. To validate the numerical results, a comparison of the present results is made with the earlier published results and is found to be in good agreement.

The effects of magnetic parameter, Prandtl number, Eckert number and Biot numbers on the velocity and temperature fields are presented graphically and discussed for various values of thermo-physical parameters. It has been found that magnetic field decelerates the fluid velocity for both cases of Newtonian nanofluid and pseudo-plastic nanofluid because of the generated drag-like Lorentz force. This is of great benefit in magnetic materials processing operations, utilizing static transverse uniform magnetic field, as it allows a strong regulation of the flow field.

The numerical study is valid for two-dimensional, steady, laminar film flow of Ostwald-de-Waele power law non-Newtonian nanofluid along an inclined plate. A uniform transverse magnetic field of strength B₀ is applied perpendicular to the wall. Assume that the base fluid and the nano-solid particles are in thermal equilibrium with no slip effects. The interaction of magnetic field with nanofluid has several potential implications and may be used to deal with the problems such as cooling nuclear reactors by liquid sodium and inducting the flow meter which depends on the potential difference in the fluid along the direction perpendicular to the motion and to the magnetic field.

The study has significant applications in magnetic field control of materials processing systems.

The results of the present study may be attentiveness to the engineers and applied mathematicians who are interested in hydrodynamics and heat transfer enhancement associated with film flows.

The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by stretching sheets. Heat transfer effects are accounted in view of viscous dissipation and nonlinear thermal radiation.

Optimal homotopic asymptotic method procedure is adopted to obtain the analytical solution of nonlinear ordinary differential equations.

It has been noticed that Hartmann and Brinkman number has reverse characteristics against entropy generation and Bejan number.

To the best of the authors’ knowledge, no such analysis has been reported to date.

The purpose of this paper is to present an inclusive study of the mixed convective flow involving micropolar fluid holding kerosene/water-based TiO₂ nanoparticle towards a vertical Riga surface with partial slip. The outcomes are confined for opposing and assisting flows.

Similarity equations are acquired and then worked out numerically by the Keller box technique.

Impacts of significant parameters on microrotation velocity, temperature distribution, velocity profile together with the Nusselt number and the skin friction are argued with the help of graphs. Two solutions are achieved in opposing flow, while the solution is unique in assisting flow. It is also monitored that the separation of boundary layer delays because of micropolar parameter and accelerates because of volume fraction.

The authors trust that all these results are new and significant for researchers.