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Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

The ternary hybrid nanofluids have potential in different technological arenas such as biomedical engineering, solar energy, atomic reactors, the automotive industry, and heat pipes. Given these facts, along with the recent advancements in nanotechnology and their extensive applications, this research focuses on the MoS₂-Fe₃O₄-ZrO₂/CH₃OH ternary nanofluid flow through bidirectional stretching sheets. We have transformed the coupled nonlinear partial differential equations for the advanced model into nondimensional ordinary differential equations using similarity transformations, and then semi-analytically apply the homotopy analysis methodology (HAM). We have displayed the physical features of potential factors graphically alongside the flowing factors based on velocity and temperature. We presented a physical evaluation in tabular format for the rate of heat transmission and compared the results with existing work to ensure their validity. These meaningful outcomes indicate that the axial fluid velocity is compressed by the magnetic interaction, inertial drag, porosity and stretchable ratio, while it is augmented by the Powell-Eyring factor and the changed Hartmann value. The effect of increasing transverse speed boosts inertial drag.

The investigation delves into the examination of Jeffreys fluid flow within a porous medium, incorporating a temperature-dependent heat source and throughflow, while also taking into account the presence of an external electric field. The eigenfunction, also known as the critical Rayleigh number, is obtained to determine the initiation of convection by employing Galerkin processes during the linear stability analysis. Subsequently, the findings are scrutinized by means of graphical illustrations to explore the impacts of various factors, including the Jeffreys parameter, heat source, throughflow, and electric field. Upon careful examination of the outcomes, it becomes evident that specific parameters, such as the Jeffreys parameter, heat source, and throughflow parameters, exert an influence in stabilizing the system under consideration. The investigation evidently points toward an observation that an augmentation in the electric field parameter results in an accelerated onset of convection. This observation implies that the external electric field assumes a role as a destabilizing element within the system, thereby intensifying the convective tendencies exhibited within the medium. The results demonstrated that elevated throughflow characteristics played a significant role in the postponement of convection onset, while a rise in the heat source parameter dependent on temperature was found to enhance the overall stability of the system. Additionally, it was observed that the downward throughflow exhibited a greater stabilizing influence when juxtaposed with the upward throughflow, particularly in scenarios involving the Jeffreys term and electric fields. The implications of these findings suggest a complex interplay between throughflow parameters, temperature-dependent heat sources, and external forces, highlighting the intricate dynamics governing convection initiation and system stability in the studied environment.

This paper considers two-dimensional electrically conducting and incompressible ternary hybrid nanofluid flow on a stretching sheet with the convective boundary condition and heat source effect. Relevant similarity formulas are effectuated in converting the governing equations into a system of ordinary differential equations (ODEs) and are further treated numerically using the spectral quasilinearization method (SQLM), with error analysis. The prominent dimensionless parameters controlling the flow, and heat transfer characteristics are discussed. The results of this study show that Eckert number, heat source parameter, and magnetic effect boost the temperature profile. This work expected significant information for the future applications of innovative heat transfer devices, as well as a valuable reference for researchers to study flow behavior under various assumptions.

This study emphasizes the dual exposition of the impact of convective condition and the significant effects of magnetic field, heat source and velocity slip on hybrid nanofluid flow over the exponentially shrinking sheet. The hybrid nanofluid is regarded as a contemporary variety of nanofluid; consequently, it is utilized to enhance the efficiency of heat transfer. By applying the Tiwari–Das model, the key objective of the current research is to investigate the impact of involving factors Biot number, Eckert number, volume fraction, magnetohydrodynamic (MHD), slip and suction on the temperature and velocity profiles. In addition, the Nusselt number and skin friction variations have been explored against the suction effect on the solid volume fraction of copper ${\varphi }_2\in$ [1–3%] and the Biot number $\mathrm{\text{Bi}}\in$ [1–3%]. The nonlinear partial differential equations are converted to a set of an ordinary differential equations by incorporating exponential similarity vectors. Eventually, ordinary differential equations are rectified utilizing MATLAB bvp4c solver. The results demonstrate the presence of dual exposition for suction with varying values of copper volume fraction and the Biot number. The heat transmission rate is observed to escalate in both cases as the strength of the Biot and Eckert numbers intensifies in the range of 1–3%. In summary, the results show that duality and non-unique solutions occur in the aiding flow situation when the suction $S\ge S_{\mathrm{\text{ci}}}$, while there is no flow and unique solutions of hybrid nanofluid feasible when $S<S_{\mathrm{\text{ci}}}$.

In recent days, entropy generation has attracted the attention of several researchers due to its applications in manufacturing electronic devices, heat exchangers, conservation of energy, and generation of power. Further, activation energy is an essential requirement in automobile and chemical industries, nuclear reactors, and so on. This paper investigation aims to examine the entropy generation and the mass and energy transfer in the magneto-hydro dynamic movement of convective Carreau-Yasuda nano liquid past a porous stretching sheet with the consequences of activation energy, energy source, and binary chemical reaction. Also, the analysis of the impact of viscous and Joule dissipation in the presence of suction/injection into the Buongiorno model is an essential objective of this study. By introducing a similarity variable, the partial differential equations are altered into a system of ordinary differential equations. Numerical solutions to the modified equations are determined by utilizing a BVP5C MATLAB package. The findings are presented visually for several relevant flow characteristics and explained carefully. The thermophoresis parameter and activation energy parameter optimize the concentration of nanoparticles. These outcomes further indicate that as the larger Brinkmann and permeability parameters the entropy generation is broadened. It is discovered that an augmentation in thermal and solutal Grashof numbers is associated with greater velocity distribution.

This research leads to carrying out the productivity and the efficiency of the carbon nanotubes (CNTs) that have extensive applications in solar collectors. Due to the superior thermal as well as electrical properties, the use of CNTs has an important contribution to the nanotechnology revolution. Therefore, owing to the aforementioned vital points, this investigation intended to put forth the thermophysical properties of both single and multi-walled CNT nanofluids past a stretching surface. Additionally, an electrically conducting nanofluid flow phenomenon enriches due to the inclusion of dissipation (Ohmic heating) and external heat source/sink. The dimensional form of the three-dimensional fluid flow phenomena is transformed to a non-dimensional form with the use of similarity transformation and further numerical procedure is implemented to solve the nonlinear governing equations. The substantial significance of the characterizing parameters is presented briefly via figures and the comparative analysis with the earlier investigation is deployed through the table. However, the main findings of this study are as follows: A significant attenuation in the shear rate is marked for the enhanced inertial drag but it augments for the augmented values of the magnetization; further, particle concentrations of both the CNTs favor accelerating the fluid momentum as well as temperature distribution.

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno’s relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile $\phi (\eta )$. Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number.