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The significant increase in thermal efficiency and the rate of energy exchange used in fuel dynamics and automobile coolants are leading to a better understanding of nanofluids. This computational analysis explores the thermal conductivity performance for radiative cross-flow of a nanofluid across an expanding/constricting sheet with a suction effect as a result of its application. To compute or calculate the magnificent point of nanofluid flow, the entropy, and asymmetrical heat source/sink effects are also elicited. The boundary layers traverse a stream-wise procedure for expanding and contracting sheets. Additionally, the study examines the features of heat transfer and cross-flow of nanofluids using numerical simulations. By employing similarity variables, the basic PDE equations of the current model are transformed into ODEs, and they are subsequently evaluated using the bvp4c method. Therefore, the effects of embedded flow variables on drag force, heat transfer rate, and entropy generation profiles have been framed using parametric research. Multiple solutions are offered for a specific range of the contracting parameter as well as the mass suction parameter. In addition, the heat transfer rate accelerates due to the heat source and decelerates due to the heat sink. The literature that is already published has been compared favorably, and it reveals many commonalities.

A number of scientists have indicated interest in the promising area of research that involves improving heat transmission by utilizing nanoparticles. The dynamic properties of nanofluids reflect several applications in the cooling process, thermal engineering, heat exchangers, magnetic cell separation, energy production, hyperthermia, etc. In light of the appealing implications of nanofluids, the current research aims to explore the melting process of MHD hybrid AA7072 and AA7075 alloy nanoparticles from a movable cylinder. It also incorporates the irregular Thompson and Troian slip effect to simulate the intricate features of the nanofluid flow. The primary nonlinear partial differential equations (NPDEs) are converted into nonlinear ordinary differential equations (NODEs) with the use of the similarity technique. These converted equations are unraveled numerically via applying the built-in program bvp4c in MATLAB. It is visually examined that physical parameters affect the temperature and skin friction. The outcomes suggest that double solutions are found in a certain range of movable cylinder parameter. In addition, the skin friction is decelerated due to the critical shear rate and velocity slip factors while it is enhanced with the influence of suction and nanoparticles volume fraction. Moreover, the temperature is uplifted due to nanoparticles volume fraction and is declined due to Stefan number. In case of quanitative descriptions, the skin friction boosted up by almost 3.64% and 1.18% for the particular upper and lower branch outcomes due to the superior influences of nanoparticle volume fraction. Also, the skin friction decelerated for the branch of upper and lower solutions at about 5.26% and 22.55%, respectively, due to the larger velocity slip parameter.

The fluid flow through blunt bodies that are yawed and un-yawed frequently happens in many engineering applications. The practical significance of deep-water applications such as propagation control, splitting the boundary layer over submerged blocks, and preventing recirculation bubbles is explained by the fluid flow across a yawed cylinder. The current work examined the mixed convective flow and convective heat transfer by incorporating water-based graphene oxide nanofluid around a yawed cylinder with viscous dissipation and irregular heat source/sink. To investigate the heat diffusion across the system of buoyancy effects, the mathematical formulation of the problem was modeled in terms of coupled, nonlinear partial differential equations. The boundary value problem of the fourth-order (bvp4c) solver was operated to find the non-similarity solution. The outcomes indicated that the velocity in both directions enlarged owing to the higher impacts of yaw angle for the phenomenon of assisting flow but decreased for the instance of opposing flow, while the temperature of nanofluid increased because of heightened estimations of yaw angle for both assisting and opposing flows. In addition, with larger impacts of nanoparticle volume fraction, the shear stresses were enhanced by about 0.76% and 0.93% for the case of assisting flow, while for the case of opposing flow, they improved by almost 0.65% and 1.38%, respectively.

The physiological systems and biological applications that have arisen during the past 15 years depend heavily on the microscale and nanoscale fluxes. Microchannels have been utilized to develop new diagnostic assays, examine cell adhesion and molecular transport, and replicate the fluid flow microenvironment of the circulatory system. The various uses of MHD boundary flow in engineering and technology are extensive, ranging from MHD power generators and the polymer industry to MHD flow meters and pumps and the spinning of filaments. In this investigation, the (Magnetohydrodynamic) MHD flow of Prandtl nanofluid is investigated along with mixed convection, energy activation, microorganism, and chemical reaction. The flow model is considered through partial differential equations in dimensionless form which is then integrated numerically via considering the Bvp4c technique. The outcome is numerous emerging physical parameters over velocity profile, temperature, mass concentration, and microorganism with the separate pertinent quantities such as the Prandtl fluid parameter, elastic fluid parameter, magnetic field, mixed convection parameter, activation energy, chemical reaction, Brownian motion, thermophoretic force, Prandtl number, and Schmidt number. The friction factor, rate of heat transfer and Sherwood number, and density of microbes are revealed numerically and graphically. The outcomes indicate that the Prandtl fluid parameter and elastic fluid parameter tend to enhance the velocity profile. It is also noted that the Prandtl fluid parameter depreciates the thermal rate with the addition of the concentration profile while the opposite trend is recorded for activation energy. Obtained numerical outcomes are correspondingly compared with the current statistics in limiting cases and a close match is obtained.

Water has attracted plenty of attention as a lubricant for manufacturing due to the fact that it is inexpensive, environmentally friendly, and efficient. Because of their outstanding mechanical capabilities, water dispensability, and range of real applications, graphene oxide (GO) materials have the potential to augment the effectiveness of water lubrication. With this encouragement, we inspect the impact of induced magnetism on the fluid flow near a stagnation point dispended with water-based GO nanoparticles caused by a movable surface with a homogeneous–heterogeneous chemical reaction. The leading equations and their related boundary constraints are first transformed into a non-dimensional form through the utilization of the similarity technique. The consequent equations are then numerically solved by employing the bvp4c scheme. Those figures are used to exemplify the stimulation of the relevant constraints on the fluid flow, induced magnetic profiles, temperature profiles, concentration profiles, heat transfer, and friction factor. It is observed that the nanoparticle’s volume fraction enhances the heat transfer rate, as well as the friction factor. The heat transfer and friction factor escalate by almost 11.71% and 0.96% for the respective upper-branch solutions due to the larger impacts of nanoparticles’ volume fractions, while for the lower-branch solutions, they are augmented at about 21.8% and 0.66%, respectively. In addition, double solutions can be found in the limited values of a movable parameter.

Given the importance and use of electrically conducted nanofluids, this work aims to examine an engine-oil-based nanofluid including various nanoparticles. In the current study, a fractional model for inspecting the thermal aspect of a Brinkman-type nanofluid, composed of (molybdenum disulfide (MOS2) and graphene oxide (GO) nanoparticles flows on an oscillating infinite inclined plate, which characterizes an asymmetrical fluid flow, heat, and mass transfer. Furthermore, the Newtonian heating effect, magnetic field, and slip boundary conditions were taken into account. The objectives for implementing the Prabhakar-like fractional model are justified because this fractional algorithm has contemporary definitions with no singularity restrictions. Furthermore, the guided fractional model was solved using the Laplace transform and several inverse methods. The obtained symmetrical solutions have been visually analyzed to investigate the physics of several relevant flow parameters on the governed equations. Some exceptional cases for the momentum field are compiled to see the physical analysis of the flowing fluid symmetry. The results show that the thermal enhancement can be progressively improved with the interaction of the molybdenum disulfide-engine oil-based nanofluid suspension, rather than with the graphene oxide mixed nanoparticle fluid. Furthermore, the temperature and momentum profiles enhance due to the factional parameters for molybdenum disulfide and the graphene oxide-engine oil-based nanofluid suspension. This study’s graphical and numerical comparison with the existing literature has shown a very close resemblance with the present work, which provides confidence that the unavailable results are accurate. The results show that an increase improved the heat transmission in the solid nanoparticle volume fractions. In addition, the increment in the mass and heat transfer was analyzed in the numerical evaluation, while the shear stress was enhanced with the enhancement in the Prabhakar fractional parameter α.

This study examines a viscous, incompressible, free-convective Casson fluid flow over an inclined plate, which characterizes an asymmetrical nanofluid flow and heat transfer behavior. Here, the two different nanofluids are basically made of molybdenum disulfide (MoS2) with CMC-based fluid and graphene oxide (GO) nanoparticles with CMC-based fluid to form a particular (CMC/MoS2) nanofluid and (CMC/GO) nanofluid. The Newtonian heating effect, slip boundary, porosity, and inclined magnetic effects are also considered. When memory effects are present, conventional PDEs are unable to investigate and evaluate the physical behavior of various flow parameters. We employed the Prabhakar fractional derivative, the best and most current fractional mathematical operator, to tackle the considered nanofluid problem. Using the integral transform approach, Laplace transforms, the non-dimensional governed model is converted into a fractional model and solved. The graphical analysis examines the influence and symmetrical behavior of significant physical and fractional parameters. The numerical effects of the Nusselt number, Sherwood number, and skin friction are also looked at, at various sundry values of the time. As a result, we conclude that increasing Prabhakar fractional constraints causes the thermal and momentum profiles to decelerate down. In addition, for two distinct values of time, 0.8 and 1.8, improvements of 3.823% and 5.042%, respectively, are observed in the mass transfer rate for the higher impacts of the Prabhakar fractional parameter, α, while the heat transfer rate declines by 10.065% and 15.908%, respectively. Also, the shear stress upsurges by 0.881% and 2.482%, respectively, for the change values of time 0.8 and 1.8 with higher values of Prabhakar fractional parameter α. Furthermore, with varying time, the accompanying criteria are satisfied, and the velocity and temperature fields both expand asymptotically in the y-direction and decline away from the plate. When comparing the two nanofluids, the (CMC/MoS2) nanofluid has a somewhat higher thermal and flow rate than the (CMC/GO) nanofluid. The studies indicated that increasing the volume percentage of nanoparticles causes heat transmission to be enriched.

The current exploration aims to inspect the features of thermal radiation on the buoyancy or mixed convective fluid flow induced by nanofluid through a stretching permeable bended sheet. The impact of activation energy and binary reaction along with slip migration is taken into account to discuss the fine points of water-based alumina nanoparticle flow. The structure of the curved sheet is assumed to be stretchable and the bended texture is coiled within a circular section with radius Rb. The similarity technique is utilized to reduce the leading partial differential equations into ordinary differential equations. These reduced equations are then deciphered numerically by employing the bvp4c method. The outcomes of the model were constructed in the form of several figures and bar graphs for the case of opposing and assisting flows with varying distinct embedded control parameters. The results display that the velocity field curves escalate with a higher radius of curvature parameter while temperature and concentration profiles shrink. More precisely, the outcomes show that the temperature distribution profile increases with the increase in nanoparticle’s volume fraction as well as thermal radiation parameter. Meanwhile, the concentration and velocity fields are decelerated with higher impacts of nanoparticle volume fraction. In addition, the heat and mass transfer rates were significantly improved for the higher value of the radiation and Schmidt number. On the other hand, the growing values of the velocity slip factor decrease the shear stress. Furthermore, the results are compared with the previous results in the limiting cases and observed a tremendous harmony.

In many industries, extremely high-performance cooling is a crucial requirement. However, the fundamental challenge to developing energy-efficient heat transfer fluids required for cooling is insufficient thermal conductivity. In this case, the utilization of nanofluid is effective to overcome these challenges. The current study aims to examine the two-dimensional (2D) stretching wall jet heat transfer fluid flow induced by a water-based alumina nanofluid embedded in a porous medium with buoyancy force. In addition, irregular heat sink/source and slip effects are assessed. The leading partial differential equations are changed into ordinary differential equations by incorporating similarity variables, then these equations are computationally or numerically worked out via the boundary-value problem of fourth-order (bvp4c) technique. The pertinent factors influencing the symmetry of the hydrothermal performance including friction factor, velocity, and temperature profiles, are illustrated using tables and graphs. The symmetrical outcomes reveal that the velocity declines in the presence of nanoparticles, whereas the temperature uplifts both assisting and opposing flows. Moreover, the friction factor augments due to porosity while the heat transfer rate declines.

The radiated flow of magnetized viscous fluid subject to the viscous dissipation phenomenon is numerically studied. The radiative phenomenon is addressed with nonlinear relations. Further, analysis is performed by using the slip effects and convective thermal flow constraints. The transformed problem is numerically evaluated using the Keller Box method. The physical parameter effects, such as the magnetic parameter for the velocity profile, Prandtl number, Brownian motion parameter and Biot number for the energy profile and Lewis number, and the thermophoresis parameter for the concentration profile are discussed. The obtained results suggest applications in enhancing the heat transfer phenomenon, thermal system, energy generation, heat transmission devices, power generation, chemical reactions, etc.