Search Results (46)

This research presents a physics-informed deep learning framework for investigating the magnetohydrodynamic flow of a dissipative non-Newtonian micropolar nanofluid induced by a stretching sheet, incorporating Stefan blowing, internal heat generation, and the zero nanoparticle mass flux condition. The physical model consists of the interplay between the microrotation dynamics, resistance of porosity on the microrotation, Brownian diffusion, and thermophoretic transport phenomenon. The numerical solutions for the nonlinear yielded equations that result from the above interaction are obtained by employing a PINN that considers the laws of physics and boundary conditions. With this technique, the flow behavior, temperature, concentration, and microrotation fields can be predicted accurately without requiring huge datasets. This shows the ability of PINNs to numerically treat highly-coupled nonlinear transport equations in a very efficient manner compared to other traditional methods. The important discoveries from this study include that the porous and magnetic factors increased the skin friction coefficient, but the magnetic effect and viscous dissipation decreased the rate of heat transfer, and the thermophoresis effect decreased the rate of mass transfer while the Brownian effect increased it. The precision of the PINN algorithm is confirmed by comparison of the results with the earlier findings, which proves very high accuracy and hence the robustness of the current computing framework. Results of this research are useful for the development of some thermal management systems, energy converters, cooling methods, chemical reaction processes, fuel cell technology, porous media reactors, and ocean engineering involving the transport of complicated non-Newtonian nanofluids. Full article

This article investigates the impact of Arrhenius energy and the radius of a nanoparticle subject to an irregular heat source on tangent-hyperbolic nanofluid flow over a stretching sheet with nonlinear radiation. The convective boundary effect, higher-order slip, and micropolarity are all included for a water-based $Cu$ nanofluid. The present study investigates the significance of a nanoparticle’s radius under inclined MHD conditions. The thermally convective flow of the nanofluid is optimized for the heat-transfer rate using the response surface technique. The modeled governing equations are converted into a system of first-order ODEs using the proper similarity transformations, and the BVP5C algorithm—a finite-difference-based solver—is then used to solve these ODEs numerically. Microrotation, thermal boundary-layer thickness, and the skin-friction coefficient all decrease as the nanoparticle radius increases. The thermal layer thickens as the Biot number increases. As the higher-order slip parameter coefficient increases, the results indicate that the skin friction and local Nusselt number fall. Using tables, figures, contour plots, and surface plots, the effects of several influencing factors on the rates of heat and mass transfer, as well as on the skin-friction factor, are demonstrated. The study uses “Response Surface Methodology” (RSM) in conjunction with “Analysis of Variance” (ANOVA) to optimize the most important factors, which are probably the magnetic parameter and the nanoparticle radius that control the flow and heat-transfer properties. Additionally, with a Nusselt number $R^2$ value of $99.96$, indicating an excellent fit, the suggested model exhibits amazing precision. The reliability and efficiency of the estimated model are assessed using the residual versus fitted plot. Full article

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe₃O₄) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer’s differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials. Full article

This study investigates the magnetohydrodynamics of a micropolar fluid consisting of a hybrid nanofluid with mixed convection effects. By using the dimensionless set of variables, the resulting equations of ordinary differential equations are solved numerically using the bvp4c solver in MATLAB. In the present work, the water-based alumina–copper hybrid nanofluid is analytically modeled with modified thermophysical properties. The study reveals that the highest critical value of opposing flow is the hybrid nanofluid (ϕ₁ = ϕ₂ = 2%). By comparing the hybrid nanofluid with Cu–water nanofluid (ϕ₁= 0%, ϕ₂= 1%) as well as water (ϕ₁= 0%, ϕ₂= 0%), hybrid nanoparticle volume fraction enhances the dynamic viscosity performance and surface shear stress. In addition, the augmentation of the nanoparticle volume fraction and magnetic field parameter will increase the physical quantities Re_x^1/2 C_f, Re_x M_x, and Re_x^−1/2 Nu_x. The result from the stability inquiry discloses that the first solution is more physically stable and trustworthy. It is proven that magnetohydrodynamics could contribute to controlling the fluid flow in a system, i.e., engineering operations and the medical field. In addition, this theoretical research can be a benchmark for experimental research. Full article

This communication studies the importance of varying the radius $D_p$ of Copper nanoparticles for microgravity-modulated mixed convection in micropolar nanofluid flux under an inclined surface subject magnetic field and heat source. In the current era, extremely pervasive modernized technical implementations have drawn attention to free convection governed by g-jitter force connected with microgravity. Therefore, fixed inter-spacing of nanoparticles and effects of g-jitter on the inclined surface are taken into consideration. A mathematical formulation based on conservation principles was non-dimensionalized by enforcement of similarity transformation, yielding a related set of ODEs. The convective non-linearity and coupling, an FE discretization, was implemented and executed on the Matlab platform. The numerical process’ credibility was ensured for its acceptable adoption with the defined outcomes. Then, the computational endeavor was continued to elucidate the impacts of various inputs of $D_p$, the amplitude of modulation $ϵ$, material parameter $\beta$, mixed convection parameter $\lambda$, inclination angle $\gamma$, and magnetic parameter M. The enlarging size of nanoparticles accelerated the nanofluid flow due to the depreciation of viscosity and receded the fluid temperature by reducing the surface area for heat transportation. The modulated Nusselt number, couple stress, and skin friction coefficient are significantly affected by the variation of $D_p$, M, $\beta$, $\lambda$, and $ϵ$. These results would benefit experts dealing with upper space transportation and materials’ performance, such as the effectualness of chemical catalytic reactors and crystals. Full article

These days, heat transfer plays a significant role in the fields of engineering and energy, particularly in the biological sciences. Ordinary fluid is inadequate to transfer heat in an efficient manner, therefore, several models were considered for the betterment of heat transfer. One of the most prominent models is a single-phase nanofluid model. The present study is devoted to solving the problem of micropolar fluid with a single-phase model in a channel numerically. The governing partial differential equations (PDEs) are converted into nonlinear ordinary differential equations (ODEs) by introducing similarity transformation and then solved numerically by the finite difference method. Response surface methodology (RSM) together with sensitivity analysis are implemented for the optimization analysis. The study reveals that sensitivity of the skin friction coefficient (Cf_x) to the Reynolds number (R) and magnetic parameter (M) is positive (directly proportional) and negative (inversely proportional) for the micropolar parameter. Full article

The time-independent performance of a micropolar nanofluid under the influence of magneto hydrodynamics and the existence of a porous medium on a stretching sheet has been investigated. Nano-sized particles were incorporated in the base fluid because of their properties such as their extraordinary heat-enhancing ability, which plays a very important role in modern nanotechnology, cooling electronic devices, various types of heat exchangers, etc. The effects of Brownian motion and thermophoresis are accounted for in this comprehensive study. Using similarity conversion, the leading equations based on conservation principles are non-dimensionalized with various parameters yielding a set of ODEs. The numerical approach boundary value problem fourth-order method (bvp4c) was implemented as listed in the MATLAB computational tool. The purpose of this examination was to study and analyze the influence of different parameters on velocity, micro-rotation, concentration, and temperature profiles. The primary and secondary velocities reduced against the higher inputs of boundary concentration, rotation, porosity, and magnetic parameters, however, the base fluid temperature distribution grows with the increasing values of these parameters. The micro-rotation distribution increased against the rising strength of the Lorentz force and a decline is reported against the growing values of the micropolar material and rotational parameters. Full article

This numerical analysis aims to observe and analyze the combined convection characteristics of the micropolar tri-hybrid nano-liquid that moves around a cylindrical object, and, in addition, to compare its thermal behavior to that of hybrid and mono nano-fluids. For this purpose, the problem is modeled by developing the Tiwari and Das models, then the governing model is converted into dimensionless expressions, and finally, the problem is solved using the Keller box approximation. The current findings are compared with previously published results to show that the present method is sufficiently accurate for physical and engineering applications. By examining and analyzing the extent to which skin friction, the Nusselt number, velocity, angular velocity, and temperature are affected by some critical factors, the following points are revealed: A greater value of the micropolar and magnetic factors can result in curtailing the heat transmission rate, velocity, and angular velocity. Higher values of the mixed convection factor can contribute to a better rate of energy transfer and can grant the micropolar tri-hybrid nano-liquid a higher velocity. Regardless of the influencing factors, the maximum value of all considered physical groups is achieved by using ternary hybrid nano-liquids. Full article

Boosting the heat transfer rate in a base fluid is of interest to researchers; many traditional methods have been utilized to do this. One significant way is using nanofluid to boost thermal performance. This investigation sought to improve the transmission of a thermal above-stretching inclined surface over an upper surface to be influenced by the magnetic field $B_0$ along the microgravity $g*\left(\tau \right)=g_0(1+acos\left(\pi \omega t\right))$. The G-jitter impacts were analyzed for three colloidal fluids flow; the mono micropolar nanofluid (alumina/water), micropolar hybrid nanofluid (alumina–titanium)/water, and micropolar trihybrid nanofluid (alumina–titanium–silicon)/water. Using suitable transformation, the governing formulation was changed into an ordinary differential equation. In a Matlab script, a computational code was composed to evaluate the impacts of the involved parameters on fluid dynamics. The fluid flow motion and thermal performance for the trihybrid case were greater than the mono and hybrid nanofluid cases subject to a microgravity environment. The fluid velocity and microrotation function decreased in opposition to the magnetic parameter’s increasing strength, but with an increasing trend in the fluid temperature function. Fluctuations in the velocity gradient and heat flow gradient increased as the modulation amplitude increased. Full article

The bioconvective flow of non-Newtonian fluid induced by a stretched surface under the aspects of combined magnetic and porous medium effects is the main focus of the current investigation. Unlike traditional aspects, here the viscoelastic behavior has been examined by a combination of both micropolar and second grade fluid. Further thermophoresis, Brownian motion and thermodiffusion aspects, along with variable thermal conductivity, have also been utilized for the boundary process. The solution of the nonlinear fundamental flow problem is figured out via convergent approach via Mathematica software. It is noted that this flow model is based on theoretical flow assumptions instead of any experimental data. The efficiency of the simulated solution has been determined by comparing with previously reported results. The engineering parameters’ effects are computationally evaluated for some definite range. Full article

The utilization of hybrid nanofluids (HNs) to boost heat transfer is a promising area of study, and thus, numerous scientists, researchers, and academics have voiced their admiration and interest in this area. One of the main functions of nanofluids is their dynamic role in cooling small electrical devices such as microchips and associated gadgets. The major goal of this study is to perform an analysis of the buoyancy flow of a shrinking/stretching sheet, whilst considering the fascinating and practical uses of hybrid nanofluids. The influence of a nonlinear heat source/sink induced by a micropolar fluid is also inspected. Water-based alumina and copper nanoparticles are utilized to calculate the fine points of the fluid flow and the features of heat transfer. The governing equations are framed with acceptable assumptions and the required similarity transformations are used to turn the set of partial differential equations into ordinary differential equations. The bvp4c technique is used to solve the simplified equations. Dual solutions are presented for certain values of stretching/shrinking parameters as well as the mixed convective parameter. In addition, the shear stress coefficient in the first-branch solution (FBS) escalates and decelerates for the second-branch solution (SBS) with the superior impact of the magnetic parameter, the mass transpiration parameter, and the solid nanoparticles volume fraction, while the contrary behavior is seen in both (FB and SB) solutions for the larger values of the material parameter. Full article

In recent times, heat and mass transportation have had some of the most recognized and attractive research areas in computational fluid dynamics. It is useful in the modeling of the flow of nuclear reactors, bioinformatics, the medical discipline, etc. Driven by the execution of the flow in the manufacturing application, the goal of the present analysis is to explore the novel effect of micropolar fluid configured by an exponentially elongated sheet positioned horizontally in a porous channel. The impact of activation energy, internal heating, and heat and mass transfer features are integrated into the revised flow model. A mathematical framework for different flow fields is developed in order to highlight the significant aspects of the thermal and concentration slip effects evaluated on the extended plat surface, with the aid of appropriate transformation factors to diminish the nonlinear fundamental flow equations (PDEs) to a system of (ODEs). Precise numerical treatment for a wide range of pertinent parameters is adopted to solve the nonlinear system through a built-in algorithm in the MATHEMATICA platform. The features of prominent emerging parameters against various flow fields are viewed and addressed through plotted visuals. The influence of the factors on skin friction, heat, and mass coefficients offered through 3D animation is evaluated. The temperature profile improves with ascending values of Brownian parameter and thermophoretic diffusion force but diminishes with subject expansions in Prandtl number and thermal slip parameter. It has been noticed that the concentration outlines increase for reaction rate and activation energy parameters but dwindle for expending values of porosity parameter, Lewis number, and concentration slip parameter. Skin fraction values increase due to the growing nature of the micropolar and second-grade fluid parameters. Nusselt numbers upsurge for increasing thermophoretic diffusion parameters while exhibiting a declining trend for Brownian motion parameters. Full article

Conventional liquids have poor thermal conductivity, thus limiting their use in engineering. Therefore, scientists and researchers have created nanofluids, which consist of nanoparticles dispersed in a base fluid, to improve heat transfer properties in various fields, such as electronics, medicine, and molten metals. In this study, we examine the micropolar nanofluid flow in a stagnation region of a stretching/shrinking sheet by employing the modified Buongiorno nanofluid model. The nanofluid consists of magnetite (Fe₃O₄) nanoparticles. The similarity equations are solved numerically using MATLAB software. The solution is unique for the shrinking strength $\lambda \ge -1$. Two solutions are found for the limited range of $\lambda$ when ${\lambda }_c<\lambda <-1$. The solutions terminate at $\lambda ={\lambda }_c$ in the shrinking region. The rise in micropolar parameter $K$ contributes to the increment in the skin friction coefficient ${\mathrm{Re}}_x^{1/2}{C}_f$ and the couple stress ${\mathrm{Re}}_x{M}_w$, but the Nusselt number ${\mathrm{Re}}_x^{-1/2}N{u}_x$ and the Sherwood number ${\mathrm{Re}}_x^{-1/2}S{h}_x$ decrease. These physical quantities intensify with the rise in the magnetic parameter $M$. Finally, we investigated the stability of the solutions over time. This work contributes to the dual solution and time stability analysis of the current problem. In addition, critical values of the main physical parameters are also presented. These critical values are usually known as the separation values from laminar to turbulent boundary layer flows. In this case, once the critical value is achieved, the process for the specific product can be planned according to the desired output to optimize the productivity. Full article

This article investigates the significance of varying radius of copper nanoparticles for non-Newtonian nanofluid flow due to an extending sheet in the presence of a magnetic field and porous medium. The modern technological applications of non-Newtonian nanofluids have attracted researchers in the current era. So, the impacts of the radius of nanoparticles with micropolar fluid have been taken into consideration. Three-dimensional leading equations (PDEs) for momentum, concentration, and temperature are transformed into ODEs by applying the appropriate similarity transformation. The numerical approach bvp4c is applied to obtain the problem’s solution numerically. The influence of the nanoparticles’ radius and various physical parameters on the microrotation, velocity, and temperature profile are analyzed. The velocity profile decreases against the magnetic field (M), rotational parameter ($\Gamma$), and Forchheimer number (Fr), but the temperature distribution has increasing behavior for these parameters, and the microrotation is augmented for rising inputs of the magnetic parameter and boundary parameter ($\beta$). It is also observed that the temperature reduces against the material parameter (∇) and Forchheimer number ($Fr$). The skin friction coefficients and Nusselt number decrease against the growing strength of the Forchheimer number $\left(Fr\right)$. At the stretching surface, the skin friction factor and Nusselt number are numerically and graphically calculated. Full article

The heat and mass transfer of the unsteady flow of a micropolar fluid over a curved stretching surface was considered in this study. The Brownian motion and thermophoresis effects were explored in this analysis. The effects of suction/injection cases on the curved surface were discussed. Under flow assumptions, a mathematical model was designed employing boundary layer approximations using partial differential equations. A suitable transformation was developed using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique, namely bvp4c. The involved physical parameters’ influences are described in the form of graphs as well as numerical results in the form of tables. Our current work is helpful in the engineering and industrial fields. The unsteadiness parameter increases which Nusselt number at increased but concentrations declined. The thermophoresis parameter increases when increasing the Nusselt number because the small number of nanoparticles enhances the heat transfer rate. The temperature profile declined due to increasing values of unsteadiness parameter for both cases of suction and injection cases. Full article