Dual solutions of magnetized radiative flow of Casson Nanofluid over a stretching/shrinking cylinder: Stability analysis.

The enhanced thermal efficiency exhibited by Casson nanofluids offers significant practical applications across various industrial and engineering sectors. This study focuses on the mathematical investigation of the steady magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid through a stretched/shrinking cylinder, taking into account the effects of suction and thermal radiation. The governing partial differential equations (PDEs) have been subjected to a similarity transformation, resulting in a set of nonlinear ordinary differential equations (ODEs). These ODEs were solved numerically utilizing the code of bvp4c in the software of Matlab which offers high accuracy (4th order). The employed nanofluid model incorporates the effects of Brownian motion and thermophoresis. The present study illustrates the graphical depictions of the impacts of different governing parameters, namely Hartmann (M) number, curvature (γ) parameter, Brownian motion (Nb) parameter, mass suction (S) parameter, thermal radiation (Rd) parameter, and thermophoresis (Nt) parameter, on heat transfer, flow, and mass transfer characteristics. Comprehensive determination and visual presentation of the coefficient of skin friction, local Nusselt number, and local Sherwood number were conducted for a range of estimates of applied parameters. Based on our examination, it has been determined that dual similarity solutions are present within a specific range of mass suction parameters. The relationship between the Casson parameter and various fluid dynamic properties, such as skin friction coefficient, heat transfer rate, and mass transfer rates, has been found to exhibit a decreasing trend. Furthermore, the stability analysis discovered that the first solution exhibits linear stability, whereas the second solution displays linear instability. Additionally, the motivation behind this study is to enhance industrial performance through the optimization of thermal power generation systems, thereby increasing their overall efficiency.

Dual solutions of unsteady flow of copper-alumina/water based hybrid nanofluid with acute magnetic force and slip condition.

Suspending particles of tiny solid in a fluid used to transport energy can enhance its thermal conductivity and heat transport properties. Our main goal of this examination is to study the radiative unsteady two-dimensional (2D) flow on a continuously diminishing, horizontal sheet. with suction for the hybrid water-based nanofluid and an aligned field of magnetic, including the combined suction, magnetic, and velocity slip conditions effect. The Tiwari & Das model of nanofluid equations is used, which takes into consideration the solid volume percentage. Equations of similarity are derived by employing the transformations of similarity, and the associated equations have been simplified numerically by employing the bvp4c method in MATLAB software for a variety of values of the nanoparticle volume fraction, the unsteadiness, and the wall mass suction in water. It is discovered that, within the given the unsteadiness parameter range, two solutions exist. Moreover, it is found that the fluid velocity slows down in 1st solution as volume fraction of copper nanoparticles rises but speeds up in the second solution at first before slowing down again. Using a temporal stability analysis, it is found that only one of the dual branches is stable over the long run, while the other is unstable.

Magnetized mixed convection hybrid nanofluid with effect of heat generation/absorption and velocity slip condition.

Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al2O3-Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al2O3) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%-10% copper nanoparticles and 1%-500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f ″ ( 0 ) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport - θ ' ( 0 ) decreases. As heat generation/absorption increases 1%-500%, - θ ' ( 0 ) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S ≥ S c i in assisting flow case, while no fluid flow is possible when S < S c i .

Thermal stable properties of solid hybrid nanoparticles for mixed convection flow with slip features.

Following to improved thermal impact of hybrid nanomaterials, wide range applications of such materials is observed in the thermal engineering, extrusion systems, solar energy, power generation, heat transfer devices etc. The hybrid nanofluid is a modified form of nanofluid which is beneficial for improving energy transfer efficiency. In current analysis, the solid nanoparticles aluminium ([Formula: see text]) and copper ([Formula: see text]) have been mixed with water to produce a new hybrid nanofluid. The investigation of a steady two-dimensional mixed convection boundary layer flow of the resultant hybrid nanofluid on a vertical exponential shrunk surface in the existence of porous, magnetic, thermal radiation, velocity, and thermal slip conditions is carried out. Exponential similarity variables are adopted to transform the nonlinear partial differential equation into a system of ordinary differential equations which has been then solved by employing the shooting method in Maple software. The obtained numerical results such as coefficient of skin friction [Formula: see text], heat transfer rate [Formula: see text], velocity [Formula: see text] and temperature [Formula: see text] distributions are presented in the form of different graphs. The results revealed that duality exists in solution when the suction parameter [Formula: see text] in assisting flow case. Due to non-uniqueness of solutions, a temporal stability analysis needs to be performed and the result indicates that the upper branch is stable and realizable compared to the lower branch.

Effect of Thermal Radiation on Three-Dimensional Magnetized Rotating Flow of a Hybrid Nanofluid.

The effect of thermal radiation on the three-dimensional magnetized rotating flow of a hybrid nanofluid has been numerically investigated. Enhancing heat transmission is a contemporary engineering challenge in a range of sectors, including heat exchangers, electronics, chemical and biological reactors, and medical detectors. The main goal of the current study is to investigate the effect of magnetic parameter, solid volume fraction of copper, Eckert number, and radiation parameter on velocity and temperature distributions, and the consequence of solid volume fraction on declined skin friction and heat transfer against suction and a stretching/shrinking surface. A hybrid nanofluid is a contemporary type of nanofluid that is used to increase heat transfer performance. A linear similarity variable is−applied to convert the governing partial differential equations (PDEs) into corresponding ordinary differential equations (ODEs). Using the three-stage Labatto III-A method included in the MATLAB software's bvp4c solver, the ODE system is solved numerically. In certain ranges of involved parameters, two solutions are received. The temperature profile θη upsurges in both solutions with growing values of EC and Rd. Moreover, the conclusion is that solution duality exists when the suction parameter S≥Sci, while no flow of fluid is possible when S

Darcy-Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis.

Nanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydrodynamic (MHD) Darcy-Forchheimer nanofluid flow across an exponentially contracting sheet is presented. In this mathematical model, the effects of viscous dissipation, joule heating, first-order velocity, and thermal slip conditions are also examined. Using similarity transformations, a system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs). The problem is quantitatively solved using the three-step Lobatto-three formula. This research studied the effects of the dimensionlessness, magnetic field, ratio of rates, porosity, Eckert number, Prandtl number, and coefficient of inertia characteristics on fluid flow. Multiple solutions were observed. In the first solution, the increased magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters reduce the velocity field along the η-direction. In the second solution, the magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters increase the η-direction velocity field. For engineering purposes, the graphs show the impacts of factors on the Nusselt number and skin friction. Finally, the stability analysis was performed to determine which solution was the more stable of the two.

Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis.

In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: dual solutions.

In this paper, we explore dual solutions of MHD flow, heat and mass transfer of micropolar nanofluid over a linear vertical shrinking surface with buoyancy effects, which was not considered in the previous works. The governing fluid flow equations of this problem are transformed into nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs) by applying similarity variables. The resultant BVPs are converted into initial value problems (IVPs) by using shooting method which then resolved by employing Runge Kutta of order four. The impacts of the governing parameters, such as suction parameter, material parameter, Richardson number, magnetic parameter, Prandtl number, thermophoresis and Brownian motion parameters on velocity, angular velocity, temperature, and concentration are illustrated graphically. The results indicate that the existence of a range of dual solutions and no-solutions. When Richardson number ( δ ) is increased, the reduction of the velocity of micropolar nanofluid has occurred in the second solution. The stability analysis on dual solutions, however, reveals that only the first solution is stable.

Quadruple solutions of mixed convection flow of magnetohydrodynamic nanofluid over exponentially vertical shrinking and stretching surfaces: Stability analysis.

BACKGROUND AND OBJECTIVE: The last two and half decades are witnessed a great surge in the use convective fluids for enhancement of heat transfer of minerals ethylene glycol, oil and water due to their numerous applications in the industrial segments including chemical production, microelectronics, power generation, transportation, and air-conditioning. For this purpose, different procedures were applied to upgrade the thermal conductivity of common fluid but could not. Further, Choi and Eastman in 1995 introduced nanofluid which has good thermal properties as compared to common fluids. After that, it can be seen that researchers, mathematicians, and scientists tried to understand the principles of nanofluids and how to implicate them in many different practical applications. In this work, the Buongiorno model has been considered for nanofluid. One of the prime objectives is to consider all possible multiple solutions of the model because these solutions cannot be seen experimentally. METHODS: The governing equations of fluid flow have been transformed in the form of ordinary differential equations. These equations have been solved by two methods namely, shooting method and three-stage Lobatto IIIa formula. RESULTS: The effects of different parameters on temperature, velocity, concentration profiles, skin friction coefficient, Sherwood number, and reduced Nusselt number were obtained and presented graphically. It was noticed that four solutions existed at definite ranges of the parameters for high suction over both surfaces for the first time. The results of the stability analysis revealed that only the first solution is more stable and possess physical reliability compared to the remaining solutions. CONCLUSION: The graphs also indicated that the fluid velocity decreases as the thermophoresis parameter increases but the opposite behavior observed for both temperature and concentration profiles in the first solution. Furthermore, it was detected that the concentration profile declined at the higher values of the Brownian motion parameter.

Analysis of dual solution for MHD flow of Williamson fluid with slippage.

This study investigates the numerical solutions of MHD boundary layer and heat transfer of the Williamson fluid flow on the exponentially vertical shrinking sheet, having variable thickness and thermal conductivity under effects of the velocity and thermal slip parameters. It is also assumed that shrinking/stretching velocity, as well as the wall temperature, has the exponential function form. In this study, the continuity, momentum and energy equations with buoyancy parameter and Hartmann number are incorporated especially in the Williamson fluid flow case. Similarity transformation variables have been employed to formulate the ordinary differential equations (ODEs) from partial differential equations (PDEs). The resultant ODEs are solved by shooting method with Runge Kutta of fourth order method in Maple software. The effects of the different applied non-dimensional physical parameters on the boundary layer and heat transfer flow problems are presented in graphs. The effects of Williamson parameter, Prandtl number, and slip parameters on velocity and temperature profiles have been thoroughly demonstrated and discussed. The numerical results show that the buoyancy force and the slip parameters contribute to the occurrence of the dual solutions on the boundary layer and heat transfer flow problems. Furthermore, the stability analysis suggests that the first solution is stable and physically possible.