Vertical Stretching Sheet Research Articles

Newtonian Heating on Casson Mixed Convection Transport by Ternary Hybrid Nanofluids over Vertical Stretching Sheet: Numerical Study

Numerous physical characteristics occurring from the structure and micro-motions of fluid nanoparticles can be examined using the governing models of nanofluids. Also, It can describe the demeanor of a vast field of actual fluids. This achieved a significant turn in the enhancement of heat transfer that improves manufacturing and engineering modernization. Depending on that, the assumptions that form our aims are numerically examining energy transport and heat transfer via Casson ternary hybrid nanofluids that contain the states of combined convection flow over a vertical stretching sheet. Also, Newtonian heating boundary conditions and magnetohydrodynamics (MHD) effects are investigated. Mathematical models (governing equations) that emulate and construct the conduct of these boosted ternary hybrid nanofluids are formed by developing the Tiwari and Das models. These governing equations are converted to partial differential equations (PDEs) employing appropriate substitutions. An accurate and efficient method called the Keller box numerical method is executed to get outcomes to the physical model. These numerical calculations are found and presented by employing MATLAB codes, to acquire tables of numerical outcomes, and graphic exhibits, which provide the impacts of important parameters on the physical quantities supporting heat transfer. Furthermore, the new results, in the Newtonian fluid case, were compared with prior literature, which were in excellent agreement. The studied problem parameters are examined at a Casson parameter domain of 1 to 5, a mixed convection parameter domain of -1 to 3, a conjugate parameter of 0.2 to 1, a magnetic parameter domain of 0.1 to 5, and a nanoparticle volume fraction parameter of 0.001 to 0.008. The numerical consequences deduced that the local skin friction rises when the conjugate and mixed convection parameters are increased. But the opposite case happens when the effects are obtained for the nanoparticle volume fraction, magnetic, and Casson parameters. Also, the Nusselt number rises with growing nanoparticle volume fraction and Casson parameters.

Buoyancy Assisting and Opposing Mixed Convective MHD Flow of Nanofluid along a Vertical Stretching Sheet

Buoyancy Assisting and Opposing Mixed Convective MHD Flow of Nanofluid along a Vertical Stretching Sheet

Two-Phase Flow of Eyring–Powell Fluid with Temperature Dependent Viscosity over a Vertical Stretching Sheet

In this work, the mixed convection flow of non-Newtonian Eyring–Powell fluid with the effects of temperature dependent viscosity (TDV) were studied together with the interaction of dust particles under the influence of Newtonian Heating (NH) boundary condition, which assume to move over a vertical stretching sheet. Alternatively, the dusty fluid model was categorized as a two-phase flow that consists of phases of fluid and dust. Through the use of similarity transformations, governing equations of fluid and dust phases are reduced into ordinary differential equations (ODE), then solved by efficient numerical Keller–box method. Numerical solution and asymptotic results for limiting cases will be presented to investigate how the flow develops at the leading edge and its end behaviour. Comparison with the published outputs in literature evidence verified the precision of the present results. Graphical diagrams presenting velocity and temperature profiles (fluid and dust) were conversed for different influential parameters. The effects of skin friction and heat transfer rate were also evaluated. The discovery indicates that the presence of the dust particles have an effect on the fluid motion, which led to a deceleration in the fluid transference. The present flow model can match to the single phase fluid cases if the fluid particle interaction parameter is ignored. The fluid velocity and temperature distributions are always higher than dust particles, besides, the opposite trend between both phases is noticed with β. Meanwhile, both phases share the similar trend in conjunction with the rest factors. Almost all of the temperature profiles are not showing a significant change, since the viscosity of fluid is high, which can be perceived in the figures. Furthermore, the present study extends some theoretical knowledge of two-phase flow.

Computational Analysis of MHD Nonlinear Radiation Casson Hybrid Nanofluid Flow at Vertical Stretching Sheet

The stagnation point flow of unsteady compressible Casson hybrid nanofluid flow over a vertical stretching sheet was analyzed. The comparative study of Yamada Ota, Tiwari Das, and Xue hybrid nanofluid models was performed. The Lorentz force was applied normal to flow directions. The effect of nonlinear radiation was studied. We considered the SWCNT (signal wall carbon nanotube) and MWCNT (multi-wall carbon nanotube) with base liquid (water). Under the flow suppositions, a mathematical model was settled by means of boundary layer approximations in terms of partial differential equations. The suitable transformation was developed by 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 named bvp4c. The impacts of pertinent flow parameters on skin friction, Nusselt number, and temperature and velocity distributions were depicted through tabular form as well as graphical form. In this study, the Yamada Ota model achieved a higher heat transfer rate compared to the Tiwari Das and Xue hybrid nanofluid models. The skin friction (CfxRe−1/2) increased and temperature gradient (NuxRe−1/2) declined due to the increment of solid nanoparticle concentration (ϕ2). Physically, skin friction increased because the higher values of the solid nanoparticles increased resistance to the fluid motion.

Numerical Solution of Heat Transfer Flow of Casson Hybrid Nanofluid over Vertical Stretching Sheet with Magnetic Field Effect

In this study, heat transfer flow of Casson hybrid nanofluid over vertical stretching sheet with magnetic field effect is studied. Copper oxide and graphite oxide in methanol are considered as the hybrid nanoparticles. This analysis of study points out several aspects of flow physically which is related to transportation of heat. The conservation of partial differential equations (PDEs) are taken place into non-linear coupled ordinary differential equations (ODEs) by using transformation of dimensionless variables, and solution of these ODEs is performed using Chebyshev differential quadrature method (CDQM). Effects of many involved parameters like M, , , a/c, denotes the magnetic parameter, Casson parameter, the nanoparticles volume fraction and ratio parameter are shown through tables for skin friction and Nusselt number. Moreover, it is presented as sketching on temperature and velocity profiles briefly. Results revealed that the Casson hybrid nanofluid has highest value when <1 for Nusselt number, skin friction, and temperature profile. Moreover, it is lowest value when >1 for velocity profile and Nusselt number. It also is observed that, when the magnetic field and Cason parameter increase, this leads to an increase in the temperature profile and a decrease in the Nusselt number and the velocity profile. A comparison study is also made which compares the present result with published data is executed and findings meet with them.

Analysis of Variable Viscosity and Thermal Conductivity of MHD flow of Mixed Convection over a Nonlinear Vertical Stretching Sheet

In this present study we examine analytically the MHD flow problem close by a stagnation point on a stretching sheet which is nonlinear. Similarity transformation is used to modify the fluid flow governing equations into a system of ordinary differential equations .The modified equations are resolved with the assist of MATLAB bvp4c. The influence of viscosity parameter, thermal conductivity parameter, suction parameter and magnetic parameter on velocity and temperature are computed and presented through graphs.

Mhd Based Micropolar Fluid Flow with Temperature Dependent Properties at Vertical Stretching Sheet: An Application of Generalized Fourier-Fick Law

Mhd Based Micropolar Fluid Flow with Temperature Dependent Properties at Vertical Stretching Sheet: An Application of Generalized Fourier-Fick Law

Heat and Mass Transfer in Stagnation Point Flow of Maxwell Nanofluid Towards a Vertical Stretching Sheet with Effect of Induced Magnetic Field

This paper presents a mathematical model analysis of heat and mass transfer in a two-dimensional flow of electrically conducting, thermally radiative, and chemically reactive Maxwell nanofluid towards a vertical stretching and permeable sheet embedded in a porous medium. Boundary layer approximation and suitable transformations are used to reduce the governing differential equations convenient for computation. Eventually, the transformed nonlinear differential equations along with the corresponding boundary conditions are solved in the framework of optimal homotopy analysis method. The effects of induced magnetic field, buoyancy force, viscous dissipation, heat source, Joule heating, and convective boundary condition are analyzed in detail. The rates of heat, mass, and momentum transfer with respect to the relevant parameters are also examined in terms of the local Nusselt number, Sherwood number, and skin friction coefficients, respectively. Among the many results of the study, it is shown that the induced magnetic field, flow velocity, and temperature profiles are increasing functions of the Maxwell parameter. The results of the present study are also in a close agreement with previously published results under common assumptions.

Dual Solutions in Mixed Convection Stagnation-Point Flow Over a Vertical Stretching Sheet with External Magnetic Field and Radiation Effect

The purpose of this research is to study the problem of mixed convection stagnation-point flow on a vertical stretching sheet with external magnetic field, with the effect of radiation is taken into account. The partial differential equations are reduced to ordinary differential equations using similarity transformation. The transformed boundary layer equations are then solved numerically via bvp4c in MATLAB software. The effects of different values of radiation parameter and Hartmann number on the skin friction coefficient and local Nusselt number, velocity and temperature profiles are presented and discussed. The effect of radiation parameter and Hartmann number are also considered for both assisting and opposing flows. Dual solutions are found to exist in the opposing flow only, while for assisting flow, unique solution exists. It is also found that the radiation parameter enhances the boundary layer separation, and the Hartmann number delays the boundary layer separation.

Mixed Convection Flow of Powell–Eyring Nanofluid near a Stagnation Point along a Vertical Stretching Sheet

A stagnation-point flow of a Powell–Eyring nanofluid along a vertical stretching surface is examined. The buoyancy force effect due to mixed convection is taken into consideration along with the Brownian motion and thermophoresis effect. The flow is investigated under active and passive controls of nanoparticles at the surface. The associating partial differential equations are converted into a set of nonlinear, ordinary differential equations using similarity conversions. Then, the equations are reduced to first-order differential equations before further being solved using the shooting method and bvp4c function in MATLAB. All results are presented in graphical and tabular forms. The buoyancy parameter causes the skin friction coefficient to increase in opposing flows but to decrease in assisting flows. In the absence of buoyancy force, there is no difference in the magnitude of the skin friction coefficient between active and passive controls of the nanoparticles. Stagnation has a bigger influence under passive control in enhancing the heat transfer rate as compared to when the fluid is under active control. Assisting flows have better heat and mass transfer rates with a lower magnitude of skin friction coefficient as compared to opposing flows. In this case, the nanofluid parameters, the Brownian motion, and thermophoresis altogether reduce the overall heat transfer rates of the non-Newtonian nanofluid.

Mathematical Formulation on Non-Newtonian Dusty Fluid over Vertical Stretching Sheet

Mathematical Formulation on Non-Newtonian Dusty Fluid over Vertical Stretching Sheet

MHD Mixed Convective Boundary Layer Flow of Third Grade Fluid towards a Vertical Stretching Sheet

MHD Mixed Convective Boundary Layer Flow of Third Grade Fluid towards a Vertical Stretching Sheet

Effects of Radiation and Eckert Number on MHD Flow with Heat Transfer Rate Near a Stagnation Point Over a Non-Linear Vertical Stretching Sheet

This work investigates the effects of radiation and Eckert number on an MHD flow with heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the sixth order Runge-Kutta method with shooting technique. Tabular and graphical results are provided to examine the physical nature of the problem. Heat transfer rate at the surface decreases with radiation, Eckert number and as radiation increases, the flow temperature also increases for velocity ratio parameters ɛ <<i>1</i> and ɛ ><i>1.</i>

Mixed Convection in MHD Flow and Heat Transfer Rate Near a Stagnation-Point on a Non-Linear Vertical Stretching Sheet

This work investigates the mixed convection in a Magnetohydrodynamic (MHD) flow and heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the fourth order Runge-Kutta method with shooting technique. The influence of pertinent flow parameters on velocity, temperature, surface drag force and heat transfer rate are computed and analyzed. Graphical and tabular results are given to examine the nature of the problem. The heat transfer rate at the surface increases with the mixed convection.

The Investigation of a Fluid-Solid Interaction Mathematical Model under Combined Convective Jeffrey Flow and Radiation Effect Embedded Newtonian Heating as the Thermal Boundary Condition over a Vertical Stretching Sheet

The investigation on the interaction between solid and fluid under combined convective flow has been carried out mathematically. The Jeffrey fluid model is taken as the fluid phase and the model is being embedded with the dust particles (solid phase). This two-phase model is constructed by introducing the fluid-particles interaction forces in the momentum equations of the fluid and dust phases, respectively. The natural and forced convections together with the aligned magnetic field are considered on the fluid flow. Also, the Newtonian heating as thermal boundary condition is induced on the vertical stretching sheet. In order to reduce the complexity of the model, the governing equations are transformed from partial differential equation into ordinary differential equation via suitable similarity transformation. The solutions are obtained in terms of velocity and temperature profiles for the fluid and particles phases respectively whereby the Keller-box method is utilized to obtain the desired outcomes. The influences of several significant physical parameters are visualized graphically to clarify the flow and heat transfer characteristic for both phases. The investigation found that the fluid’s velocity is affected by the presence of the dust particles which led to decelerate the fluid transference. The present flow model is able to be compared with the single-phase fluid cases if the fluid-particle interaction parameter is ignored.

MHD Boundary Layer Flow and Heat Transfer of Nano fluid over a Vertical Stretching Sheet in the Presence of a Heat Source

The nanoparticles used in nanofluid are prepared for carbides and oxides. In this paper, a nanofluid flow over a stretching sheet in the presence of viscous dissipation, heat source, and magnetic field was numerically explored with the help of the Runge-Kutta shooting technique and the effects of various parameters were analyzed using graphical representation.

A Progress on the Development of Mathematical Model on Two-Phase Flow over a Vertical Stretching Sheet

The investigation on flow and heat transfer are important in the engineering applications, for example, extrusion of metal and polymer, cooling of electronic devices, heat exchanger and chemical processing equipment. Since the investigations on the real applications are costly and sometime hazardous, the study on mathematical model representing the fluid flow and heat transfer’s problem are considered to overcome this limitation. This paper will present the progress on the development of mathematical model on non-Newtonian two-phase model where the fluid flow is studied together with the dust particles. The review will include the discussions on existing problems, its methodology as well as the significance outcomes. The main contributions on this paper is to present the research gap and the possible development for future investigations on the problem under the mathematical model of fluid flow and heat transfer.

MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect

A steady laminar flow over a vertical stretching sheet with the existence of viscous dissipation, heat source/sink, and magnetic fields has been numerically inspected through a shooting scheme based Runge—Kutta–Fehlberg-integration algorithm. The governing equation and boundary layer balance are expressed and then converted into a nonlinear normal system of differential equations using suitable transformations. The impact of the physical parameters on the dimensionless velocity, temperature, the local Nusselt, and skin friction coefficient are described. Results show good agreement with recent researches. Findings reveal that the Nusselt number at the sheet surface augments, since the Hartmann number, stretching velocity ratio A, and Hartmann number Ha increase. Nevertheless, it reduces with respect to the heat generation/absorption coefficient δ.

English

English

Impacts of Magnetic Field and Radiation Absorption on Mixed Convective Jeffrey Nano Fluid Flow Over a Vertical Stretching Sheet with Stability and Convergence Analysis

Impacts of Magnetic Field and Radiation Absorption on Mixed Convective Jeffrey Nano Fluid Flow Over a Vertical Stretching Sheet with Stability and Convergence Analysis