Unsteady Stretching Sheet Research Articles

Influence of Heat Source on Thin Film Flow of Ferrofluid Past an Unsteady Stretching Sheet

In this work, the impact of a heat source on the thin-film ferrofluid flow over an unstable stretching sheet in the presence of an external magnetic field has been examined. The governing partial differential equations are transformed into a system of ordinary differential equations by similarity transformation. The resultant system of ordinary differential equations is solved numerically through shooting technique involving Runge-Kutta-Fehlberg (RKF45) method. To improve the initial guess values, the Newton-Raphson method is used. The significance of magnetization parameter, Prandtl number and heat source parameter on the flow and heat transmission process have been graphically analysed. The decrease in film thickness is observed for growing values of heat source parameter.

The Flow of a Thermo Nanofluid Thin Film Inside an Unsteady Stretching Sheet with a Heat Flux Effect

This research investigated the flow and heat mass transmission of a thermal Buongiorno nanofluid film caused by an unsteady stretched sheet. The movement of the nanoparticles through the thin film layer is caused by the strength of the heat flow and the stretching force of the sheet working together. The thermal thin-film flow and heat mechanism, and the properties of mass transfer along the film layer, were comprehensively investigated. The consequences of the heat generation, magnetic field, and dissipation phenomenon were also thoroughly examined. Using appropriate dimensionless variables, the fundamental time-dependent equations of thin film nanofluid flow and heat mass transfer were modeled and converted to the ordinary differential equations system. Mathematica version 12 is the software that was used to build the numerical code here. Next, the shooting technique was applied to numerically solve the transformed equations. The elegance of the shooting technique and evidence of the consistency, dependability, and precision of our acquired results is that the results are more effective than those for the thin film nanofluid equations that are now available. There is a significant degree of consistency between the recently calculated results and the results that have been published for a limiting condition. Investigations were conducted into the effects of a variety of parameters on the flow of nanoliquid films, including the Nusselt number, skin friction, and Sherwood number. In addition, a detailed overview of the physical embedded parameters is provided through graphs and tables. However, the important features of the most relevant outcomes are the effects of higher porous and unsteadiness parameters on minimizing the thickness of the thin film; and the viscoelastic parameter has the reverse effect. Additionally, it is seen that the temperature profile improves as a result of higher thermophoresis and Brownian motion parameter values.

Flow and Heat Transfer Analysis of a Thin Film Ferromagnetic Liquid over an Unsteady Stretching Sheet

A two-dimensional, unsteady flow of a thin layer of ferromagnetic liquid over a stretching sheet is considered. The flow is exposed to an external magnetic field in the direction of the stretching sheet. The boundary layer equations with the associated boundary conditions are transformed into ODEs using suitable similarity transformations. The resultant system of ODEs is numerically solved using the shooting technique by appropriately guessing the initial values and then correcting them by the Newton-Raphson scheme. The effects of the dimensionless parameters on the flow and heat exchange characteristics are graphically analyzed. It is found that the thickness of the film reduces with magnetization and unsteadiness parameters.

Aligned Magnetic Field and Radiation Effects on Biomagnetic Fluid over an Unsteady Stretching Sheet with Various Slip Conditions

The aim of the present study is to analyze the effects of aligned magnetic field and radiation on biomagnetic fluid flow and heat transfer over an unsteady stretching sheet with various slip conditions. The magnetic field is assumed to be sufficiently strong enough to saturate the ferrofluid, and the variation of magnetization is approximated by a linear function of temperature difference. The governing boundary layer equations with boundary conditions are simplified by suitable transformations. Numerical solution is obtained by using the bvp4c function technique in MATLAB software. The numerical results are derived for the velocity, temperature, the skin friction coefficient, and the rate of heat transfer. The evaluated results are compared with analytical study documented in scientific literature. The present investigation illustrates that the fluid velocity is decreased with the increasing values of radiation parameter, magnetic parameter, and ferromagnetic interaction parameter, though is increased as the Prandtl number, Grashof number, permeable parameter and thermal slip parameter are increased. In this investigation, the suction/injection parameter had a good impact on the skin friction coefficient and the rate of heat transfer.

Effect of Thermal Radiation on Biomagnetic Fluid Flow and Heat Transfer over an Unsteady Stretching Sheet

This study examines the influence of thermal radiation on biomagnetic fluid, namely blood that passes through a two-dimensional stretching sheet in the presence of magnetic dipole. This analysis is conducted to observe the behavior of blood flow for an unsteady case, which will help in developing new solutions to treat diseases and disorders related to human body. Our model is namely biomagnetic fluid dynamics (BFD), which is consistent with two principles: ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD), where blood is treated as electrically conductive. It is assumed that the implemented magnetic field is sufficiently strong to saturate the ferrofluid, and the variation of magnetization with temperature may be approximated with the aid of a function of temperature distinction. The governing partial differential equations (PDEs) converted into ordinary differential equations (ODEs) using similarity transformation and numerical results are thus obtained by using the bvp4c function technique in MATLAB software with considering applicable boundary conditions. With the help of graphs, we discuss the impact of various parameters, namely radiation parameter, unsteady parameter, permeability parameter, suction parameter, magnetic field parameter, ferromagnetic parameter, Prandtl number, velocity and thermal slip parameter on fluid (blood) flow and heat transfer in the boundary layer. The rate of heat transfer and skin friction coefficient is also computationally obtained for the requirement of this study. The fluid velocity decreases with increasing values of the magnetic parameter, ferromagnetic interaction parameter, radiation parameter whereas temperature profile increases for the unsteady parameter, Prandtl number, and permeability parameter. From the analysis, it is also observed that the skin friction coefficient decreases and the rate of heat transfer increases respectively with increasing values of the ferromagnetic interaction parameter. The most important part of the present analysis is that we neither neglect the magnetization nor electrical conductivity of the blood throughout this study. To make the results more feasible, they are compared with the data previously published in the literature and found to be in good accuracy.

Effect of Non-linear Radiation on MHD Mixed Convection Flow of a Micropolar fluid Over an Unsteady Stretching Sheet

The current analysis explores the results of non-linear radiation on an unsteady stretching mixed Micropolar fluid. Issue modelling leads to a framework of PDE, reworked by transformations into non-linear ODEs. The Homotopy analysis methodology is applied to resolve the matter. The diagrams address the impact of the Magnetic parameter, unsteadiness parameter, Eckert number, Micropolar parameters, buoyancy parameters, Radiation parameter, Temperature ratio and Schmidt number on velocity, temperature, and concentration gradients. Amount of Nusselt number will increase in massive Prandtl number values, within the case of the high values of the unsteadiness parameter skin friction, wall couple stress and Sherwood decrease.

Heat Transfer of Thin Film Flow Over an Unsteady Stretching Sheet with Dynamic Viscosity

This research paper explains the impact of dynamics viscosity of water base GO-EG/GO-W nanofluid over a stretching sheet. The impact of different parameter for velocity and temperature are displayed and discussed. The similarity transformation is used to convert the partial differential equation to nonlinear ordinary differential equation. The solution of the problem is obtained by using the optimal homotopy analysis method (OHAM). The BVPh 2.0 package function of Mathematica is used to obtain the numerical results. The result of important parameter such as magnetic parameter, Prandtl number, Eckert number, dynamic viscosity, nanoparticles volume fraction and unsteady parameter for both velocity and temperature profiles are plotted and discussed. The BVPh 2.0 package is used to obtain the convergences of the problem up to 25 iteration. The skin friction coefficient and Nusselt number is explained in table form.

Magnetohydrodynamic Fluid Flow due to an Unsteady Stretching Sheet with Thermal Radiation, Porous Medium, and Variable Heat Flux

A shooting method has been introduced for determining the numerical solution of the ordinary differential equations which describe the Newtonian magnetohydrodynamic laminar fluid flow due to an unsteady stretching sheet together with the presence of thermal radiation and variable heat flux. The variable viscosity and variable conductivity are taken into consideration. Absence of magnetic field in some studies restricts the development of the energy-efficient heat transfer mechanism as is desired in numerous applications. The present study encompasses parameters such as unsteadiness parameter, porous parameter, viscosity parameter, magnetic number, radiation parameter, and conductivity parameter. It has been consummated that the proposed model is superior to other existing models for the industrial fluid.

Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet

Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity. Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically. The sheet is permeable, and there is an injection effect at the surface of the stretching sheet. The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c. The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer. However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet. The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness. Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process.

Entropy Generation in MHD Second-Grade Nanofluid Thin Film Flow Containing CNTs with Cattaneo-Christov Heat Flux Model Past an Unsteady Stretching Sheet

Entropy generation plays a significant role in several complex processes, extending from cosmology to biology. The entropy generation minimization procedure can be applied for the optimization of mechanical systems including heat exchangers, elements of nuclear and thermal power plants, ventilation and air-conditioning systems. In order to present our analysis, entropy generation in a thin film flow of second grade nanofluid holding single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with a Cattaneo–Christov heat flux model is studied in this article. The flow is considered passing a linearly extending surface. A variable magnetic field with aligned angle ε is functioned along the extending sheet. With the aid of the homotopy analysis method (HAM), the fluid flow model is elucidated. The impressions of embedded factors on the flow are obtainable through figures and discussed in detail. It is observed that the velocity profile escalated with the increasing values of volume fraction of nanoparticles and second grade fluid parameter. The higher values of volume fraction of nanoparticles, second grade fluid parameter, non-linear heat source/sink, and thermal radiation parameter intensified the temperature profile. Surface drag force escalated with heightening values of nanoparticles volume fraction, unsteadiness, film thickness, magnetic, and second grade fluid parameters. Entropy generation increased with enhancing values of magnetic parameter, Brinkman number, and Reynolds number.

Flow and Heat Transfer in a Nanofluid Thin Film Over an Unsteady Stretching Sheet

This study analyzes the heat transfer of a thin film flow on an unsteady stretching sheet in nanofluids. Three different types of nanoparticles are considered; copper Cu, alumina Al2O3 and titania TiO2 with water as the base fluid. The governing equations are simplified using similarity transformations. The resulting coupled nonlinear differential equations are solved by the Homotopy Analysis Method (HAM). The analytical series solutions are presented and the numerical results obtained are tabulated. In particular, it shows that the heat transfer rate decreases when nanoparticles volume fraction increases.

Boundary Layer and Heat Transfer Analysis in Liquid Film of Nanofluid Over an Unsteady Stretching Sheet

Boundary Layer and Heat Transfer Analysis in Liquid Film of Nanofluid Over an Unsteady Stretching Sheet

Thermal Radiation and Chemical Reaction Effects on an Unsteady Stretching Sheet

Thermal Radiation and Chemical Reaction Effects on an Unsteady Stretching Sheet

MHD Flow and Heat Transfer Characteristics in a Casson Liquid Film Towards an Unsteady Stretching Sheet with Temperature-Dependent Thermal Conductivity

Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work.

Dufour and Soret Effect with Thermal Radiation on the Nano Film Flow of Williamson Fluid Past Over an Unsteady Stretching Sheet

Dufour and Soret Effect with Thermal Radiation on the Nano Film Flow of Williamson Fluid Past Over an Unsteady Stretching Sheet

English

English

Combined Effects of Thermal Radiation and Magnetic Field on Heat and Mass Transfer in a Thin Liquid Film of a Nanofluid Over an Unsteady Stretching Sheet

Combined Effects of Thermal Radiation and Magnetic Field on Heat and Mass Transfer in a Thin Liquid Film of a Nanofluid Over an Unsteady Stretching Sheet

Flow and Heat Transfer over an Unsteady Stretching Sheet in a Micropolar Fluid with Convective Boundary Condition

This article is concerned with the flow of micropolar fluid over an unsteady stretching surface with convective boundary condition. The governing partial differential equations are first converted into ordinary differential equations using appropriate transformations and then solved for the series solutions. Influence of micropolar parameter, unsteadiness parameter, boundary parameter, Prandtl number and Biot number on the flow and heat transfer characteristics is examined. Numerical values of local Nusselt number and skin friction coefficient are presented and analyzed. It is observed that temperature is an increasing function of Biot number.

Slip Flow of Powell-Eyring Liquid Film Due to an Unsteady Stretching Sheet with Heat Generation

This paper is focused on the study of the viscous Powell-Eyring liquid thin film flow and heat transfer driven by an unsteady stretching sheet in the presence of slip velocity and non-uniform heat generation. A system of equations for momentum and thermal energy are reduced to a set of coupled non-linear ordinary differential equations with the aid of dimensionless transformation. The resulting seven-parameter problem has been solved numerically by using an efficient shooting technique coupled with the fourth-order Runge-Kutta algorithm over the entire range of physical parameters. To interpret various physical parameters governing the flow and heat transfer which appear in the momentum and energy equations, the results are presented graphically. The present results are compared with some of the earlier published work in some limiting cases and are found to be in an excellent agreement. This favorable comparison lends confidence in the numerical results to be reported in the present work. Furthermore, the effects of the parameters governing the thin film flow and heat transfer are examined and discussed through graphs and tables. Also, the values of the local skin-friction coefficient and the local Nusselt number for different values of physical parameters are presented through tables. Additionally, the obtained results for some particular cases of the present problem appear in good agreement with the literature review.

Computational Modeling of an MHD Flow of a Non-Newtonian Fluid Over an Unsteady Stretching Sheet with Viscous Dissipation Effects

Computational Modeling of an MHD Flow of a Non-Newtonian Fluid Over an Unsteady Stretching Sheet with Viscous Dissipation Effects