Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect (original) (raw)
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International Journal of Mechanical and Materials Engineering
Background: The objective of the present study is to analyse the steady second-order slip flow and heat transfer of an incompressible viscous water-based nanofluid over a stretching/shrinking sheet both analytically and numerically. Methods: Using the scaling group transformations, a system of partial differential equations governing the flow and thermal fields is transformed into a system of ordinary differential equations. An exact solution to the momentum equation is obtained, and the solution of the energy equation is obtained in terms of a hypergeometric function for different water-based nanofluids containing Au, Ag, Cu, Al, Al 2 O 3 and TiO 2 nanoparticles. Numerical solutions are obtained using a fourth-order Runge-Kutta method coupled with a shooting iteration technique. Results: It is found that there exist a unique solution in the case of a stretching sheet with suction, but there is no solution in both stretching and shrinking sheets with injection. Dual solutions are obtained in a shrinking sheet beyond a suction critical point. The presence of nanoparticles decreases the suction critical point. Conclusions: Excellent agreement is observed between the analytical and numerical results. The effects of important physical parameters are analysed in detail. The corresponding local skin-friction coefficient and the reduced Nusselt number are also calculated and displayed in tables.
Thermal Science, 2015
In this article, the semi-analytical numerical technique known as the homotopy analysis method is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary-layer decreases and thermal boundary-layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.
Partial Slip Flow and Heat Transfer over a Stretching Sheet in a Nanofluid
Mathematical Problems in Engineering, 2013
The boundary layer flow and heat transfer of a nanofluid over a stretching sheet are numerically studied. Velocity slip is considered instead of no-slip condition at the boundary as is usually appears in the literature. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. Numerical solutions of these equations are obtained using finite element method (FEM). The variations of velocity and temperature inside the boundary layer as well as the skin friction coefficient and the heat transfer rate at the surface for some values of the governing parameters, namely, the nanoparticle volume fraction and the slip parameter are presented graphically and discussed. Comparison with published results for the regular fluid is presented and it is found to be in excellent agreement.
International Journal of Thermal Sciences, 2012
The objective of the present study is to analyze the development of the slip effects on the boundary layer flow and heat transfer over a stretching surface in the presence of nanoparticle fractions. In the modeling of nanofluid the dynamic effects including the Brownian motion and thermophoresis are taken into account. In the case of constant wall temperature a similarity solution is presented. The solution depends on a Prandtl number, slip factor, Brownian motion number, Lewis number, and thermophoresis number. The dependency of the local Nusselt and local Sherwood numbers on these five parameters is numerically investigated. To the best of author's knowledge, the effects of slip boundary condition in the presence of dynamic effects of nano particles have not been investigated yet. The results of the present paper show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter.
Mathematical Problems in Engineering, 2022
The behavior of hybrid nanofluid and stagnation point flow toward a stretched surface along with melting heat transfer, second-order slip, electric field, and magnetic field effect is investigated in this study. Hybrid nanoparticles alumina A l 2 O 3 and copper (Cu) are considered with the base fluids water H 2 O . The PDEs with corresponding boundary constraints are transformed into a set of nonlinear ODEs using similarities transformation. The set of nonlinear ODEs are analyzed analytically using semianalytical method HAM in Mathematica software. Dual solution is determined which relaying on the emerging parameters included magnetic field, volume fractions, electric field, dimensionless surface velocity slip factors, Eckert number, and Prandtl number. The results are shown in the velocity and temperature curves as well as skin friction coefficient and local Nusselt number. The analysis shows that velocity profile is an increasing function of slip parameter, electric field, while r...
Journal of Chemical Engineering & Process Technology
The effects of Soret and Dufour parameters on the boundary layer flow in nanofluid over stretching/ shrinking with time dependent is studied using Buongiorno model. The system of partial differential equations is transformed to the system of ordinary differential equations by applying similarity transformation. The results are obtained numerically using bvp4c in Matlab. The reduced skin friction coefficient reduced Nusselt number, velocity, temperature and concentration profiles are shown graphically with different values of Soret effect, Dufour effect, mass flux parameter, unsteadiness parameter, thermophoresis as well as Brownian motion parameter where the dual solutions are obtained. The unsteadiness parameter and mass flux parameter expand the range of solution for stretching/ shrinking parameter. Meanwhile, the Soret and Dufour parameters are found to affect the heat transfer rate at the surface. In order to determine the stability of the solutions, stability analysis is performed.
The aim of the paper is to analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The obtained ordinary differential equations are solved by variational finite element method (FEM). The effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, viscoelastic parameter, Prandtl number, Lewis number and the slip parameter on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The present study is of great interest in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers' technology, and materials' processing and exploiting.
Mathematics
An investigation has been done on the hybrid nanofluid slip flow in the existence of heat generation over an exponentially stretching/shrinking permeable sheet. Hybridization of alumina and copper with water as the base fluid is considered. The mathematical model is simplified through the similarity transformation. A numerical solver named bvp4c in Matlab software is utilized to facilitate the problem-solving process and dual solutions are attained. The influences of several pertinent parameters on the main physical quantities of interest and the profiles are scrutinized and presented in the form of graphs. Through the stability analysis, only the first solution is considered as the physical solution. As such, the findings conclude that the upsurges of volume fraction on the copper nanoparticle could enhance the skin friction coefficient and the local Nusselt number.
Latin American Applied Research - An international journal, 2020
The present paper investigates the problem of flow and heat transfer in a two dimensional boundary layer flow of a nanofluid over a non-linear, permeable stretching/shrinking sheet by considering the effects of suction/blowing, momentum slip, thermal slips and thermal radiation. Three different types of spherical nanoparticles such as , and are considered by taking water as the base fluid. With the aid of suitable similarity transformations, the governing non-linear partial differential equations are transformed to ordinary ones. A new analytical method namely DTM-BF, based on the differential transformation method (DTM) and base function (BF), has been applied to get approximate analytic solutions of these equations in an unbounded domain. Comparison of the present numerical results has been done with the corresponding results available in the literature and they have been found to be in good agreement. The effects of different physical parameters on the flow and temperature prof...