Second order velocity slip and thermal jump of Cu-water nanofluid over a cone in the presence of nonlinear radiation and nonuniform heat source/sink using homotopy analysis method

2019 ◽  
Vol 49 (1) ◽  
pp. 86-102 ◽  
Author(s):  
C. S. Sravanthi
Keyword(s):  
Heat Source ◽  
Homotopy Analysis Method ◽  
Velocity Slip ◽  
Second Order ◽  
Analysis Method ◽  
Nonlinear Radiation ◽  
Homotopy Analysis ◽  
Source Sink

scholarly journals Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

2018 ◽  
Vol 23 (1) ◽  
pp. 137-159 ◽  
Author(s):  
C.S. Sravanthi ◽  
R.S.R. Gorla
Keyword(s):  
Heat Source ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Analysis Method ◽  
Nanoparticle Concentration ◽  
Convective Boundary ◽  
Maxwell Nanofluid ◽  
Homotopy Analysis ◽  
Exponentially Stretching ◽  
Source Sink

AbstractThe aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

scholarly journals Simultaneous solutions for first order and second order slips on micropolar fluid flow across a convective surface in the presence of Lorentz force and variable heat source/sink

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
K. Anantha Kumar ◽  
V. Sugunamma ◽  
N. Sandeep ◽  
M. T. Mustafa
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Micropolar Fluid ◽  
Velocity Slip ◽  
Second Order ◽  
Nonlinear Odes ◽  
Similarity Transformations ◽  
Runge Kutta Method ◽  
Micropolar Fluid Flow ◽  
Source Sink

Abstract This report presents the flow and heat transfer characteristics of MHD micropolar fluid due to the stretching of a surface with second order velocity slip. The influence of nonlinear radiation and irregular heat source/sink are anticipated. Simultaneous solutions are presented for first and second-order velocity slips. The PDEs which govern the flow have been transformed as ODEs by the choice of suitable similarity transformations. The transformed nonlinear ODEs are converted into linear by shooting method then solved numerically by fourth-order Runge-Kutta method. Graphs are drowned to discern the effect of varied nondimensional parameters on the flow fields (velocity, microrotation, and temperature). Along with them the coefficients of Skin friction, couple stress, and local Nussel number are also anticipated and portrayed with the support of the table. The results unveil that the non-uniform heat source/sink and non-linear radiation parameters plays a key role in the heat transfer performance. Also, second-order slip velocity causes strengthen in the distribution of velocity but a reduction in the distribution of temperature is perceived.

scholarly journals Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Ahmad El-Ajou ◽  
Omar Abu Arqub ◽  
Shaher Momani
Keyword(s):  
Homotopy Analysis Method ◽  
Series Solution ◽  
Convergent Series ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Analysis Method ◽  
Convergence Region ◽  
New Approach ◽  
Homotopy Analysis ◽  
And Control

In this paper, series solution of second-order integrodifferential equations with boundary conditions of the Fredholm and Volterra types by means of the homotopy analysis method is considered. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The homotopy analysis method provides us with a simple way to adjust and control the convergence region of the infinite series solution by introducing an auxiliary parameter. The proposed technique is applied to a few test examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.

scholarly journals Effects of Nanolayer and Second Order Slip on Unsteady Nanofluid Flow Past a Wedge

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1043 ◽  
Author(s):  
Zhu ◽  
Cao
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Fundamental Equations

This paper presents the study of unsteady nanofluids flow and heat transfer past a wedge with second order velocity slip and temperature jump. The model is modified by considering the existence of a nanolayer together with the effects of thermophoresis and Brownian motion. The fundamental equations were transformed into ordinary differential equations by a new set of similarity transformations and solved by using the homotopy analysis method (HAM). We determined that the error reached 10-6 and the effectiveness of HAM was attained. The influence of second-order slip on the fluid skin-friction coefficient was analyzed and we determined that the Nusselt number decreases and skin friction coefficient rises with an increase in the thickness of the nanolayer.

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