Nonlinear study of heat transfer in nanofluid saturated horizontal porous medium

2017 ◽  
Vol 3 (01) ◽  
Author(s):  
Alok Srivastava ◽  
Vineet Kumar ◽  
B. S. Bhadauria ◽  
I. Hashimt
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Landau Equation ◽  
High Accuracy ◽  
Analysis Method ◽  
Nonlinear Stability Analysis ◽  
Governing Equations ◽  
Ginzburg Landau ◽  
Homotopy Analysis ◽  
Saturated Porous Layer

The present paper deals with weak nonlinear stability analysis of heat transfer in a nanofluid saturated porous layer. We consider a set of new boundary conditions for the nanoparticle fraction, which is physically more realistic. The new boundary condition is based on the assumption that the nanoparticle fraction adjusts itself so that the nanoparticle flux is zero on the boundaries. We use Darcy model that incorporates the effects of Brownian motion and thermophoresis. The governing equations has been reduced to Ginzburg-Landau equation and solved by homotopy analysis method (HAM). The obtained results have been compared with the numerical results obtained by Mathematica NDSolve. The results are valid for the feasible domain with high accuracy. Thermal Nusselt number and Nanoparticle Nusselt number are calculated for different values of parameters. The results have been depicted graphically.

Throughflow and G-Jitter Effects on Oscillatory Convection in a Rotating Porous Medium

2020 ◽  
Vol 12 (6) ◽  
pp. 781-791
Author(s):  
S. H. Manjula ◽  
Palle Kiran ◽  
B. S. Bhadauria
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transport ◽  
Landau Equation ◽  
Nonlinear Stability Analysis ◽  
Periodic Mode ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
The Impact

The impact of vertical throughflow and g-jitter effect on rotating porous medium is investigated. A feeble nonlinear stability analysis associate to complex Ginzburg-Landau equation (CGLE) has been studied. This weakly nonlinear analysis performed for a periodic mode of convection and quantified heat transport in terms of the Nusselt number, which is governed by the non-autonomous advanced CGLE. Each idea, rotation and throughflow is used as an external mechanism to the system either to extend or decrease the heat transfer. The results of amplitude and frequency of modulation on heat transport are analyzed and portrayed graphically. Throughflow has dual impact on heat transfer either to increase or decrease heat transfer in the system. Particularly the outflow enhances and inflow diminishes the heat transfer. High centrifugal rates promote heat transfer and low centrifugal rates diminish heat transfer. The streamlines and isotherms area portrayed graphically, the results of rotation and throughflow on isotherms shows convective development.

Flow and Heat Transfer of Nanofluids Over a Rotating Porous Disk with Velocity Slip and Temperature Jump

2015 ◽  
Vol 70 (5) ◽  
pp. 351-358 ◽  
Author(s):  
Chenguang Yin ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Temperature Fields ◽  
Analysis Method ◽  
Governing Equations ◽  
Porous Disk ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Good Agreement

AbstractIn this article, we discuss the flow and heat transfer of nanofluids over a rotating porous disk with velocity slip and temperature jump. Three types of nanoparticles – Cu, Al2O3, and CuO – are considered with water as the base fluid. The nonlinear governing equations are reduced into ordinary differential equations by Von Karman transformations and solved using homotopy analysis method (HAM), which is verified in good agreement with numerical ones. The effects of involved parameters such as porous parameter, velocity slip, temperature jump, as well as the types of nanofluids on velocity and temperature fields are presented graphically and analysed.

Effect of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets

2010 ◽  
Vol 65 (11) ◽  
pp. 961-968 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Nawaz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Tabular Form ◽  
Analysis Method ◽  
Navier Stokes Equations ◽  
Homotopy Analysis

This investigation describes the effects of heat transfer on magnetohydrodynamic (MHD) axisymmetric flow of a viscous fluid between two radially stretching sheets. Navier-Stokes equations are transformed into the ordinary differential equations by utilizing similarity variables. Solution computations are presented by using the homotopy analysis method. The convergence of obtained solutions is checked. Skin friction coefficient and Nusselt number are given in tabular form. The dimensionless velocities and temperature are also analyzed for the pertinent parameters entering into the problem.

scholarly journals Solving generalized quintic complex Ginzburg–Landau equation by homotopy analysis method

2018 ◽  
Vol 9 (4) ◽  
pp. 607-613 ◽  
Author(s):  
Soheila Naghshband ◽  
Mohammad Ali Fariborzi Araghi
Keyword(s):  
Homotopy Analysis Method ◽  
Landau Equation ◽  
Analysis Method ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Homotopy Analysis

Hydromagnetic Flow and Heat Transfer of a Jeffrey Fluid over an Oscillatory Stretching Surface

2015 ◽  
Vol 70 (7) ◽  
pp. 567-576 ◽  
Author(s):  
Nasir Ali ◽  
Sami Ullah Khan ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Physical Space ◽  
Jeffrey Fluid ◽  
Computational Domain ◽  
Analysis Method ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Oscillatory Stretching Surface ◽  
Oscillatory Stretching Sheet

AbstractThe flow and heat transfer of a Jeffrey fluid over an oscillatory stretching sheet is investigated using the boundary-layer approximations. The flow is induced due to infinite elastic sheet that is stretched periodically. The number of independent variables in the governing equations was reduced by using appropriate dimensionless variables. This dimensionless system has been solved by using the homotopy analysis method (HAM) and a finite difference scheme, in which a coordinate transformation was used to transform the semi-infinite physical space to a bounded computational domain. A comparison of both solutions is provided. The effects of involved parameters are illustrated through graphs and discussed in detail.

scholarly journals Soret and dufour effects on hydromagnetic flow of Eyring-Powell fluid over oscillatory stretching surface with heat generation/absorption and chemical reaction

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 533-543 ◽  
Author(s):  
Khan Ullah ◽  
Nasir Ali ◽  
Zaheer Abbas
Keyword(s):  
Analysis Method ◽  
Governing Equations ◽  
Convective Boundary ◽  
Soret And Dufour Effects ◽  
Electrically Conducting ◽  
Homotopy Analysis ◽  
Oscillatory Stretching Surface ◽  
And Diffusion ◽  
Local Sherwood Number ◽  
Oscillatory Stretching Sheet

In this article, we have investigated thermal-diffusion and diffusion-thermo effects on unsteady flow of electrically conducting Eyring-Powell fluid over an oscillatory stretching sheet by using convective boundary conditions. A set of appropriate variables are used to reduce number of independent variables in governing equations. Series solution is computed using homotopy analysis method. The effects of various parameters of interest on the velocity filed, temperature profile, concentration profile, skin friction, local Nusselt number and local Sherwood number are illustrated graphically and discussed in detail.

scholarly journals An efficient analytic approach for solving Hiemenz flow through a porous medium of a non-Newtonian Rivlin-Ericksen fluid with heat transfer

2018 ◽  
Vol 7 (4) ◽  
pp. 287-301
Author(s):  
Kourosh Parand ◽  
Yasaman Lotfi ◽  
Jamal Amani Rad
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Analytic Method ◽  
Analysis Method ◽  
Wide Range ◽  
Hiemenz Flow ◽  
Homotopy Analysis ◽  
Flow Through

AbstractIn the present work, the problem of Hiemenz flow through a porous medium of a incompressible non-Newtonian Rivlin-Ericksen fluid with heat transfer is presented and newly developed analytic method, namely the homotopy analysis method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This flow impinges normal to a plane wall with heat transfer. It has been attempted to show capabilities and wide-range applications of the homotopy analysis method in comparison with the numerical method in solving this problem. Also the convergence of the obtained HAM solution is discussed explicitly. Our reports consist of the effect of the porosity of the medium and the characteristics of the Non-Newtonian fluid on both the flow and heat.

Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models

2016 ◽  
Vol 26 (3/4) ◽  
pp. 671-693 ◽  
Author(s):  
Ioan Pop ◽  
Mohammad Ghalambaz ◽  
Mikhail Sheremet
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Base Fluid ◽  
Average Nusselt Number ◽  
Solid Phase ◽  
Porous Matrix ◽  
Governing Equations ◽  
Content Type ◽  
Brownian Motion And Thermophoresis

Purpose – The purpose of this paper is to theoretically analysis the steady-state natural convection flow and heat transfer of nanofluids in a square enclosure filled with a porous medium saturated with a nanofluid considering local thermal non-equilibrium (LTNE) effects. Different local temperatures for the solid phase of the nanoparticles, the solid phase of porous matrix and the liquid phase of the base fluid are taken into account. Design/methodology/approach – The Buongiorno’s model, incorporating the Brownian motion and thermophoresis effects, is utilized to take into account the migration of nanoparticles. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the finite element method is utilized to solve the governing equations. Findings – The results show that the increase of buoyancy ratio parameter (Nr) decreases the magnitude of average Nusselt number. The increase of the nanoparticles-fluid interface heat transfer parameter (Nhp) increases the average Nusselt number for nanoparticles and decreases the average Nusselt number for the base fluid. The nanofluid and porous matrix with large values of modified thermal capacity ratios (γ p and γ s ) are of interest for heat transfer applications. Originality/value – The three phases of nanoparticles, base fluid and the porous matrix are in the LTNE. The effect of mass transfer of nanoparticles due to the Brownian motion and thermophoresis effects are also taken into account.

Series solutions of stagnation slip flow and heat transfer by the homotopy analysis method

2009 ◽  
Vol 52 (6) ◽  
pp. 893-899 ◽  
Author(s):  
Jun Cheng ◽  
ShiJun Liao ◽  
R. N. Mohapatra ◽  
K. Vajravelu
Keyword(s):  
Heat Transfer ◽  
Homotopy Analysis Method ◽  
Slip Flow ◽  
Series Solutions ◽  
Analysis Method ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

scholarly journals Falkner-Skan Flow of a Maxwell Fluid with Heat Transfer and Magnetic Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Qasim ◽  
S. Noreen
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Prandtl Number ◽  
Comparative Study ◽  
Homotopy Analysis Method ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Analysis Method ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic fi…eld with heat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method (HAM). Effects of the involved parameters, namely, the Deborah number, Hartman number, and the Prandtl number, are examined carefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted.

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