A solution of coupled nonlinear differential equations arising in a rotating micropolar nanofluid flow system by Hermite wavelet technique

Author(s):  
S. Kumbinarasaiah ◽  
K. R. Raghunatha ◽  
Mohammadreza Rezazadeh ◽  
Mustafa Inc
Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1379 ◽  
Author(s):  
Rafique ◽  
Anwar ◽  
Misiran ◽  
Khan ◽  
Seikh ◽  
...  

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor.


2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. Nadeem ◽  
Abdul Rehman ◽  
K. Vajravelu ◽  
Jinho Lee ◽  
Changhoon Lee

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.


2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Zahir Shah ◽  
Saeed Islam ◽  
Hamza Ayaz ◽  
Saima Khan

The present research aims to examine the micropolar nanofluid flow of Casson fluid between two parallel plates in a rotating system with effects of thermal radiation. The influence of Hall current on the micropolar nanofluids have been taken into account. The fundamental leading equations are transformed to a system of nonlinear differential equations using appropriate similarity variables. An optimal and numerical tactic is used to get the solution of the problem. The convergence and comparison have been shown numerically. The impact of the Hall current, Brownian movement, and thermophoresis phenomena of Casson nanofluid have been mostly concentrated in this investigation. It is found that amassed Hall impact decreases the operative conductivity which intends to increase the velocity field. The temperature field enhances with larger values of Brownian motion thermophoresis effect. The impacts of the Skin friction coefficient, heat flux, and mass flux have been deliberate. The skin friction coefficient is observed to be larger for k=0, as compared to the case of k=0.5. Furthermore, for conception and visual demonstration, the embedded parameters have been deliberated graphically.


Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4191 ◽  
Author(s):  
Khuram Rafique ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran ◽  
Ilyas Khan ◽  
Asiful H. Seikh ◽  
...  

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating effects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret effect reduces the heat flux rate and wall shear stress.


2017 ◽  
Vol 65 (3) ◽  
pp. 383-390 ◽  
Author(s):  
M. Bilal ◽  
S. Hussain ◽  
M. Sagheer

AbstractIn the present article, magneto-micropolar nanofluid flow with suction or injection in a porous medium over a stretching sheet for the heat and mass transfer is analyzed numerically. Both Hall and ion-slip effects are considered along with variable thermal diffusivity. The governing partial differential equations are transformed to ordinary differential equations using usual similarity transformations. These coupled non-linear differential equations are solved using the shooting method. Effects of prominent parameter on velocities, temperature and concentration are discussed graphically. Numerical values of skin-friction coefficient, local Nusselt number and local Sherwood number are also tabulated and discussed.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anwar Saeed ◽  
Abdelaziz Alsubie ◽  
Poom Kumam ◽  
Saleem Nasir ◽  
Taza Gul ◽  
...  

AbstractIn this investigation, heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface is considered. The innovative characteristics and aims of this work are to note that the transportation heat couple stress model involves EMHD, viscous dissipation, Joule heating, and heat absorption, and omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the SWCNTs and MWCNTs in pure human blood. This mathematical model is an appropriate model for biological advantages including testing of human blood for drug deliveries to various parts of the human body. Particularly, the Prandtl number used for the blood is 21 and very large as compared to the other base fluids. Necessary modifications are used to translate the defining partial differential equations and boundary conditions into a layout that can be computed. To obtain mathematical approximations for the resulting scheme of nonlinear differential equations, the innovative homotopy analysis method (HAM) is used. The explanation for velocity, energy, and entropy are exposed and the flow against various influential factors ($$E,\;M,\;k,\;Q,\;S\;{\text{and}}\;Ec$$ E , M , k , Q , S and E c ) is discussed graphically. The numerical values are calculated and summarized for dimensionless $$C_{{fx}} \;{\text{and}}\;Nu_{x} .$$ C fx and N u x . In addition, the current study is compared for various values of $$\Pr$$ Pr to that published literature and an impressive agreement in terms of finding is reported. It has also been noticed that the $$M$$ M and $$E$$ E factors retard the hybrid nanofluid flow, while the temperature of fluid becomes upsurges by the rise in these factors. 11.95% enhancement in the heat transfer rate has been attained using the hybrid nanofluids.


2018 ◽  
Vol 3 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Mangalagama Dewasurendra ◽  
Kuppalapalle Vajravelu

AbstractVery recently, Liao has invented a Directly Defining Inverse Mapping Method (MDDiM) for nonlinear differential equations. Liao’s method is novel and can be used for solving several problems arising in science and engineering, if we can extend it to nonlinear systems. Hence, in this paper, we extend Liao’s method to nonlinear-coupled systems of three differential equations. Our extension is not limited to single, double or triple equations, but can be applied to systems of any number of equations.


Author(s):  
Khuram Rafique ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran

In this paper, micropolar nanofluid boundary layer flow over a linear inclined stretching surface with the magnetic effect is investigated. Buongiorno’s model utilized in this study for the thermal efficiencies of the fluid flow in the presence of Brownian motion and thermophoresis properties. The nonlinear problem for micropolar nanofluid flow over an inclined sheet is established to study the heat and mass exchange phenomenon by considering portent flow parameters to strengthen the boundary layers. The governing nonlinear partial differential equations are changed to nonlinear ordinary differential equations by using suitable similarity transformations and then solved numerically by applying the Keller-Box method. A comparison of the setup results in the absence of the incorporated impacts is performed with the accessible results and perceived in a decent settlement. Numerical and graphical outcomes are additionally presented in tables and diagrams.


Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.


2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving

Sign in / Sign up

Export Citation Format

Share Document