Lie symmetry analysis, invariant subspace method and q-homotopy analysis method for solving fractional system of single-walled carbon nanotube

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Xiaoyu Cheng ◽  
Jie Hou ◽  
Lizhen Wang
Keyword(s):  
Carbon Nanotube ◽  
Invariant Subspace ◽  
Homotopy Analysis Method ◽  
Lie Symmetry ◽  
Subspace Method ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Single Walled Carbon Nanotube ◽  
Homotopy Analysis ◽  
Fractional System

scholarly journals The carbon-nanotube nanofluid sprayed on an unsteady stretching cylinder together with entropy generation

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989445 ◽  
Author(s):  
Taza Gul ◽  
Muhammad Waqas ◽  
Waqas Noman ◽  
Zafar Zaheer ◽  
Iraj S Amiri
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Thin Layer ◽  
Entropy Generation ◽  
Homotopy Analysis Method ◽  
Single Wall Carbon Nanotubes ◽  
Bejan Number ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis

The water-based single- and multiple-wall carbon nanotubes nanofluid over the surface of an unsteady stretched cylinder has been studied. The thin film of the carbon-nanotube nanofluid has been focused for the heat transfer enhancement applications. The well-known thermal conductivity model for the revolving tube materials like single- and multiple-walled carbon nanotubes defined by Xue were used. The modeled problem has been solved through the optimal homotopy analysis method using the BVPh 2.0 package. The distribution of the thin layer has been regulated through the pressure term using the variable thickness of the nanoliquid. The entropy generation has mainly focused during the motion of the thin layer for the both sorts of carbon nanotubes. The important features of the entropy generation and Bejan number under the influence of the physical constraints have been compared for the both types of single-wall carbon nanotubes and multiple-wall carbon nanotubes and discussed. The well-known BVPh 2.0 package of the optimal homotopy analysis method has been used to find the outcomes.

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

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