Thermosoluted Marangoni convective flow towards a permeable Riga surface

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 535-544
Author(s):  
Anum Shafiq ◽  
Ghulam Rasool ◽  
Lehlohonolo Phali ◽  
Chaudry Masood Khalique
Keyword(s):  
Differential Equations ◽  
Mass Flux ◽  
Soret Effect ◽  
Analysis Method ◽  
Dufour Effect ◽  
Convergence Of Series ◽  
Opposite Trend ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
The Impact

AbstractThis study reveals the characteristics of chemical reaction on Marangoni mixed convective stream towards a penetrable Riga surface. The heat and mass phenomena are analysed within the sight of Dufour and Soret impacts. The administering partial differential equations system is converted into three nonlinear ordinary differential equations utilizing appropriately adjusted transformations. The resultant system of highly nonlinear equations is analytically solved by invoking the homotopy analysis method. Thereafter, the convergence of series solutions is discussed. The impact of appropriate parameters on various flow fields is thoroughly explained with the help of graphs and tables. The wall drag coefficient and relevant flux rates are arranged and discussed for dimensionless parameters. The outcomes show that the stronger Dufour effect of liquid causes a notable incremental variation in heat and mass flux, whereas an opposite trend is noted in the heat flux rate for the Soret effect. However, the mass flux is still found increasing for the stronger Soret effect.

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.

scholarly journals The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions Over a Stretching Sheet with Jeffrey Fluid.

2021 ◽  
Author(s):  
Vijay Patel ◽  
Jigisha Pandya
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

In this research paper, the Homotopy Analysis Method is used to investigate the twodimensional electrical conduction of a magneto-hydrodynamic (MHD) Jeffrey Fluid across a stretching sheet under various conditions, such as when electrical current and temperature are both present, and when heat is added in the presence of a chemical reaction or thermal radiation. Applying similarity transformation, the governing partial differential equation is transformed into terms of nonlinear coupled ordinary differential equations. The Homotopy Analysis Method is used to solve a system of ordinary differential equations. The impact of different numerical values on velocity, concentration, and temperature is examined and presented in tables and graphs. The fluid velocity reduces as the retardation time parameter(2) grows, while the fluid velocity inside the boundary layer increases as the Deborah number () increases. The velocity profiles decrease when the magnetic parameter M is increased. The results of this study are entirely compatible with those of a viscous fluid. The Homotopy Analysis Method calculations have been carried out on the PARAM Shavak high-performance computing (HPC) machine using the BVPh2.0 Mathematica tool.

scholarly journals Serious Solutions for Unsteady Axisymmetric Flow over a Rotating Stretchable Disk with Deceleration

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 96 ◽  
Author(s):  
Sadiq
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Axisymmetric Flow ◽  
Analysis Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Rotating Stretchable Disk ◽  
Comparison Table

In this article, the author has examined the unsteady flow over a rotating stretchable disk with deceleration. The highly nonlinear partial differential equations of viscous fluid are simplified by existing similarity transformation. Reduced nonlinear ordinary differential equations are solved by homotopy analysis method (HAM). The convergence of HAM solutions is also obtained. A comparison table between analytical solutions and numerical solutions is also presented. Finally, the results for useful parameters, i.e., disk stretching parameters and unsteadiness parameters, are found.

scholarly journals Concentration Flux Dependent on Radiative MHD Casson Flow with Arrhenius Activation Energy: Homotopy Analysis Method (HAM) with an Evolutionary Algorithm

2020 ◽  
Vol 38 (4) ◽  
pp. 785-793
Author(s):  
Kohilavani Naganthran ◽  
Ahmad Zeeshan ◽  
Md. Faisal Md. Basir ◽  
Nasir Shehzad ◽  
Roslinda Nazar ◽  
...  
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Radiation Effects ◽  
Chemical Properties ◽  
Research Field ◽  
Heat Transfer Analysis ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

Heat transfer analysis in nanofluids is an active research field due to its extraordinary physical and chemical properties. In the current study, the focus lies on the effects of Stefan blowing when a non-Newtonian Casson base fluid flows over a surface which stretches linearly. A uniform transverse magnetic field is employed. The chemical reaction in the fluid with activation energy and radiation effects have also been engaging the attention. Fundamental laws of conservation are employed to model governing equations of flow. Similarity transform is introduced to reduce the said system of partial differential equations to ordinary differential equations which are in turn tackled analytically using Homotopy Analysis Method with genetic algorithms to optimise the series solution. The impact of pertaining parameters on the dimensionless velocity, temperature and concentration were presented explicitly. This study relevant to remedies for malign tissues, cells or clogged arteries of the heart.

The Approximate Analytical Solution of the MHD Flow of a Power-Law Fluid

2013 ◽  
Vol 431 ◽  
pp. 198-201
Author(s):  
Jing Zhu ◽  
Lian Cun Zheng
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Velocity Ratio ◽  
Mhd Flow ◽  
Convergent Series ◽  
Analysis Method ◽  
Governing System ◽  
Homotopy Analysis ◽  
Incompressible Mhd ◽  
Good Agreement

This paper presents a theoretical analysis for the incompressible MHD stagnation-point flows of a Non-Newtonian Fluid over stretching sheets.The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. By using the homotopy analysis method, a convergent series solution is obtained. The reliability and efficiency of series solutions are illustrated by good agreement with numerical results in the literature.Besides, the effects of the power-law indexthe magnetic field parameter and velocity ratio parameter on the flow are investigated.

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

2010 ◽  
Vol 65 (11) ◽  
pp. 935-949 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian ◽  
Abbas Saadatmandi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Analysis Method ◽  
Partial Differential ◽  
Integer Order ◽  
Homotopy Analysis

In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

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