Fisher–Kolmogorov–Petrovsky– Piscounov Reaction and n-Diffusion Cattaneo Telegraph Equation

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Ulrich Olivier Dangui-Mbani ◽  
Jize Sui ◽  
Liancun Zheng ◽  
Bandar Bin-Mohsin ◽  
Goong Chen
Keyword(s):  
Power Law ◽  
Adomian Decomposition Method ◽  
Relaxation Parameter ◽  
Spatial Variable ◽  
Recombination Reaction ◽  
Temperature Profiles ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Power Law Index ◽  
Temporal Variable

This paper presents research for a class of recombination reaction and diffusion problems in which the Cattaneo relaxation, n-diffusion flux, and p-Fisher–Kolmogorov–Petrovsky–Piscounov (KPP) reaction are considered. Approximate analytical solutions are obtained by Adomian decomposition method (ADM) and shown graphically. Some interesting results for spatial variable and temporal variable evolution are obtained. For specified spatial variable, the temperature profiles decrease with respect to the increase of relaxation parameter and power-law index n but decrease with respect to Fisher–KPP reaction parameter p. For specified temporal variable, the temperature profiles are seem oscillating with values of the relaxation parameter and power-law index n.

MHD Natural Convection Slip Flow through Vertical Porous Plates with Time-Periodic Boundary Conditions

2018 ◽  
Vol 388 ◽  
pp. 135-145
Author(s):  
Samuel Olumide Adesanya ◽  
L. Rundora ◽  
R.S. Lebelo ◽  
K.C. Moloi
Keyword(s):  
Convective Flow ◽  
Decomposition Method ◽  
Hartmann Number ◽  
Slip Flow ◽  
Adomian Decomposition Method ◽  
Periodic Boundary Conditions ◽  
Temperature Profiles ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Time Periodic

In this work, the convective flow of heat generating hydromagnetic fluid through a leaky channel is investigated. Due to channel porosity, the asymmetrical slip conditions are imposed on both walls. The coupled dimensionless partial differential equations are reduced to a system of second-order boundary-value problems based on some flow assumptions and solved by Adomian decomposition method (ADM). Variations in velocity and temperature profiles are presented and discussed in detail. The result of the analysis revealed that increasing Hartmann number decreases the flow velocity while the slip parameters enhance the flow.

scholarly journals Approximate analytical solutions of non-linear local fractional heat equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 837-841 ◽  
Author(s):  
Shuxian Deng
Keyword(s):  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Heat Equations ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractional Heat Equation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Non Linear

Consider the non-linear local fractional heat equation. The fractional complex transform method and the Adomian decomposition method are used to solve the equation. The approximate analytical solutions are obtained.

scholarly journals Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Norhasimah Mahiddin ◽  
S. A. Hashim Ali
Keyword(s):  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Slight Variation ◽  
Tumour Invasion ◽  
Invasion And Metastasis ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition

The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

scholarly journals Effects of heat source/sink on magnetohydrodynamic flow and heat transfer of a non-Newtonian power-law fluid on a stretching surface

2016 ◽  
Vol 20 (6) ◽  
pp. 1801-1811 ◽  
Author(s):  
Kishan Naikoti ◽  
Kavitha Pagdipelli
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Differential Equations ◽  
Power Law ◽  
Skin Friction Coefficient ◽  
Temperature Profiles ◽  
Slip Parameter ◽  
Source Sink ◽  
Power Law Index

Non-Newtonian boundary layer flow and heat transfer characteristics over a stretching surface with thermal radiation and slip condition at the surface is analyzed. The flow is subject to a uniform transverse magnetic field. The suitable local similarity transformations are used to transform the non-linear partial differential equations into system of ordinary differential equations. The non-linear ordinary differential equations are linearized by using Quasi-linearization technique. The implicit finite difference scheme has been adopted to solve the obtained coupled ordinary differential equations. The important finding in this communication is the combined effects of Magnetic field parameter M, power law index n, slip parameter l, radiation parameter R, surface temperature parameter g , heat source/sink parameter S, local Eckert number Ec, temperature difference parameter r, generalized local Prandtl number Pr on velocity and temperature profiles and also the skin-friction coefficient -f''(0)and heat transfer coefficient -?'(0) results are discussed. The results pertaining to the present study indicate that as the increase of magnetic field parameter, slip parameter decreases the velocity profiles, where as the temperature profiles increases for both Newtonian and non-Newtonian fluids. The power law index n and heat source/sink parameter decreases the dimensionless velocity and temperature profiles. The effect of radiation parameter, Eckert number leads to increase the dimensionless temperature. It is found that increasing the slip parameter has the effect of decreasing the skin-friction coefficient-f''(0)and heat transfer coefficient-?'(0).With the increase of power law index n is to reduce the skin-friction coefficient and increase the heat transfer coefficient.

A decomposition solution of variable thickness absorber plate solar collectors with power law dependent thermal conductivity

2021 ◽  
pp. 1-26
Author(s):  
Pranab Kanti Roy
Keyword(s):  
Thermal Conductivity ◽  
Cross Section ◽  
Power Law ◽  
Exact Analytical Solution ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Physical Parameters ◽  
Absorber Plate ◽  
Triangular Cross Section ◽  
Adomian Decomposition

Abstract We present a mathematical model of flat-plate solar collector whose thermal conductivity is a power law function of temperature, and non-dimensional length is governed by a profile index. The rectangular, convex and triangular shape absorber plates are obtained by changing the value of an index of non-dimensional length 0, ½ and 1, respectively. The energy equation governing the temperature of rectangular absorber plate is a non-singular-type equation, and convex and triangular cross-section absorber plate are two different singular type equations. One non-singular and two different singular value equations are solved separately by different operators, as explained separately in classical and modified Adomian decomposition method (ADM) theory respectively. The results obtained for the case of the rectangular, convex and triangular cross-section plate are validated by comparison with the exact analytical solution for special case as available in literature. The effects of various thermo-physical parameters such as power law thermal conductivity parameter, Biot number, aspect ratio, absorbed solar heat flux, overall heat transfer coefficient on the temperature distribution are analyzed.

scholarly journals Temperature Dependent Viscosity of a Third Order Thin Film Fluid Layer on a Lubricating Vertical Belt

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
T. Gul ◽  
S. Islam ◽  
R. A. Shah ◽  
I. Khan ◽  
L. C. C. Dennis
Keyword(s):  
Thin Film ◽  
Variable Viscosity ◽  
Fluid Layer ◽  
Adomian Decomposition Method ◽  
Slip Boundary Condition ◽  
Thin Film Flow ◽  
Third Order ◽  
Temperature Dependent Viscosity ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition

This paper aims to study the influence of heat transfer on thin film flow of a reactive third order fluid with variable viscosity and slip boundary condition. The problem is formulated in the form of coupled nonlinear equations governing the flow together with appropriate boundary conditions. Approximate analytical solutions for velocity and temperature are obtained using Adomian Decomposition Method (ADM). Such solutions are also obtained by using Optimal Homotopy Asymptotic Method (OHAM) and are compared with ADM solutions. Both of these solutions are found identical as shown in graphs and tables. The graphical results for embedded flow parameters are also shown.

scholarly journals Estimation of the Shear Stress Parameter of a Power-Law Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Samer S. Al-Ashhab ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Decomposition Method ◽  
Positive Curvature ◽  
Adomian Decomposition Method ◽  
Terminal Point ◽  
Stress Parameter ◽  
Adomian Decomposition ◽  
Higher Order Terms ◽  
Numerical Integrators

We apply the Adomian decomposition method to a power-law problem for solutions that do not change the sign of curvature. In particular we consider solutions with positive curvature. The power series obtained via the Adomian decomposition method is used to estimate the shear stress parameter as well as the instant of time where the solution reaches its terminal point of a steady state. We compare our results with estimates obtained via numerical integrators. More importantly we illustrate that the error is predictable and can be reduced without further effort or using higher order terms in the approximating series.

Sign in / Sign up

Export Citation Format

Share Document