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.

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.

Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Jafari
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Decomposition Methods ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

Closed-form solution for a rectangular stepped fin involving all variable thermal parameters and nonlinear boundary conditions

2016 ◽  
Vol 231 (5) ◽  
pp. 992-1010 ◽  
Author(s):  
Kuljeet Singh ◽  
Ranjan Das ◽  
Rohit K Singla
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Conditions ◽  
Thermal Parameters ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Adomian Decomposition

In this paper, the implementation of the Adomian decomposition method is demonstrated to solve a nonlinear heat transfer problem for a stepped fin involving all temperature-dependent means of heat transfer and nonlinear boundary conditions. Unlike conventional insulated tip assumption, to make the present problem more practical, the fin tip is assumed to disperse heat by convection and radiation. Thermal parameters such as the thermal conductivity, the surface heat transfer coefficient and the surface emissivity are considered to be temperature-dependent. Adomian polynomials are first obtained and then a set of Adomian decomposition method results is validated with pertinent results of the differential transformation method reported in the literature. Effects of different thermo-physical parameters on the temperature distribution and the efficiency have been exemplified. The study reveals that for a given set of conditions, the stepped fin may perform better than the straight fin.

EXACT SOLUTION OF VAN DER POL NONLINEAR OSCILLATORS ON FINITE DOMAIN BY PADE APPROXIMANT AND ADOMIAN DECOMPOSITION METHODS

2021 ◽  
Vol 10 (6) ◽  
pp. 2755-2766
Author(s):  
E.U. Agom ◽  
F.O. Ogunfiditimi
Keyword(s):  
Exact Analytical Solution ◽  
Adomian Decomposition Method ◽  
Nonlinear Oscillators ◽  
Decomposition Methods ◽  
Padé Approximant ◽  
Finite Domain ◽  
Van Der Pol ◽  
Pade Approximant ◽  
Adomian Decomposition ◽  
The Given

This paper is concerned with a thorough investigation in achieving exact analytical solution for the Van der Pol (VDP) nonlinear oscillators models via Adomian decomposition method (ADM). The models are nonlinear time dependent second order ordinary differential equations. ADM has already been applied, in existing literatures, to obtain approximate results. But, we adapt the method by adjusting the source term; a procedure that is base on the asymptotic Taylor's series expansion on the term that would have resulted to proliferation of terms during the invertible process. Then, the rational Pade Approximant is applied to clarify and get a better understanding of the uniqueness and convergence of our findings. Two models were used as illustrations and their result pictured to indicate their behaviour in the given domains. And, we found that the adaptation on the models yielded exact results which were further displayed in constructed tables.

Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
A. Vahabzadeh ◽  
M. Fakour ◽  
D. Ganji ◽  
I. Rahimipetroudi
Keyword(s):  
Heat Transfer ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Physical Parameters ◽  
One Dimensional ◽  
Adomian Decomposition ◽  
Analytical Accuracy ◽  
Study Heat Transfer ◽  
The One

AbstractIn this study, heat transfer and temperature distribution equations for logarithmic surface are investigated analytically and numerically. Employing the similarity variables, the governing differential equations have been reduced to ordinary ones and solved via Homotopy perturbation method (HPM), Variational iteration method (VIM), Adomian decomposition method (ADM). The influence of the some physical parameters such as rate of effectiveness of temperature on non-dimensional temperature profiles is considered. Also the fourth-order Runge-Kutta numerical method (NUM) is used for the validity of these analytical methods and excellent agreement are observed between the solutions obtained from HPM, VIM, ADM and numerical results.

Simultaneous Impacts of Fe3O4{\text{Fe}_{3}}{\text{O}_{4}} Particles and Thermal Radiation on Natural Convection of Non-Newtonian Flow Between Two Vertical Flat Plates Using ADM

2020 ◽  
Vol 45 (2) ◽  
pp. 173-189
Author(s):  
Ameur Gabli ◽  
Mohamed Kezzar ◽  
Lilia Zighed ◽  
Mohamed Rafik Sari ◽  
Ismail Tabet
Keyword(s):  
Natural Convection ◽  
Thermal Radiation ◽  
Research Work ◽  
Adomian Decomposition Method ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Flat Plates ◽  
Newtonian Flow ◽  
Nanofluid Flow ◽  
Adomian Decomposition

AbstractThe main aim of this research work is to show the simultaneous effects of ferro-particles ({\text{Fe}_{3}}{\text{O}_{4}}) and thermal radiation on the natural convection of non-Newtonian nanofluid flow between two vertical flat plates. The studied nanofluid is created by dispersing ferro-particles ({\text{Fe}_{3}}{\text{O}_{4}}) in sodium alginate (SA), which is considered as a non-Newtonian base fluid. Resolution of the resulting set of coupled non-linear second order differential equations characterizing dynamic and thermal distributions (velocity/temperature) is ensured via the Adomian decomposition method (ADM). Thereafter the obtained ADM results are compared to the Runge–Kutta–Feldberg based shooting data. In this investigation, a parametric study was conducted showing the influence of varying physical parameters, such as volumic fraction of {\text{Fe}_{3}}{\text{O}_{4}} nanoparticles, Eckert number ({E_{c}}) and thermal radiation parameter (N), on the velocity distribution, the skin friction coefficient, the heat transfer rate and the temperature distribution. Results obtained also show the advantages of ferro-particles over other types of standard nanoparticles. On the other hand, this investigation demonstrates the accuracy of the adopted analytical ADM technique.

scholarly journals Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mohsen Torabi ◽  
Hessameddin Yaghoobi ◽  
Andrea Colantoni ◽  
Paolo Biondi ◽  
Karem Boubaker
Keyword(s):  
Thermal Conductivity ◽  
Adomian Decomposition Method ◽  
Solution Technique ◽  
Inverse Transformation ◽  
Algebraic Equations ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Differential Transformation ◽  
Adomian Decomposition ◽  
Temperature Dependent Thermal Conductivity

Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

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.

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