Lie symmetry analysis and numerical solutions for thermo-solutal chemicallyreacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermo-solutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of non-reactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (micro-rotation component), temperature and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number and reaction parameter. Numerical results for steady state skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined

Hall Current and Joule Heating Effects on Flow of Couple Stress Fluid with Entropy Generation

In this work, an analytical study of the effects of Hall current and Joule heating on the entropy generation rate of couple stress fluid is performed. It is assumed that the applied pressure gradient induces fluid motion. At constant velocity, hot fluid is injected at the lower wall and sucked off at the upper wall. The obtained equations governing the flow are transformed to dimensionless form and the resulting nonlinear coupled boundary value problems for velocity and temperature profiles are solved by Adomian decomposition method. Analytical expressions for fluid velocity and temperature are used to obtain the entropy generation and the irreversibility ratio. The effects of Hall current, Joule heating, suction/injection and magnetic field parameters are presented and discussed through graphs. It is found that Hall current enhances both primary and secondary velocities and entropy generation. It is also interesting that Joule heating raises fluid temperature and encourages entropy production. On the other hand Hartman number inhibits fluid motion while increase in suction/injection parameter leads to a shift in flow symmetry

Adomian Decomposition Method for Solving Coupled KdV Equations

In this article, we study a numerical solution of the coupled kdv equation with initial condition by the Adomian Decomposition Method.The solution is calculated in the form of aconvergent power series with easily computable components. Numerical results obtained by this method have been compared with the exact solution to show that the Adomian Decomposition method is a powerful method for the solution of coupled kdv equation

Numerical resolution of Emden's equation using Adomian polynomials

Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.This work has been supported by the Ministerio de Ciencia e Innovación, project TIN2009-10581

Adomian Decomposition Method for Solving the Equation Governing the Unsteady Flow of a Polytropic Gas

In this article, we have discussed a new application of Adomian decomposition method on nonlinear physical equations. The models of interest in physics are considered and solved by means of Adomian decomposition method. The behavior of Adomian solutions and the effects of different values of time are investigated. Numerical illustrations that include nonlinear physical models are investigated to show the pertinent features of the technique

Numerical study of chemical reaction effects in magnetohydrodynamic Oldroyd B oblique stagnation flow with a non-Fourier heat flux model

Reactive magnetohydrodynamic (MHD) flows arise in many areas of nuclear reactor transport. Working fluids in such systems may be either Newtonian or non-Newtonian. Motivated by these applications, in the current study, a mathematical model is developed for electrically-conducting viscoelastic oblique flow impinging on stretching wall under transverse magnetic field. A non-Fourier Cattaneo-Christov model is employed to simulate thermal relaxation effects which cannot be simulated with the classical Fourier heat conduction approach. The Oldroyd-B non-Newtonian model is employed which allows relaxation and retardation effects to be included. A convective boundary condition is imposed at the wall invoking Biot number effects. The fluid is assumed to be chemically reactive and both homogeneous-heterogeneous reactions are studied. The conservation equations for mass, momentum, energy and species (concentration) are altered with applicable similarity variables and the emerging strongly coupled, nonlinear non-dimensional boundary value problem is solved with robust well-tested Runge-Kutta-Fehlberg numerical quadrature and a shooting technique with tolerance level of 10−4. Validation with the Adomian decomposition method (ADM) is included. The influence of selected thermal (Biot number, Prandtl number), viscoelastic hydrodynamic (Deborah relaxation number), Schmidt number, magnetic parameter and chemical reaction parameters, on velocity, temperature and concentration distributions are plotted for fixed values of geometric (stretching rate, obliqueness) and thermal relaxation parameter. Wall heat transfer rate (local heat flux) and wall species transfer rate (local mass flux) are also computed and it is observed that local mass flux increases with strength of heterogeneous reactions whereas it decreases with strength of homogeneous reactions. The results provide interesting insights into certain nuclear reactor transport phenomena and furthermore a benchmark for more general CFD simulations

Thermo-Diffusion Effects of a Stagnation Point Flow in a Nanofluid with Convection using the Adomian Decomposition Method

The Thermo-diffusion solution effects a stagnation point flow of a nanofluid with convection using. Adomian Decomposition Method (ADM) is presented. The Partial differential equation representing the problem was reduced to an ordinary differential equation by introducing some similarity transformation variables. The transformed equations were solved using the ADM and the results were compared with existing results in the literatures. There is a good agreement between the method and the existing one, which indicate reliability of the method. The physical parameters that occurred in the solutions such as magnetic parameter, thermal Grashof numbers, concentration Grashof numbers, nano Lewis number, velocity ratio, Prandtl number were varied to determine their respective effects. It was observed that when the wall velocity is higher than the free stream velocity, the fluid velocity drop and rises when velocity at free stream is higher than the wall velocity .&nbsp

Numerical study of oxygen diffusion from capillary to tissues during hypoxia with external force effects

A mathematical model to simulate oxygen delivery through a capillary to tissues under the influence of an external force field is presented. The multi-term general fractional diffusion equation containing force terms and a time dependent absorbent term is taken into account. Fractional calculus is applied to describe the phenomenon of sub-diffusion of oxygen in both transverse and longitudinal directions. A new computational algorithm, i.e., the new iterative method (NIM) is employed to solve the spatio-temporal fractional partial differential equation subject to appropriate physical boundary conditions. Validation of NIM solutions is achieved with a modified Adomian decomposition method (MADM). A parametric study is conducted for three loading scenarios on the capillary-radial force alone, axial force alone and the combined case of both forces. The results demonstrate that the force terms markedly influence the oxygen diffusion process. For example, the radial force exerts a more profound effect than axial force on sub-diffusion of oxygen indicating that careful manipulation of these forces on capillary tissues may assist in the effective reduction of hypoxia or other oxygen depletion phenomena

AN EFFICIENT METHOD FOR SOLVING SINGULARLY PERTURBED TWO POINTS FRACTIONAL BOUNDARY-VALUE PROBLEMS

In this thesis, we present numerical method for approximating the solutions of singularly perturbed two points boundary value problems in both cases: ordinary derivatives and fractional derivatives. We use the Caputo derivation for the fractional case. The method starts with solving the reduced problem then the boundary layer correction problem. A series method; namely, the Adomian decomposition method is used to solve the boundary layer correction problem, and then the series solution is approximated by the , - Pade’ approximation of order. Numerical and theoretical results are presented to show the efficiency of the method. Singularly perturbed problems arise frequently in many real-life applications and they are among the hardest numerical approximation problems. Fractional Calculus has been in the minds of mathematicians for 300 years and still contains many mesteries. In recent decades, fractional calculus has been the object of ever increasing interest, due to its applications in different areas of science and engineering