An approximate solution of fokker-planck equation for one dimensional groundwater recharge through porous media

The nonlinear Fokker-Planck equation arising for one-dimensional groundwater recharge through porous media, is in the form of partial differential equation which has been solved by using Homotopy Analysis method with the help of first approximate solution ()0,ZTθfor given auxiliary parameter 0q=. The solution is physically interpreted and concluded that during one-dimensional recharge through unsaturated porous media, the moisture content of the soil is parabolically increasing as depth Z increases for given0T\u3e. The graph of the solution is given by using Maple coding

Study on Approximate Analytical Method with Its Application Arising in Fluid Flow

This chapter is about the, Variational iteration method (VIM); Adomian decomposition method and its modification has been applied to solve nonlinear partial differential equation of imbibition phenomenon in oil recovery process. The important condition of counter-current imbibition phenomenon as vi=−vn, has been considered here main aim, here is to determine the saturation of injected fluid Sixt during oil recovery process which is a function of distance ξ and time θ, therefore saturation Si is chosen as a dependent variable while xandt are chosen as independent variable. The solution of the phenomenon has been found by VIM, ADM and Laplace Adomian decomposition method (LADM). The effectiveness of our method is illustrated by different numerical

A mathematical modelling of imbibition phenomenon in inclined homogenous porous media during oil recovery process

The approximate solution of imbibition phenomenon governed by non-linear partial differential equation is discussed in the present paper. Primary oil recovery process due to natural soil pressure, but in the secondary oil recovery process water flooding plays an important role. When water is injected in the injection well for recovering the reaming oil after primary oil recovery process, it comes to contact with the native oil and at that time the imbibition phenomenon occurs due to different viscosity. For the mathematical modelling, we consider the homogeneous porous medium and optimal homotopy analysis method has been used to solve the partial differential equation governed by it. The graphical representation of the solution is given by MATHEMATICA and physically interpreted

Study on fingero imbibition phenomena in inclined porous media by optimal homotopy analysis method

The approximate solution of fingero imbibition phenomena governed by a nonlinear partial differential equation is discussed in the present paper. The primary oil recovery process was due to natural soil pressure, but in the secondary oil recovery process water flooding plays an important role. When water is injected through the injection well for recovering the reaming oil after primary oil recovery process, it comes to contact with the native oil and at that time the fingero imbibition phenomena occur due to different viscosity. For the mathematical modeling, we consider the homogeneous inclined porous medium and comparative study of without inclination and with inclination has been done, and also optimal homotopy analysis method has been used to solve the partial differential equation governed by the mathematical modeling. The graphical representation of the solution is given by MATHEMATICA and physically interpreted. Keywords: Fingero imbibition, Homogeneous porous media, Optimal homotopy analysis method, Oil recovery proces

Combination of integral and projected differential transform methods for time-fractional gas dynamics equations

The present paper discusses the solution of nonlinear homogeneous and nonhomogeneous time-fractional gas dynamic equations arising in shock fronts by a new combination of new integral and projected differential transform method. The new integral projected differential transform method (NIPDTM) makes the calculation very simpler and in this method the nonlinear term can be easily handled by projected differential transform without using Adomian’s polynomial and He’s polynomial, which can be taken as a big advantage of this method. This method is more exertive and easy to handle such fractional differential equation in comparison to other methods. The results obtain from illustrative examples shows the competency and accordance of the proposed method. Keywords: New integral transform method, Projected differential transform method, Time-fractional gas dynamic equation, Caputo fractional derivative, Mittag-Leffler functio

Tobacco Cessation Counseling: A Humanistic Approach by Non-Human

“Counselling is a professional relationship that empowers diverse individuals, families, and groups to accomplish mental health, wellness, education, and career goals. It’s a type of applied psychology”. When used for helping an individual in quitting a habit it requires using cognitive therapies. Artificial Intelligence (AI) has been increasingly used in the healthcare sector, but its use for counseling purposes is still questionable.  Recently a virtual health worker has been introduced by World Health Organization (WHO) representing increased use of AI in healthcare. This article also explores the features of this virtual health worker and how the counseling process is done by a human health professional and what is different in counseling done by a virtual health worker.Counselling&nbsp

Multifocal polymorphous cutaneous tuberculosis with Poncet’s disease: A case report

Extrapulmonary tuberculosis (ETB) involving skin with multiple lesions is an uncommon presentation of mycobacterial infection. Cutaneous tuberculosis (TB) having multiple lesions with Poncet’s disease (tuberculous Rheumatism) is rarely reported. We hereby report a multifocal cutaneous tuberculosis with Poncet’s disease in a 19-year-old immunocompetent female