In this paper we propose a fuzzy Laplace transform to solve fuzzy initial value problem under strongly generalized differentiability concept. The fuzzy Laplace transform of derivative was used to solve Nth-order fuzzy initial value problem. To illustrate applicability of proposed method we plot graphs for different values of r-level sets by using Mathematica Software.
Spontaneous imbibition is the process in which the wetting phase is drawn into a porous medium by means of capillary force. Cocurrent and countercurrent spontaneous imbibitions are defined as wetting and non-wetting fluid flow in identical, and opposite directions respectively. The mathematical model is developed for cocurrent imbibition phenomenon in the inclined oil formatted homogeneous porous medium. An approximate analytical solution of the governing equation is derived by homotopy analysis method. The graphical and numerical solutions are discussed.
Boussinesq’s equation is one-dimensional nonlinear partial differential equation which represents the infiltration phenomenon. This equation is frequently used to study the infiltration phenomenon in unsaturated porous medium. Infiltration is the process in which the groundwater of the water reservoir has entered in the unsaturated soil through vertical permeable wall. An approximate analytical solution of nonlinear partial differential equation is presented by homotopy analysis method. The convergence of homotopy analysis solution is discussed by choosing proper value of convergence control parameter. The solution represents the height of free surface of infiltrated water.
This work deals with the analytical solution of advection dispersion equation arising in solute transport along unsteady groundwater flow in finite aquifer. A time dependent input source concentration is considered at the origin of the aquifer and it is assumed that the concentration gradient is zero at the other end of the aquifer. The optimal homotopy analysis method (OHAM) is used to obtain numerical and graphical representation.
Abstract. An approximate solution of longitudinal dispersion phenomena occurring in two phase miscible fluid flow through porous media has been obtained by using the group theoretic approach. The longitudinal dispersion coefficient is assumed to be directly proportional to the concentration of the fluid for a distance x and at any time t > 0. The graphical representation for the concentration of the fluid for a distance x and at time t > 0 has been obtained using Mat lab coding.
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