The present paper discusses the analysis of solution of groundwater flow in inclined porous media. The problem related to groundwater flow in inclined aquifers is usually common in geotechnical and hydrogeology engineering activities. The governing partial differential equation of one-dimensional groundwater recharge problem has been formed by Dupuit's assumption. Three cases have been discussed with suitable boundary conditions and different slopes of impervious incline boundary. The numerical as well as graphical interpretation has been given and its coding is done in MATLAB.

In nature, groundwater is a key element, in many geological and hydrochemical processes, which sustains spring discharge, river base flow, lakes, and wetlands. Groundwater, extracted from deep geological formations (called aquifers) through pumping wells, constitutes an important component of many water resource systems. Groundwater recharge problem has been discussed by many researchers with different viewpoints. Patel et al. [

Bear and Alexander [

In nature, groundwater is in very large land scale; to understand this problem, we form a mathematical model such that the homogenous porous media are laid on impervious inclined layer with

This figure represents unconfined aquifer on incline impervious boundary with positive slope.

If the flow rates in the direction of

But here we have considered only one-dimensional fluid flow in mathematical model (considering fluid flow in

By using Dupuit’s assumption for the model we get

By rewriting the above equation,

Equation (

As per Figure

The solution of (

To determine constants of integration

Three cases have been considered in analysis and consistency of the mathematical model and its solution with suitable boundary conditions and different slopes of impervious incline boundary.

In first case, let the total heads of channels 1 and 2 be

This figure represents the free surface of water table:

In the second case, let the total heads of channels 1 and 2 be

This figure represents the free surface of water table:

This case is considered for the same pressure head of both channels 1 and 2 for this mathematical model. Therefore,

The numerical value of

Equation (

Figure

This figure represents the free surface of water table for equal pressure head and

Differentiates (

Also, Darcy’s law gives the flow rate of the system as

Thus, (

In the first case, as distance

The present mathematical model has referenced the method of Hantush and Cruz [

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are thankful to Professor M. N. Mehta for his valuable suggestions and the Department of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat, for providing research facilities.