A transient flow formation of an incompressible fluid through a horizontal porous channel assuming a ramped pressure gradient is considered with the velocity slip boundary conditions. The flow is a laminar flow caused by ramped pressure gradient along the flow direction. The equation governing the flow is modeled, and solved by the Laplace transformation technique to obtain a semi-analytical solution under slip boundary conditions. It was noted that the flow velocity increases as the slip parameter is increased.

The transient flow formation in a horizontal porous channel assuming a ramped pressure gradient is presented. The equation governing the flow is modeled into a partial differential equation (PDE) which is solved by employing the Laplace transformation technique to transform the PDE to an ordinary differential equation (ODE). The obtained ODE is solved by employing the method of undetermined coefficients to obtain the velocity profile in the Laplace domain. The Riemann sum approximation technique is then adopted to change the obtained solution from the Laplace domain into the time domain. For accuracy checks, the numerical results of the obtained equation are reckoned with previously published work, and an excellent agreement is found. For a clearer understanding of the impact of various flow parameters entering the solutions obtained, graphical and tabular representations are offered using MATLAB software. We noticed that the velocity is slower with ramped pressure gradient compared to a constant pressure gradient. This is because the motion of the fluid occurs gradually with ramped pressure gradient.