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Ph.D.
(Science)
A DIFFERENTIAL TRANSFORM APPROACH FOR
SOLVING REAL LIFE PROBLEMS

Ph.D. Scholar : Sharma Aruna Suryanarayan
Research Supervisor : Dr. Amit Parikh

Regi. No.: 20276491004
Abstract :
Flow in porous media is a fascinating field that bridges theory and practical applications
right from groundwater flow to oil recovery process. The research interest in fluid flow
through porous media has gained significant attention in the recent years. This research
area holds importance in almost all branches of engineering such Reservoir Engineering,
Petroleum Engineering, Civil Engineering, Groundwater hydrology, Biomedical engineering
etc. The partial differential equations governing the multiphase flow makes mathematics
crucial in petroleum engineering. Fluid flowing through porous media has been explained
using various mathematical models. Many man- made and natural systems encounter
porous media. Because of the deteriorating groundwater quality hydrologists have shown
interest in the multiphase flows for groundwater and observed that contaminants can
enter water bearing rocks from surface or landfills where chemicals are dumped or illegal
waste is disposed. It is crucial to predict how the contaminants flow to find effective
solutions. This is an upcoming field in flow through porous media and because of the
complex nature, solution is obtained using mathematical techniques. Saltwater intrusion
in coastal areas is another concern for environmental engineers. Multiphase flow and
transport phenomenon in natural porous media has been observed to occur in oil
recovery, Aquifers, biological tissues and plants. Research on multiphase flows focuses
mainly on underground petroleum reservoirs

Recently research in the area of in-tissue drug delivery has understood that since porous
materials have an enlarged surface area and large pore volumes, they are useful for drug
delivery. One dimensional groundwater movement is of great importance for hydrologists,
agriculturists and water resource sciences. Various mathematical models have been
developed to describe the physical phenomenon occurring due to simultaneous
movement of oil and water in porous media. Mathematical formulation of these
phenomenon leads to highly non-linear partial differential equations. However, finding
exact solution is difficult. Many researchers are working on finding an approximate
solution using different numerical techniques

This present study focuses on obtaining an approximate solution to real life problems
related to flow in porous media. In the current research work, we investigated the

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