RESEARCH

My research interest lies at the intersection of the following disciplines:

MATHEMATICAL MODELLING & FLUID MECHANICS

• Imbibition Phenomena in Porous Media: Formulating partial differential equations to model fluid dynamics, utilizing the Exponential Capillary Pressure Model to analyze imbibition in porous structures.

• Non-Newtonian Viscoelastic Fluids: Modeling flow and heat transfer mechanisms, specifically addressing turbine cooling by injecting non-Newtonian viscoelastic fluid through a porous wall.

• Convective Drying Processes: Investigating the thermal physics and coupled mass transfer mechanisms involved in the convective drying of porous materials, such as carrot slabs.

SEMI-ANALYTICAL METHODS &  TRANSFORMS

• Differential Transform Method (DTM): Deriving recurrence relations to systematically solve complex, nonlinear ordinary and partial differential equations governing fluid flow.

• Reduced Differential Transform Method (RDTM): Applying dimensional reduction techniques via RDTM to efficiently obtain semi-analytical solutions.

• Generalized (G'/G)-Expansion Method: Constructing exact analytical solutions for nonlinear evolution equations, specifically applying this expansion technique to resolve complex porous media equations. 

• Symbolic and Numerical Simulation: Translating semi-analytical mathematical formulations into robust computational architectures using MATLAB and Maple to simulate fluid dynamic systems.

COLLABORATIVE RESEARCH & INTERDISCIPLINARY APPLICATIONS

• Physics-Informed Neural Networks (PINNs): Collaborating on the integration of classical mathematical models with Scientific Machine Learning (SciML). Contributing rigorous fluid dynamics formulations (e.g., Reynolds-parameterized flow mechanisms) to validate and inform soft and hard PINN frameworks developed by co-researchers.

• Data-Driven Predictive Modeling: Partnering in the application of artificial neural networks to enhance the predictive accuracy of simulations involving thermal physics and complex transport phenomena.