Qualifications:
PhD Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Research Interests:
My research focuses on the mathematical and computational analysis of fluid flow governed by nonlinear differential equations. I work on developing numerical methods to study heat and mass transfer in unsteady and thermally dependent flow systems. My interests include computational fluid dynamics, the numerical solution of nonlinear PDEs, and the modeling of flow phenomena such as micro-continuum models, Stokes flow, and two-dimensional mantle convection.
I am also exploring the use of modern machine learning, particularly deep learning techniques, as supportive tools for improving the efficiency and accuracy of continuum flow simulations. Deep learning models offer promising capabilities for accelerating numerical solvers, approximating complex solution fields, and reducing computational cost in large-scale simulations. In fluid flow and heat transfer problems, these methods can be used to learn surrogate models, assist in parameter estimation, and enhance the prediction of flow behavior in regimes where traditional numerical schemes become expensive or difficult to apply. My interest lies in integrating these approaches with established computational methods to create hybrid frameworks for solving nonlinear PDE-based flow problems more effectively.
Courses Taught:
- Numerical Analysis(ES-341)
- Probability and Statistics(ES-111)
- Differential Equations & Linear Algebra(MT-102)
- Calculus II(MT-202)
- Advanced Fluid Mechanics(ES-522)
- Computational Methods for Engineers(ES_531)
- Advanced Transform Techniques(ES-521)
