Research
areas & questions.

Nonlinear mechanics

Real mechanical systems can change their frequency with amplitude, couple multiple modes, or respond differently as parameters vary. Ganji’s work with collaborators examines nonlinear oscillators and engineering models using analytical approximations alongside numerical solutions.

What happens when a system no longer responds in proportion to the force applied?

• Nonlinear vibration and mechanical oscillators
• Structural deflection and dynamical response
• Approximate solutions and independent numerical checks

Heat & fluid transport

Research spans convection, heat-transfer enhancement, microchannels and nanofluids. Coupled transport equations connect fluid velocity to temperature, while magnetic and porous-media effects introduce further physical interactions.

How do fluid motion and material properties shape the movement of heat?

• Convective heat transfer and thermal management
• Nanofluid transport and magnetohydrodynamics
• Microchannels, cavities and porous media

Analytical methods

A central thread is the use of perturbation, variational, decomposition and transformation methods for engineering problems. The Akbari–Ganji method connects the choice of a trial function to algebraic constraints and residual checks.

Can a difficult differential equation become a solution we can reason about?

• Akbari–Ganji method and residual matching
• Homotopy perturbation and variational iteration
• Differential transformation and convergence analysis

From models
to computation

Numerical methods provide a complementary way to solve and test engineering models. Books on control volume finite elements, FlexPDE and thermal energy storage bring geometry, discretization and boundary conditions into the discussion.

A useful approximation must earn its accuracy.

Compare methods on the same equation, test the residual, check physical conditions and examine convergence. These habits are built into the site’s learning notebook.