Adamu Gizachew Chanie

About Me

Welcome to my personal website! I am Adamu Gizachew, A university lecturer at Addis Ababa Science and Technology University. My research interests include Applied and computational mathematics, Fluid mechanics, and Fractional calculus. I am passionate about teaching, research, and solving real-world mathematical problems.

Selected Papers

Current Project

Project Title:Magnetohydrodynamic (MHD) Flow of Non-Newtonian Viscoelastic Fluids: An In-Depth Analysis

Introduction

The study of magnetohydrodynamic (MHD) flow of non-Newtonian viscoelastic fluids is an important topic in fluid mechanics, with applications in engineering, geophysics, biomedical sciences, and industrial processes. Unlike Newtonian fluids, which have a constant viscosity independent of shear rate, non-Newtonian fluids exhibit complex rheological behavior, including shear-thinning, shear-thickening, and viscoelastic properties. When such fluids interact with electromagnetic fields, their flow dynamics become even more intricate, leading to new theoretical challenges and practical applications.

Key Concepts and Components

1. Magnetohydrodynamics (MHD)

• MHD is the study of electrically conducting fluids in the presence of magnetic fields.
• It combines the principles of fluid dynamics and electromagnetism, primarily governed by the Navier-Stokes equations coupled with Maxwell's equations.
• The Lorentz force, induced by the interaction between the fluid’s motion and the magnetic field, modifies the flow behavior.

2. Non-Newtonian Fluids

• These fluids do not obey Newton’s law of viscosity (τ = μ γ‌), where τ is shear stress, μ is viscosity, and γ‌ is the shear rate.
• They can be categorized into different types, such as:
  • Shear-thinning (pseudoplastic)
  • Shear-thickening (dilatant)
  • Viscoelastic

3. Viscoelastic Fluids

• A viscoelastic fluid exhibits both viscous (fluid-like) and elastic (solid-like) behavior under deformation.
• Common models used to describe such fluids include:
  • Oldroyd-B Model
  • Maxwell Model
  • Jeffreys Model
• These models introduce additional stress components that account for the fluid's memory effects, meaning past deformations influence present behavior.

4. Mathematical Modeling

• The governing equations for the MHD flow of viscoelastic fluids typically include:
  • Continuity Equation: Ensuring mass conservation.
  • Momentum Equation: Modified Navier-Stokes equation incorporating MHD effects and non-Newtonian stress tensors.
  • Constitutive Equations: Describing the stress-strain relationship specific to the chosen viscoelastic fluid model.
  • Energy Equation (if thermal effects are considered): Includes Joule heating and viscous dissipation.
• These equations are often nonlinear and require numerical methods (e.g., finite difference, finite element, spectral methods) for solutions.

Applications and Importance

1. Engineering and Industrial Applications

• Polymer Processing: Used in extrusion and injection molding.
• Cooling of Nuclear Reactors: MHD coolants enhance heat dissipation.
• Metal and Glass Manufacturing: MHD control of molten metals and glass-forming processes.

2. Biomedical Applications

• Blood Flow in Magnetic Fields: Useful for magnetic drug targeting and blood flow regulation.

3. Geophysical and Astrophysical Applications

• Magma Flow: Movement of magma influenced by Earth’s magnetic field.
• Astrophysical Plasmas: Understanding the behavior of electrically conducting fluids in cosmic magnetic fields.

Challenges and Open Research Questions

• How does fluid elasticity affect boundary layer separation in MHD flows?
• What are the stability criteria for MHD viscoelastic flows in porous and confined domains?
• How do temperature-dependent properties influence viscoelastic MHD behavior?
• Can novel numerical schemes be developed to solve the highly nonlinear governing equations more efficiently?

Conclusion

The study of MHD flow of non-Newtonian viscoelastic fluids is a fascinating interdisciplinary field that bridges fluid dynamics, electromagnetism, and applied mathematics. Understanding these flows is essential for optimizing industrial processes, advancing medical technologies, and exploring geophysical and astrophysical phenomena. The complexity of governing equations makes this a challenging yet rewarding area of research, with numerous open problems waiting to be explored.