A numerical study on MHD Casson fluid flow in a non-uniform rough channel with temperature-dependent properties using OHAM

• The study investigates the interplay between magnetohydrodynamic (MHD) effects, the rheological behavior of the Casson fluid model, and temperature-dependent fluid properties that vary along the channel length. • It examines the impact of fluid characteristics and irregular channel geometry on fluid flow, highlighting the importance of these factors in real-world scenarios. • The study highlights the critical role of surface roughness in determining the drag force experienced by an object moving through a fluid. • The findings show that variable fluid properties must be meticulously controlled in the design of medical and engineering equipment, such as effective chemical reactors, distillation and separation processes, and drug delivery systems. • The study reveals that the interaction between fluid particles and magnetically activated rough surfaces significantly influences fluid dynamics. This study explores the complex dynamics of magnetohydrodynamic (MHD) Casson fluid in a non-uniform rough channel, focusing on the effects of temperature-dependent viscosity and variable thermal conductivity under no-slip boundary conditions. The study employs an innovative approach by utilising a rough surface with irregular textures to analyse flow patterns and assess drag forces on channel objects. A novel mathematical model, governed by continuity, momentum, and heat transfer equations, is developed and transformed into dimensionless, nonlinear Ordinary Differential Equations (ODEs) using non-dimensional quantities and fundamental assumptions. The Optimal Homotopy Analysis Method (OHAM) is applied to solve these equations to enhance convergence speed and accuracy. The research explores the impact of surface roughness on velocity profiles and temperature distributions under various physical constraints. Numerical simulations are conducted to determine skin friction coefficients and Nusselt numbers. Furthermore, the study examines the influence of confined boluses on fluid flow in diverse physiological conditions. A comprehensive analysis is performed to elucidate the combined effects of surface roughness on fluid passage, including flow separation, pattern alterations, pressure distribution and drop, heat transfer characteristics, and flow resistance. The intricate interplay between temperature-dependent viscosity, varying thermal conductivity, and surface roughness is thoroughly investigated to explain the complex dynamics of MHD Casson fluid movement in non-uniform channels. Implementing a magnetic field over the rough, non-uniform channel is found to provide stability and prevent fluid overflow. This research has significant real-world applications, including soil erosion prevention, blood flow regulation in arteries, and optimisation of hydropower channels and penstocks. By enhancing our understanding of flow dynamics through rough and non-uniform channels, this study contributes valuable insights into both theoretical fluid mechanics and practical engineering applications.