In this work, linear stability of an electrically conductive fluid experiencing Poiseuille flow for minimum Reynolds value under a normal magnetic field is analysed using the Chebyshev collocation method. The neutral curves of linear instability are derived by utilising Qualitat and Zuverlassigkeit (QZ) method. Instability of the magnetohydrodynamics for plane Poiseuille flowis introduced by solving the generalised Orr–Sommerfeld equation to determine the growth rates, wave number and spatial shapes of the eigenmodes. To solve linear problems, we use numerical methods which help us at each time step of the simulation, uncoupled by physical processes, which can improve the computational performance. This article provides the stability and error analysis, presents a concise study of the Poiseuille flow, and produces computational tests to support the given theory.

Magnetohydrodynamics (MHD) is a very challenging problem which affects the stability of Poiseuille flow. Therefore, in this work we investigate the instability of an electrically conductive fluid between two parallel plates under the influence of a transverse magnetic field. We apply the Chebyshev collocation method to solve the generalised Orr–Summerfield equations to determine wave number, growth rates and spatial modes of the eigenmodes. To get the neutral curves of MHD instability, the QZ method is used. It is observed that the magnetic field has a stabilising effect on the flow and the stability increases as we increase the Hartmann number and for various wave numbers, magnetic field put down the growth of perturbation. It is concluded that effect of perturbations is little in span-wise direction for different Hartmann numbers that increase the critical values of Reynolds numbers.

Here, our aim is to investigate incompressible Carreau fluid with variable properties and nanoparticles are considered to improve the heat transfer. This communication also highlights the thermal significances of Joule heating and incorporation of activation energy. The mathematical modelling is constructed for physical phenomena by assuming boundary layer problems. The well-known numerical treatment Bvp4c is utilised to solve the nonlinear problem and transform the governing equations. The effects of different physical parameters are assessed graphically and numerical data of skin friction and Nusselt number are explored. It is noted that activation energy rate improves and it decreases with the exponential fitted rate on concentration profile. The simulations for the current model reveal that the Nusselt number decreases with increasing exponential fitted rate and elastic deformation while for activation it increases.