Chebyshev collocation simulations for instability of Hartmann flow due to porous medium: A neutral stability and growth rate assessment

Abstract

In the modern world, research in the field of thermal enhancement is going to increasing due to their diverse applications in the field of chemical industries and engineering domains. In the current study, the hydrodynamic or magnetohydrodynamics (MHD) instability of Hartmann flow in the porous medium is considered. Here, the special nature of magnetic field known as the transverse magnetic field is used in the current analysis. The investigation of hydrodynamic stability of electrically conductive for Hartmann flow in channel along with applied magnetize field is analyzed. The fluid layers are penetrated by a constant magnetize field and flow is considered through porous medium. Reynolds number (Re) is utilized to main system of hydrodynamic stability equations. A Chebyshev collocation technique is applied through numerical method to analyze magnetohydrodynamic instability system. The obtained flow equations represent system of ODEs. The current analysis makes use of a unique type of magnetic field known as the transverse magnetic field. The instabilities of nanofluids that contains nanoparticles with water as based fluid for with physical parameters are compared and discussed for growth rate and neutral graphs. These flow equations are solved numerically by using “Cheybeshev Collocation Method”. The mathematical technique “QZ (Qualitat and Zuverlassigkeit)” is applied to find out eigenvalues from comprehensive Orr-sommerfeld technique by using MATLAB software. Different embedded physical parameters Reynolds number (Re), Hartmann number (Ha) wave number (k) are compared and discussed for growth rate and neutral graphs. The instabilities of Hartmann flow in porous medium different embedded physical parameters are compared and discussed using growth rate and neutral graphs. It predicted that the flow become stable due to the magnetic field, Reynolds number and wave number the fluids transportation. The outcomes of current study are utilized in drug-delivery systems, photodynamic therapy and delivery of antitumor.

Keywords

• Instability analysis
• Chebyshev collocation method
• Electrically conducting fluid
• Porous medium
• Growth rate