Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model

Abstract

Abstract This study investigates the complex dynamics of a viscoelastic fluid subjected to magneto-hydrodynamics over a stretching sheet, incorporating the Cattaneo–Christov heat flux model. This model is especially advantageous for explaining heat transfer in materials possessing significant thermal conductivity, where the conventional Fourier’s law might not be precise. The investigation revolves around evaluating how the thermal relaxation time affects the boundary layer and how both thermal radiation and viscous dissipation influence the thermal field. The significance of this research lies in its contribution to understanding the intricate behavior of such fluids in the presence of magnetic fields and non-Fourier heat conduction. The primary objective is to analyze the impact of viscoelasticity, magnetohydrodynamics, and Cattaneo–Christov heat flux on the flow and heat transfer characteristics over the stretching sheet. The research methodology involves the application of mathematical models and numerical techniques, particularly the use of the shifted Chebyshev polynomials of the sixth-order approximation and spectral collocation technique. The major conclusion of the study underscores the significant influence of viscoelasticity, magnetic field, and Cattaneo–Christov heat flux on the transport properties of the fluid, providing valuable insights for applications in various engineering and industrial contexts. Certain notable results arising from the current issue indicate that heat transfer is more pronounced for the viscoelastic factor and magnetic parameter, whereas the thermal relaxation parameter exhibits the opposite trend. In addition, the inclusion of the Cattaneo–Christov term enhances our comprehension of thermal behavior.