Integrating the complex rheological Carreau model with the Graetz-Brinkman problem in a horizontal passage

Abstract

ABSTRACT The current investigation emphasizes the influence of viscous dissipation in laminar forced convection internal flow for horizontal conduit using the non-Newtonian fluid. A Carreau fluid model is taken into account. The hydrodynamically developed velocity profile is obtained by employing a perturbation approach. A classical Graetz approach is utilized to achieve the solution of the developed energy equation while the MATLAB built-in command bvp4c is taken into account for the solution of the Eigenvalue problem. The negligible axial conduction and uniform physical characteristics are presumed. The influence of the viscous dissipation and model parameters on non-dimensional bulk temperature and Nusselt number is deliberated for both cooling and heating situations. The current analysis is valid for small values of Weissenberg number We ≤ 1 . The findings reveal that viscous dissipation has a significant impact on temperature distribution in both developing and fully established regions.