Finite difference simulation of natural convection of two-phase hybrid nanofluid along a vertical heated wavy surface

Abstract

This study employs finite difference modelling to investigate the natural convection of a two-phase hybrid nanofluid consisting of Al[Formula: see text]O[Formula: see text] and Cu nanoparticles dispersed in water along a vertically heated wavy surface. The hybrid nanofluid has unique features that influence convective heat transfer. Numerical solutions analyze fluid flow patterns and temperature distributions, providing insights into heat exchange and thermal management. The research highlights the importance of hybrid nanofluids, notably those containing Al[Formula: see text]O[Formula: see text] and Cu in a water base, in improving overall heat transfer efficiency. The mathematical model accounts for laminar and incompressible fluid flow with a Prandtl number of Pr = 6.2, Lewis number Le = 10, and maximum [Formula: see text] concentration of hybrid nanoparticles. After transforming the governing equations into a non-dimensional form, the implicit finite difference method is used to solve them. The solution employs the in-house FORTRAN 90 code and compares its outcomes with the benchmark results. Various parameters, such as the Schmidt number (Sc = 1 to 10), volume fraction of nanoparticles ([Formula: see text] to 0.1), wavy amplitude (A = 0.0 to 0.3), and [Formula: see text] = (0.05 to 0.2), are investigated regarding temperature, velocity, local skin friction coefficient [Formula: see text], local Nusselt number (Nu), streamlines, and isotherms. Elevated volume fraction generally decreases skin friction, increases temperature, and may reduce velocity. Meanwhile, higher skin friction, temperature, velocity, and local Nusselt numbers often correlate with elevated Schmidt numbers. Changes in amplitude and [Formula: see text] affect skin friction, temperature, velocity, and local Nusselt numbers, providing information on the dynamics of fluid systems. For example, when the volume fraction (ϕ) increases from 0 to 0.1 at Y = 2, the temperature rises by [Formula: see text], while the velocity gradually decreases by [Formula: see text]. This is in contrast to findings according to when the [Formula: see text] rises from 0.05 to 0.2 at Y = 1. In this case, the temperature drops by [Formula: see text], followed by a [Formula: see text] fall in fluid velocity. Understanding these interactions enhances comprehension of heat transfer and fluid dynamics. By investigating these interactions, we not only improve our understanding of heat transfer and fluid dynamics, but also open the door to new strategies for improving thermal systems and manufacturing procedures.

Keywords

• Natural convection
• two-phase hybrid nanofluid
• vertical wavy surface
• skin friction
• heat transfer
• implicit finite difference method