Fast ADI approach for in investigating application of fractional model to a computational study on buoyant convection in a square enclosure filled with nanofluid

Abstract

This study aims to develop a Fast Alternating Direction Implicit (ADI) approach and construct a numerical investi- gation of fractional model on buoyant convective flow. The Caputo derivative is employed to capture the unsteady term in the governing partial differential equations describing the natural convective flow of nanofluids in the square cavity. A Cu-water nanofluid is chosen as the working medium, as this configuration represents many industrial and thermal applications, enabling the study of thermal performance in various heat transfer devices. In addition, the nu- merical results are obtained using the Fast ADI method based on Backward Euler techniques. A comparison is made between the results obtained from the fast ADI approach and the regular ADI technique, showcasing the significantly reduced computational time achieved by the fast ADI method. Moreover, an application problems are solved using this novel approach to investigate the heat transfer behavior of the time fractional model. The effects of the Rayleigh number and aspect ratio in a fractional model filled with a nanofluid are also explored. The obtained numerical results are compared with those of the classical model, exhibiting good agreement with existing literature and validating the developed code. Streamlines, isotherms, and average Nusselt number graphs are employed to visually represent the numerical results, facilitating better comprehension of the findings.