A fractal fractional model for thermal analysis of GO − NaAlg − Gr hybrid nanofluid flow in a channel considering shape effects

Abstract

In this work, the currently proposed fractal fractional operator with a power-law kernel is applied to study the dynamics of a hybrid nanofluid. This hybrid nanofluid is composed of graphite oxide (GO) and graphene (Gr) nanoparticles and contains sodium alginate (Sa) as the host fluid. One of the critical factors that influence the performance of hybrid nanofluids is the shape of nanoparticles therefore, an in-depth treatment is given to the shape factor and for this purpose, nanoparticles of five different shapes are considered in this analysis. The geometrical configuration of this study includes two vertical walls separated from each other by a distance h. The right wall is constantly heated while to observe the flow phenomenon two different cases are considered. In the first case, the right wall is stationary and the second case involves a moving right wall. A power-law kernel based fractal fractional operator is employed to develop the governing equations of the problem and the solutions of this newly constructed model are procured by the dint of the Laplace transformation. To anticipate the thermal efficiency of the working hybrid nanofluid a comprehensive study is conducted for the heat transfer rate. Moreover, the behavior of shear stress corresponding to the impacts of several parameters is also analyzed with the help of velocity gradient. For an extensive inspection of the problem, graphical illustrations, tables, and bar graphs are developed using the “MATLAB”. The results suggest that an improvement of 34% in the thermal efficacy of sodium alginate can be acquired by evenly distributing GO and Gr nanoparticles, which certainly enhances its practical usability. Besides, it is noticed that energy and velocity functions possess maximum values for a fractal fractional operator as equated to those of the fractional operator. Hence, it can be concluded that a joint fractal fractional approach delineates the memory effects more effectively as compared to the individual classical or fractional approaches.