A fractal-fractional model-based investigation of shape influence on thermal performance of tripartite hybrid nanofluid for channel flows

Diathermal oils have piqued the interest of several researchers in recent years due to their numerous industrial applications. The core aim of this study is the development of a novel fractal-fractional model to analyze the thermal performance of an oil-based tripartite hybrid nanofluid for channel flows. Graphene (Gr), magnesium oxide (MgO), and copper (Cu) nanoparticles are simultaneously dispersed in engine oil to obtain a tripartite hybrid nanofluid. To evaluate the impacts of the shape factor on thermal performance, five different shapes (brick, blade, spherical, platelet, and cylindrical) of nanoparticles are considered. The flow of considered fluid starts due to the constant motion of the right wall, which also encounters constant heating. Meanwhile, the left wall absorbs uniform radiation impacts. The mathematical model to explain this physical process is formulated by utilizing a fractal-fractional derivative, which involves a power-law kernel in its working. This model is exposed to joint employment of classical and fractal Laplace transforms to acquire the analytic solutions. These solutions are further used to develop expressions for skin friction coefficient and Nusselt number. Based on these quantities, heat transfer rate and shear stress are estimated to analyze augmentation in the thermal potential of engine oil and to observe variation in shear stress because of parametric effects. By conducting a comparative analysis between graphs of fractional and fractal-fractional models, it is concluded that a better elucidation of memory effects can be provided through the fractal-fractional approach. Furthermore, this work highlights that dispersing three different types of nanoparticles in engine oil makes it a more effective industrial fluid with a 9.58% higher heat-conduction capacity. This significant enhancement in the thermal performance of engine oil signifies its effectiveness for lubrication and cooling applications.