Transport properties of mixed convective nano-material flow considering the generalized fourier law and a vertical surface: Concept of caputo-time fractional derivative

With improved characteristics and thermal stability, the nanoparticles show a significant interest in many engineering and industrial processes. The applications of nanomaterials include applications in solar energy systems, chemical reactors, heating and cooling processes, and many bio-medical applications. With such motivations, this investigation aims to address the mixed convection flow of different nanoparticles due to inclined surface in presence of Newtonian heating and slip effects. Two types of nanoparticles like titanium dioxide and aluminum oxide with water base fluid are used to improve the heat transfer rate. The dimensionless governing partial differential equations for this fractional mathematical modal are accomplished by using Caputo-time fractional derivative and Fourier's law of thermal conductivity. The generalized solution of energy and momentum equations is conquered by applying the Laplace transformation (LT) scheme. To illustrate some more physical insight of the problem and to develop the novelty of this article some special cases of velocity field are reflected whose physical clarification is well known in the literature. Furthermore, to investigate the physical implication of the under-deliberation problem, the graphical illustrations are performed by using math software MATHEMATICA. The interesting observations claimed from this investigation revealed that the interaction of thermal rate of change is more impressive for aluminum oxide. The temperature and velocity profiles are enhanced by varying the numerical value of the fractional constraint at large time scale.