Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative

This paper considers a particular fluid model known as the fractional free convection flow of Brinkman-type fluid. We use the Caputo derivative to describe the constructive equations of this model. The main objective of the present investigations will be to propose the exact analytical solutions using the Laplace transformation and its inverse method. After the determination of the exact solutions, the Prandtl (Pr), the Grashof parameters (Gr) and (Gm), the Schmidt parameter (Sc), the Brinkman number for fluid, and the chemical reaction parameter will attract our attention, and their impacts on the modeling will be provided and explained in term of physical viewpoints. Due to the heredity and the memory, the Caputo derivative will impact the mass diffusivity of the considered fluid. Therefore, the velocity and the temperature distributions can increase or decrease depending on the value of the order of the fractional operator. The findings of the paper will be illustrated by graphical representations. Note that in the expression of the exact solutions some well-known functions will be used as the Gaussian error function, the convolution rule, the exponential functions, and many others.

Automated summary

This paper considers a specific fluid model and describes its constructive equations using the Caputo derivative. The exact solutions are proposed using the Laplace transformation, and the impacts of various parameters on the modeling are explained in terms of physical viewpoints.