Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

Abstract

In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.

A comparative analysis of multiple fractional solutions of generalized Couette flow of couple stress fluid in a channel

“…Memory in a system means how much information the system carries. This memory in different physical phenomena can be investigated by considering fractional derivatives 22–24 . Some other applications of fractional calculus is found in Imran et al 25,26 Fractional calculus has been used in engineering, physics, chemistry, and biological problem, and some of their applications can be found in Shah and colleagues 27–29 …”

“…This memory in different physical phenomena can be investigated by considering fractional derivatives. [22][23][24] Some other applications of fractional calculus is found in Imran et al 25,26 Fractional calculus has been used in engineering, physics, chemistry, and biological problem, and some of their applications can be found in Shah and colleagues. [27][28][29] Recently, three fractional order derivatives have been developed which are applied to different real-world problems and find the accurate solutions to those problems.…”