Some exact solutions for the rotational flow of Oldroyd-B fluid between two circular cylinders

Abstract

In this article, an effort has been made to compute and inspect the rotational flow of Oldroyd-B fluid between two co-axial circular cylinders. As novelty, the rotation of both cylinders produces motion of the fluid. The velocity field and tangential stress corresponding to the motion of an Oldroyd-B fluid with fractional derivatives have been obtained using Laplace and Hankel integral transforms. The velocity profiles of the respective model are graphically presented and deliberated for the pertinent parameters. Corresponding solutions are also obtained for ordinary Oldroyd-B fluid, ordinary and fractional Maxwell fluids, ordinary and fractional second-grade fluids, and Newtonian fluid as limiting cases of our general solutions.

Analysis of Caputo-Fabrizio fractional order semi-linear parabolic equations via effective amalgamated technique

“…It is assumed that equation (20) is in dimensionless form, then with out loss of generality, integer order time derivative in equation ( 20) can be replaced by Caputo-Fabrizio time fractional derivative ( )…”

“…In this regard, many definitions of fractional derivatives and their corresponding integrals have been introduced in fractional calculus [11][12][13][14][15][16][17][18]. Atangana-Baleanu in Caputo and Riemann-Lioville sense [19], Riemann-Lioville [20], Caputo [21,22] and Caputo-Fabrizio [22] are frequently implemented fractional operators.…”

Effect of chemical reaction, heat source/sink, and thermal diffusion on transient natural convection through a tube

“…Many works have been devoted to studying this process using different solution methods and geometries. Fractional derivatives, which are quite helpful in evaluating numerical values of key parameters that affect the abovementioned problem has been considered by Jamil et al, 18,19 Tanveer et al, 20 and Ullah et al 21 Also, studies on different geometries such as the vertical plate, [22][23][24][25][26][27][28][29] the stretching surface, [30][31][32][33][34][35][36] and so on have been presented in the literature. Khan et al 37 used the stretching sheet to explore the impact of chemical reaction on the heat and mass transfer of an MHD Powell-Eyring fluid flow in the presence of thermal diffusion and Joule heating and revealed that momentum slows down while concentration thickens as chemical reaction rises.…”

Numerical investigation with stability analysis of time‐fractional Korteweg‐de Vries equations

“…[11][12][13] In fractional calculus, many definitions of fractional derivatives and integrals are given. The most used are Atangana-Baleanu, 14 Riemann-Liouville, 15 Caputo, 16 and Caputo-Fabrizio 17,18 fractional operators. The Caputo-Fabrizio fractional derivative has been used by researchers from several practical fields.…”