Electroosmotic flow of generalized Burgers’ fluid with Caputo–Fabrizio derivatives through a vertical annulus with heat transfer

Abstract

Applying the electric field to a fluid confined between capillary surfaces is the most recent technique used for studying the fluid movement. This technique is known as electroosmotic flow (EOF). The problem of the Caputo–Fabrizio time-fractional derivative of the electroosmotic generalized Burgers’ fluid through a vertical annulus with free convection heat transfer has been investigated. The annulus walls kept at constant values of a zeta potential. The dimensionless governing equations have been solved with the help of the Laplace and finite Hankel transforms. The inversion of Laplace for the transformed functions is calculated numerically. The essential features of the electroosmotic flow (EOF) and the related thermal characteristics are clearly illustrated by the variations in the velocity, the flow rate, the temperature and the Nusselt number. Moreover, comparisons with other non-Newtonian fluids have been discussed. It was found that the presence of the electric double layer (EDL) accelerates the fluid near the walls of the annulus, while in the core region, the reverse flow is noticed.

Electro‐osmotic flow of fractional second‐grade fluid with fractional Cattaneo heat flux through a vertical microchannel

“…Under the obvious parameters, we will incorporate the graphical results obtained for the velocity, flow rate, shear stress, heat transfer, and Nusselt number in this section. The range of physical parameters are as follows 26,27,30,33 :…”

“…To get the full solutions, the inverse Laplace of the transformed functions (velocity, heat, and flow rate) has been calculated numerically. The inverse can be approximated as follows 30,43,45 :…”

“…29 The new concept of Caputo-Fabrizio was used by many investigators in their research. Abd Elmaboud 30 investigated analytically the problem of EOF using the concept of Caputo-Fabrizio. He found that the EDL assists the flow in the vicinity of the annulus walls, whereas the reverse flow is noticed in the core area.…”

Electroosmotic flow of fractional Oldroyd‐B fluid through a vertical microchannel filled with a homogeneous porous medium: Numerical and semianalytical solutions

“…Appylling the method of Laplace transform for fractional derivative defined in Abd Elmaboud et al 18 and using the initial condition, Equation ( 15), the transformed Equations ( 13), (14), and (15) give:…”

“…Many studies have investigated the influence of fractional parameters for various fluids. [14][15][16][17][18][19] The derivative of fractional order is useful for dealing with viscoelastic activity. 20 Riemann-Liouville and Caputo fractional-order derivatives have been employed.…”