A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

Abstract

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

Impact of radiation absorption on Caputo fractional fluid flow over an exponentially accelerated plate

“…Findings from Raza et al [11] are in good agreement with Raza [10]. Moreover, a comparative study between Caputo and Caputo-Fabrizio using the same condition as that of Raza [10] and Raza et al [11] were published by Raza et al [12]. In the same year, Anwar and Rasheed [13] investigated the effects of fractional derivatives on Oldroyd-B nanofluid flow using the Caputo derivative.…”

Maxwell Nanofluid Flow over an Infinite Vertical Plate with Ramped and Isothermal Wall Temperature and Concentration

“…Na et al [10] analyzed free convection Maxwell nanofluid flow between vertical plates with the influence of thermal radiation. Raza and Asad [11] derived the solutions of Maxwell fluid flow considering a vertical flat plate. ey observed that increasing the fluid velocity with respect to Grashof number (Gr) and Maxwell parameter λ. e numerical solutions were obtained by Sui et al [12] calculating the Maxwell nanofluid over stretching sheet with the influence of heat and mass transfer using the homotopy analysis process.…”

A Comparative Study of Natural Convection Flow of Fractional Maxwell Fluid with Uniform Heat Flux and Radiation

“…Asjad et al [17] presented the comparisons between Caputo and Caputo-Fabrizio fractional derivatives on second-grade fluid over Newtonian heating. Raza and Ullah [18] used the fractional Maxwell fluid to compare the fractional derivatives of C and CF using the Laplace transformation. Maxwell fluid's natural convection between two parallel plates was discussed by Wang et al [19].…”