The Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional time‐derivative approach on transient free convection flow between two vertical parallel plates: A semi‐analytical solution

Abstract

AbstractA comparative analysis on semi‐analytical solution of transient free convection flow of fractional Maxwell viscoelastic fluid between two vertical parallel plates has been investigated by employing the Caputo–Fabrizio (CF) and Atangana–Baleanus in Caputo sense (ABC) fractional time derivative. The semi‐analytical solutions for dimensionless temperature, velocity, skin friction, and mass flux are obtained using both approach (CF and ABC) and solution presented in the Laplace domain. The Riemann sum approximation was used to invert all solutions from the Laplace domain to the time domain. The influence of pertinent parameters on dimensionless temperature and velocity for both CF and ABC approach are presented graphically and in tabular form and thereafter discussed. The significant result obtained from this study is that both temperature and velocity in CF and ABC increase as the time and relaxation time parameter increases, while temperature and velocity via CF and ABC model decrease when the fractional parameter increases. It is also significant to note that, temperature, velocity, skin friction, and mass flux have a higher value in the CF model than the ABC model.