Eur. Phys. J. Plus (2017) 132: 305
https://doi.org/10.1140/epjp/i2017-11579-4

Regular Article

Heat transfer at microscopic level in a MHD fractional inertial flow confined between non-isothermal boundaries

Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Opposite Sector U, 54792, Lahore Cantt., Pakistan

^* e-mail: amer.rasheed@lums.edu.pk

Received: 10 April 2017
Accepted: 1 June 2017
Published online: 13 July 2017

Abstract

Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.