Numerical Examination of the Entropic Energy Harvesting in a Magnetohydrodynamic Dissipative Flow of Stokes’ Second Problem: Utilization of the Gear-Generalized Differential Quadrature Method

The main purpose of this numerical investigation is to estimate energetically the thermo-magnetohydrodynamic (MHD) irreversibility arising in Stokes’ second problem by successfully applying the first and second thermodynamic laws to the unsteady MHD free convection flow of an electrically conducting dissipative fluid. This fluid flow is assumed to originate periodically in time over a vertical oscillatory plate which is heated with uniformly distributed temperature and flowing in the presence of viscous dissipation and Ohmic heating effects. Moreover, the mathematical model governing the studied flow is formulated in the form of dimensional partial differential equations (PDEs), which are transformed into non-dimensional ones with the help of appropriate mathematical transformations. The expressions of entropy generation and the Bejan number are also derived formally from the velocity and temperature fields. Mathematically, the resulting momentum and energy conservation equations are solved accurately by utilizing a novel hybrid numerical procedure called the Gear-Generalized Differential Quadrature Method (GGDQM). Furthermore, the velocity and temperature fields obtained numerically by the GGDQM are exploited thereafter for computing the entropy generation and Bejan number. Finally, the impacts of the various emerging flow parameters are emphasized and discussed in detail with the help of tabular and graphical illustrations. Our principal result is that the entropy generation is maximum near the oscillating boundary. In addition, this thermodynamic quantity can rise with increasing values of the Eckert number and the Prandtl number, whereas it can be reduced by increasing the magnetic parameter and the temperature difference parameter.

Comment on “The velocity field due to an oscillating plate in an Oldroyd-B fluid” by C.C. Hopkins and J.R. de Bruyn [Can. J. Phys. 92, 533 (2014)]

We correct certain errors and ambiguities in the recent pedagogical article by Hopkins and de Bruyn (Can. J. Phys. 92, 533 (2014). doi:10.1139/cjp-2013-0334 ). The early-time asymptotics of the solution to the transient version of Stokes’ second problem for an Oldroyd-B fluid in a half-space is presented, as Appendix A , to complement the late-time asymptotics given by Hopkins and de Bruyn.