An exact solution for the entropy base flow of electroosmotic magneto-nanofluid through microparallel channel

Abstract

An exact solution of steady state, electroosmotic, transient magnetohydrodynamic (MHD) flow, and heat transfer of a viscous and incompressible electrically conducting nanofluid consists of water and Cu metal, through a microparallel channel under the combined effect of pressure and vertically acting magnetic field is found. An exact solution is calculated through Laplace transform using the software of Mathematica to find the steady velocity and temperature field depending on many dimensionless parameters. The electromagnetic couple effect, the volumetric generation of heat caused by the Joule heating effect, and viscous dissipation are considered to analyze the thermally fully formed heat flow problem based on the steady part of the velocity field. The exact result of the temperature field is obtained by taking the uniform boundary heat flux. The significant parameter of heat flow known as the Nusselt number, depending on the height of the microtube, is defined. At last, the entropy generation of MHD temperature flow is analyzed. The interpretation of variations that occurred in internal and external entropy generations is given and consequences are explained.