Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions

Abstract

We establish, in this paper, the closed form analytical solutions of steady fully developed flows of couple stress fluid between two concentric cylinders, generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both, using the slip boundary conditions. The classical solutions for Newtonian fluid in the hydrodynamic case appear as a limiting case of our solutions. The velocity profiles of the flows are presented and the effect of various parameters on velocity is discussed. The results indicate that the presence of couple stresses decreases the velocity of the fluid.

Second Law Analysis for Couple Stress Fluid Flow through a Porous Medium with Constant Heat Flux

“…Therefore, the equation governing the gravity-driven steady fully developed couple stress fluid flow can be written as [17]: , and the additional term in (1) is due to the inclusion of porous materials that tend to restrict the flow. The slip boundary conditions along the channel walls are given by Devakar et al [46] as: For the thermal analysis, the lower wall of the channel is taken to be insulated while the upper plate is subjected to constant heat flux w q . Following Aksoy [17], the energy conservation equation for the chemically-inert porous medium can then be written as: …”

“…Interestingly, there is a thin line between the second law analysis approach and that described by the material cost flow accounting perspective [37][38][39] regarding waste management and achieving a cleaner production. Motivated by Hayat et al [31,[40][41][42][43][44][45][46], the present study addresses the second law analysis for a shear-induced asymmetrical slip couple stress fluid flow through saturated porous medium subjected to constant heat flux studied. To the best of our author's knowledge, the thermal analysis reported here has not been investigated despite the enormity of the work done in this area of study.…”

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

“…Rani [9] presented a numerical study on transient natural convection along vertical cylinder with variable surface temperature and mass diffusion. Devakar et al [10] presented closed form solution for Poiseuille flow, Couette flow, and generalized Couette flows of an incompressible couple stress fluid between two concentric circular cylinders with slip boundary condition. Recently, Deka et al [11] presented the analytical investigation of one-dimensional unsteady natural convection flow past an infinite vertical cylinder with heat and mass transfer under the effect of constant heat flux at the surface of the cylinder.…”

Entropy Generation Rate in Unsteady Buoyancy-Driven Hydromagnetic Couple Stress Fluid Flow Through a Porous Channel

“…The study of hydromagnetic flow of fluid that exhibits a non-symmetric stress tensor in its fluid structure [1] has been on the increase due to its numerous applications in engineering and industries. For instance, in geophysical prospecting including geothermal and petroleum reservoirs, and molten metal processing.…”