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A steady Newtonian fluid flow through annular region in curved pipes is studied in this paper. The flow takes place due to an axial pressure gradient and it is three-dimensional in nature. The equations governing the flow are highly coupled and nonlinear. The solutions are obtained, analytically, using a regular perturbation method. The effects of curvature ratio (δ) , Reynolds number (Re) and the radius ratio (l) on the axial velocity and stream function are presented graphically. It is observed that, along with curvature ratio and Reynolds number, radius ratio highly affects the fluid flow in annular curved pipes. [ABSTRACT FROM AUTHOR]

In this investigation, we have studied the problem of peristaltic flow with heat transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave travelling down its wall. The problem has been formulated in cylindrical coordinate system. The equations governing the flow have been simplified under the long wavelength and low Reynolds number assumptions. The exact solution is obtained for the temperature profile. The perturbation solutions for the velocity and pressure gradient are obtained for small couple stress parameter. Pressure difference per wavelength and frictional forces on the tube walls have been computed numerically. Results are demonstrated for various flow parameters. The better pumping results occur in vertical tube, while less pumping is seen in horizontal tube. The size of trapped bolus is small in triangular wave as compared to other waves. The present study has a wide range of applications in bio-medical engineering like the transport phenomenon in peristaltic micro pumps.

In this paper, we study the influence of heat transfer on the peristaltic transport of an incompressible magnetohydrodynamic second grade fluid in vertical symmetric and asymmetric channels. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in the wave frame of reference moving with velocity of the wave. Perturbation solutions are obtained for the stream function, temperature and pressure gradient under long wave length assumption. Pressure difference and frictional force are discussed through numerical integration. The influence of various parameters of interest on the flow are discussed and also the graphical results are obtained for different wave forms.

In the present article, the exact solutions for fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions. The effect of various parameters on velocity for each problem is discussed. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous Newtonian fluid. The results indicate that, the presence of couple stresses decreases the velocity of the fluid.

The objective of the present article is to study the magnetohydrodynamic(MHD) unsteady flow and heat transfer of two immiscible micropolar and Newtonian fluids through horizontal channel occupied with porous medium. Initially, fluids in both regions as well as both plates are at rest. At an instant of time, the flow in both regions is generated by a constant pressure gradient. The governing non-linear and coupled partial differential equations of Eringen's micropolar fluid and Newtonian fluid are solved subject to suitable initial, boundary and interface conditions. The numerical results for velocity, microrotation and temperature are obtained using Crank- Nicolson finite difference approach. The results obtained for velocities, microrotation and temperatures are presented through figures. The analysis regarding volume flow rate, skin-friction co-efficient and Nusselt number is also done and is presented through tables. It is explored that, velocity, microrotation and temperature are increasing with time and accomplishing steady state at higher time level. Velocity is decreasing with micropolarity parameter and Hartmann number, and increasing with Darcy number. Temperature enhances with increasing Brinkmann number, and declines with Prandtl number and ratio of thermal conductivities. [ABSTRACT FROM AUTHOR]

In the present article, the theoretical investigation is presented for the mixed electrokinetic and pressure‐driven transport of couple stress nanoliquids in a microchannel with the effect of magnetic field and porous medium. This topic has gained a remarkable scope in nanoscale electro‐osmotic devices. The formulation of the present mathematical problem is simplified using the Debye‐Hückel linearization assumption. The merging model has important features such as the thermal Grashof number, solutal Grashof number, Joule heating, Helmholtz‐Smoluchowski velocity. The analytical solutions are presented for the axial velocity, temperature, and solute concentration. The expressions for the heat transfer rate, solute mass transfer rate, and surface shear stress function at the walls are also presented. The results display that, the velocity of the couple stress nanofluid is less in the case of pure electro‐osmotic flow as compared to that of combined electro‐osmotic and pressure‐driven flow. When the Joule heating parameter vanishes, the temperature and solute concentration profiles are linear, otherwise nonlinear. The shear stress function is larger in the case of pure electro‐osmotic flow and it is smaller for the combined effects of electro‐osmotic and pressure gradient. The present analysis places a significant observation that the various zeta potential plays an influential role in heartening fluid velocity. The analysis is relevant to electrokinetic hemodynamics and microfluidics. [ABSTRACT FROM AUTHOR]