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 [Formula: see text], Reynolds number (Re) and the radius ratio [Formula: see text] 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.

In this paper, the unsteady flow of Newtonian fluid through a curved pipe due to a pulsatile pressure gradient has been considered. The flow is three dimensional and the partial differential equations governing the flow are highly coupled and non-linear. Approximate analytical solutions of the governing partial differential equations have been obtained without neglecting any term containing the curvature ratio. Perturbation series in terms of curvature ratio has been used for obtaining the solutions. It is interesting to note that the solutions are valid for large as well as small values of Womersley number. The effect of different parameters such as, Reynolds number, Womersley number and curvature ratio on the flow through curved pipe is discussed in this paper. It is found that the axial velocity is qualitatively periodic in nature, as expected. The Reynolds number and curvature ratio are found to shift the axial velocity towards the outer boundary of the curved pipe.

The recent investigations ensure that, the effect of an endoscope on the peristaltic flow is very important for medical diagnosis and it has many clinical applications such as gastric juice motion in the small intestine when an endoscope is inserted through it. In the current article, the influence of magnetohydrodynamic (MHD) on the peristaltic propulsion of non-Newtonian fluid (considered as couple stress fluid) in a tube consisting of endoscope has been considered. The couple stress fluid occupies the space between two co-axial inclined tubes. The inner tube is uniformly circular and rigid while the outer tube considered as sinusoidal wave. The fluid motion is discussed in a wave frame which is moving with the constant velocity. The governing equations of two-dimensional flow have been abridged under the lubrication approach. Analytical solutions have been obtained for the velocity and pressure gradient with the help of modified Bessel functions. Numerical integration is used to evaluate the pressure difference and friction forces. The effect of emerging flow parameters on the velocity, frictional forces, pressure difference, pressure gradient and trapping phenomenon have been discussed. It is noted that, the magnetic force resists the flow and pumping rate in the peristaltic flow enhances from the horizontal to vertical tube. The present study has a wide range of applications in bio-medical engineering like the transport phenomenon in peristaltic micro pumps.

In this paper, the flow of two immiscible fluids through a curved pipe induced due to a pressure gradient in axial direction is studied. The fluid in core region is assumed to be highly viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric and regularity conditions, while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio and density ratio on the axial velocity is studied through 2-dimensional graphs and contour plots.

The present research deals with the magnetohydrodynamic flow and heat transfer of two immiscible fluids through a vertical channel filled with porous medium. The flow regime is considered to be time dependent, and the two immiscible fluids being micropolar and Newtonian fluids. The governing non-linear system of coupled partial differential equations is solved using the Crank–Nicolson approach, together with Newton’s method for non-linear equations. The obtained numerical results are shown graphically, and are interpreted for various parameters of interest. The study of Nusselt number and skin-friction is carried out numerically and presented through tables. It has been found that the buoyancy forces promote the flow field and micropolarity parameter holds back the same. Nusselt number diminishes with the increasing magnetic effects at both the plates.

The present article deals with the effect of heat transfer on the axisymmetric, laminar, and steady flow of two immiscible fluids through a circular pipe. The micropolar fluid is considered in the core (inner) region and the Newtonian fluid in the peripheral (outer) region. Two separate cases are considered: one with a complete nonporous fluid region and the other having a uniform porous medium in the peripheral portion of the circular pipe. The energy equations in both regions are solved to obtain analytical solutions in terms of generalized hypergeometric function and Meijer G-function for fluid temperatures in both cases. Including the continuity of temperature and heat flux at the interface, appropriate boundary and interface conditions are applied in both the cases. The results demonstrating temperature for different fluid parameters are interpreted through graphs. It is noticed that, for both discussed cases, the fluid temperature is decreased by supplement of micropolar fluid parameter, whereas the temperature is noted to be increasing by increase of pressure gradient and Brinkman number. In the case where a porous region is considered in the peripheral part of the pipe, the permeability parameter decreases the fluid temperature in both flow regions.

The intent of the current work is to study the time-dependent MHD flow of two immiscible Newtonian and micropolar fluids in a porous pipe in presence of heat transfer. The numerical solutions for the flow under consideration are obtained using Crank–Nicolson approach. The classical no-slip condition at the boundary of the pipe is used along with the appropriate interface conditions at the interface, to solve the initial boundary value problem governing the flow. The results for fluid velocities, microrotation and temperatures with varying physical parameters are displayed through graphs and are discussed as well. The Nusselt number is also studied for the considered flow, and the results are tabulated.

The aim of this paper is to present the closed form analytical solutionsof unidirectional flows of couple stress fluid namely, Poiseuille flow, Couette flow and Couette-Poiseuille flow between two concentric circular cylinders through porous medium with slip boundary conditions. Here, the fluid flow is generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both. We present the velocity profiles of the above flows graphically and the effect of various parameters on velocity is discussed. Keywords-Couple stress fluid, Slip boundary conditions, Porous medium,Poiseuille flow.

In this paper, we have proposed a new problem independent discontinuity locator for hybridization. Along with this, a new global smoothness indicator is proposed. The hybrid weighted essentially nonoscillatory (WENO) scheme works on the principle of applying linear upwind scheme in smooth regions and WENO algorithm in nonsmooth regions to save computational cost, which is reflected in the time taken for the computation of the numerical solution. A problem independent discontinuity locator has been designed based on the properties of the existing smoothness indicators. In addition, to attain the required order of accuracy, a new global smoothness indicator is proposed, which produces a solution with better resolution at discontinuities. Numerical experiments have been included to demonstrate the application of the proposed theory to some benchmark problems. It has been shown that the newly proposed hybrid WENO scheme works faster and gives a solution of higher resolution than WENO-JS, WENO-Z, and few other more recent third-order WENO schemes.

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.

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.

This paper deals with an unsteady flow of a micropolar fluid sandwiched between Newtonian fluids through a horizontal channel. The governing time-dependent partial differential equations are solved numerically by using the Crank-Nicolson finite difference approach. The continuity of velocity and shear stress is considered at the fluid–fluid interfaces. It is observed that the fluid velocities increase with time; eventually, a steady state is reached at a certain time instant. The velocity decreases with increasing micropolarity parameter in the micropolar fluid region and remains almost unchanged in both Newtonian fluid regions.

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-Huckel 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.

Purpose The main purpose of this paper is to study the effect of heat transfer on the peristaltic flow of a magnetohydrodynamic Walters B fluid through a porous medium in an inclined asymmetric channel. Design/methodology/approach The approximate analytical solutions of the governing partial differential equations are obtained using the regular perturbation method by taking wave number as a small parameter. The solutions for the pressure difference and friction forces are evaluated using numerical integration. Findings It is noticed that the pressure gradient and pressure difference are increasing functions of inclination angle and Grashof number. The temperature and heat transfer coefficients both increase with increase in inclination angle, Darcy number, Grashof number and Prandtl number. Increase in Hartmann number and phase difference decreases the size of trapped bolus. Originality/value The problem is original, as no work has been reported on the effect of magnetohydrodynamics on the peristaltic flow of a Walters B fluid through a porous medium in an inclined asymmetric channel with heat transfer.

The present paper is concerned with the study of fully developed flow of two immiscible micropolar and Newtonian fluids through a horizontal circular cylinder. Two immiscible fluids are assumed to occupy the horizontal circular cylinder; the micropolar fluid is in the inner cylindrical region while the Newtonian fluid is in the rest of the cylinder. The flow is generated due to a constant pressure gradient in the direction of the axis of the cylinder. Two steady flow situations have been studied: In the first situation, both micropolar and Newtonian fluid flow regions are nonporous, while in the second problem the Newtonian fluid region is assumed to be porous. In both problems, the relevant coupled differential equations governing the two fluid flows are modeled. In addition to the classical no-slip condition on the boundary, the continuity of velocity and shear stress at the fluid-fluid interface is presumed for solving the governing equations analytically. The influence of various flow parameters on the fluid velocity and microrotation is studied, and the results are illustrated through graphs. It is found that, in both problems, the micropolarity parameter has a decreasing effect on the fluid velocity and microrotation. The results also indicate that the porosity parameter decreases the velocity of the fluid.

This study deals with the unsteady flow and heat transfer of micropolar and Newtonian fluids, flowing immiscibly through a circular pipe. The micropolar and Newtonian fluids occupy core and peripheral regions, respectively. Initially, the pipe and fluids in both regions are at rest; after an instant of time, a constant pressure gradient is applied to generate the flow. The equations governing the flow are time dependent, coupled and nonlinear. The solutions for velocity, microrotation and temperature are acquired numerically employing Crank–Nicolson finite difference approach. Volume flow rate is also obtained numerically and presented in tabular form. At fluid–fluid interface, continuity of velocities, shear stresses, temperatures and heat fluxes are considered. The results for velocity, microrotation and temperature are displayed graphically. It is seen that the fluid velocities, microrotation and temperatures are increasing with time and attain a steady state after a particular time level. The micropolarity parameter has a decreasing effect on the fluid velocities and temperatures.

This article is intended to study the peristaltic motion of a Prandtl nanoliquid through an inclined tapered asymmetric channel. The simultaneous effects such as magnetic field, thermal radiation and chemical reactions have been considered. The geometrical model is considered as tapered asymmetric channel because this situation is observed in the flow of uterine fluid in the uterus. The equations governing the flow are simplified under the assumptions of long wavelength and low Reynolds number. The simplified equations are complex in nature, so that the numerical solutions are presented for the simplified nonlinear partial differential equations considering slip and convective boundary conditions using computational software Mathematica via shooting method. The sundry parameters on the flow quantities have been discussed in detail through graphical and tabular forms. The observed results show that rise in the magnetic effects leads to a reduction in velocity. The radiation parameter decreases the temperature and there is an increment in the pressure gradient with an increase in energy Grashof number. This study is encouraged by exploring the nanofluid dynamics in peristaltic transport as symbolized by heat transport in biological flows, novel pharmacodynamic pumps and gastrointestinal motility enhancement.

This study deals with the MHD steady flow and heat transfer of micropolar and Newtonian fluids, flowing immiscibly through a circular pipe. The pipe is assumed to be filled with uniform porous media. The micropolar and Newtonian fluids occupy core and peripheral regions, respectively. The equations governing the flow are coupled and non-linear. The solutions for velocity, microrotation and temperature are acquired numerically employing finite difference method. At fluid–fluid interface, continuity of velocities, shear stresses, temperatures and heat fluxes are considered. The results for velocity, microrotation and temperature are displayed graphically.

This investigation deals with the influence of heat and mass transfer on magnetohydrodynamic peristaltic flow of Pseudoplastic fluid in a vertical asymmetric channel through porous medium. The flow is examined in the wave frame of reference moving with the velocity of the wave. For formulation of the problem, long wavelength and low Reynolds number assumptions are taken into account. The perturbation solution has been derived for the stream function and pressure gradient. The pressure difference is calculated numerically. The influence of various parameters of interest on velocity, pressure gradient, temperature, concentration, pressure difference, heat transfer coefficient and trapping has been investigated graphically. The graphical results are also discussed for four different wave shapes. It is found that, in all the cases the magnetic parameter and Darcy number have opposite effect on the flow variables. The size of the trapped bolus increases from porous medium to non-porous medium and it decreases with increase of magnetic effects.

The aim of the present analysis is to investigate the effects of endoscope and heat transfer on the peristaltic flow of an incompressible Walters B fluid in an inclined tube. The fluid fills the gap between coaxial uniform tubes, such that the inner tube is rigid, circular and outer tube has sinusoidal wave travelling down its wall. The governing equations for Walters B fluid model are considered in cylindrical polar coordinates in moving frame of reference. The governing coupled partial differential equations are solved analytically employing regular perturbation method. The graphical results have been discussed for velocity, pressure gradient, pressure difference, frictional force, temperature and trapping phenomena. Four different wave forms have been considered for investigation. Trapping phenomena has been presented for different wave forms. It is observed that the pressure gradient is an increasing function of volume flow rate, heat generation parameter and inclination angle. The pumping rate increases from horizontal tube to vertical tube. Best pumping can be seen when the radius of the endoscope increases. The size of the trapping bolus increases with increase of wave amplitude ratio.