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The theoretical derivation of the start‐up laminar flow of incompressible viscous fluid in a long pipe as suggested by Szymanski, could not be verified experimentally. This leads to the checking of assumption of constant pressure gradient across the ends of the pipe, on the basis of which the theoretical development was made. Recently, the problem was again investigated for viscous fluid by Otis. In the present paper, the laminar start‐up flow of elastico‐viscous fluid in a pipe, without assuming constant pressure gradient across its ends, has been investigated. The non‐linear governing equations are solved numerically and the effects of start‐up flow parameters and elastico‐viscous parameter on the velocity distribution have been studied.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

This paper aims to explore the consequence of chemical reaction on three-dimensional flow, heat and mass transfer of a Casson nano liquid over exponentially stretching surface. A numerical technique of RKF-45 method is applied to resolve the nonlinear ordinary differential equations, which are obtained by applying the similarity transformation to the nonlinear partial differential system.

Role of significant parameters on flow fields are observed graphically. Also, the strength of heat exchange (Nusselt number) and the strength of mass exchange (Sherwood number) are analyzed.

The results of numerical modeling showed that, the Prandtl number plays a key role in reducing the temperature of the system. Further, the radiation parameters manufacture a lot of heat to operating fluid and higher temperature exponent parameter and enhance the temperature of the fluid.

The results of numerical modeling showed that, the Prandtl number plays a key role in reducing the temperature of the system. Further, the radiation parameters manufacture a lot of heat to operating fluid and higher temperature exponent parameter and enhance the temperature of the fluid.

The features of coated wire product are measured by the flow and heat transport occurring in the interior of dies. Therefore, an understanding of characteristics of polymers momentum, heat mass transfer and wall shear stress is of great interest. Enhancement of heat transfer rate is fundamental need of wire coating process. Therefore, this study aims to investigate the effect of suspended nanoparticles in heat and mass transport phenomena of third-grade liquid in post-treatment of wire coating process. Buongiorno model for nanofluid is adopted. Two cases of temperature dependent viscosity are considered.

The governing equations are modelled with the help of steady-state conservation equations of mass, momentum, energy and nanoparticle concentration. Some appropriate dimensionless variables are introduced. Numerical solutions for the nonlinear problem are developed through Runge–Kutta–Fehlberg technique. The outcome of sundry variables for dimensionless flow, thermal and nanoparticle volume fraction fields are scrutinised through graphical illustrations.

The study’s numerical results disclose that the force on the total wire surface and shear stress at the surface in case of Reynolds Model dominate Vogel’s Model case. Impact of nanoparticles is constructive for force on the total wire surface and shear stress at the surface. The velocity of the coating material can be enhanced by the non-Newtonian property.

This study may provide useful information to improve the wire coating technology.

Effect of nanoparticles in wire coating analysis by using Brownian motion and thermophoresis slip mechanisms is investigated for the first time. Two different models for variable viscosity are used.

This work focuses on the laminar flow of a two‐phase particulate suspension induced by a suddenly accelerated infinite vertical permeable surface in the presence of fluid buoyancy, magnetic field, heat generation or absorption, and surface suction or blowing effects. The governing equations for this modified Stokes problem are developed based on the continuum representation of both the fluid and the particle cloud. Appropriate dimensionless variables are introduced. The resulting dimensionless equations are solved numerically by an accurate implicit finite‐difference method for two situations. The first case corresponds to an impulsive start of the surface from rest while the second case corresponds to a uniformly accelerated surface. The numerical results for these cases are illustrated graphically. Comparisons with previously published work are performed and the results are found to be in good agreement. Typical fluid‐ and particle‐phase velocity and temperature distributions as well as wall shear stress and heat transfer results are reported for various values of the particle loading, Hartmann number, wall mass transfer coefficient and the heat generation or absorption coefficient.

The authors presented the time-dependent flow of an upper-convected Maxwell (UCM) fluid in the presence of chemical reaction, thermal-diffusion and diffusion-thermo effects. The paper aims to discuss these issues.

Recent technique namely homotopy analysis method (HAM) is utilized to compute the solution of the problem.

Chemical reaction has opposite effects on the concentration field for the destructive and constructive cases. The Deborah number acts as a retarding agent.

Combined effects of thermal-diffusion, diffusion-thermo and chemical reaction are analyzed.

The National Engineering Laboratory is one of the larger stations of the British Government's Department of Scientific and Industrial Research. Current programmes include theoretical and experimental studies of non‐Newtonian lubricants, the development of new methods of measuring the compressibility of hydraulic fluids, research into the behaviour of oils under hydrostatic tension, and investigations of various aspects of the phenomenon of aeration in hydraulic fluids. The Laboratory's facilities for carrying out sponsored research and testing in this field are briefly described.

The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge.

Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks.

First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

The purpose of this study is to analyze an unsteady MHD Darcy flow of nonNewtonian hybrid nanoliquid past an exponentially accelerated vertical plate under the influence of velocity slip, Hall and ion slip effects in a rotating frame of reference. The fluids in the flow domain are assumed to be viscously incompressible electrically conducting. Sodium alginate (SA) has been taken as a base Casson liquid. A strong uniform magnetic field is applied under the assumption of low magnetic Reynolds number. Effect of Hall and ion-slip currents on the flow field is examined. The ramped heating and time-varying concentration at the plate are taken into consideration. First-order homogeneous chemical reaction and heat absorption are also considered. Copper and alumina nanoparticles are dispersed in base fluid sodium alginate to be formed as hybrid nanoliquid.

The model problem is first formulated in terms of partial differential equations (PDEs) with physical conditions. Laplace transform method (LTM) is used on the nondimensional governing equations for their closed-form solution. Based on these results, expressions for nondimensional shear stresses, rate of heat and mass transfer are also determined. Graphical presentations are chalked out to inspect the impacts of physical parameters on the pertinent physical flow characteristics. Numerical values of the shear stresses, rate of heat and mass transfer at the plate are tabulated for various physical parameters.

Numerical exploration reveals that a significant increase in the secondary flow (i.e. crossflow) near the plate is guaranteed with an augmenting in Hall parameter or ion slip parameter. MHD and porosity have an opposite effect on velocity component profiles for both types of nanoliquids. Result addresses that both shear stresses are strongly enhanced by the Casson effect. Also, hybrid nanosuspension in Casson fluid (sodium alginate) exhibits a lower rate of heat transfer than usual nanoliquid.

This model may be pertinent in cooling processes of metallic infinite plate in bath and hybrid magnetohydrodynamic (MHD) generators, metallurgical process, manufacturing dynamics of nanopolymers, magnetic field control of material processing, synthesis of smart polymers, making of paper and polyethylene, casting of metals, etc.

The originality of this study is to obtain an analytical solution of the modeled problem by using the Laplace transform method (LTM). Such an exact solution of nonNewtonian fluid flow, heat and mass transfer is rare in the literature. It is also worth remarking that the influence of Hall and ion slip effects on the flow of nonNewtonian hybrid nanoliquid is still an open question.

The purpose of this study is to examine the influence of rotation and varying gravitational strength on the onset of thermal convection in a porous medium layer numerically. The porous layer is acted to uniform rotation and inconsistent downward gravitational field which changing with depth from the layer. The authors presented three categories of gravitational strength deviancy, namely, linear, parabolic and exponential.

The higher-terms Galerkin weighted residual procedure is applied to get the eigenvalue of the problem.

The results illustrate that both rotation parameter and gravity variation parameter suspend the arrival of convection. The measurement of the convection cells decreases on enhancing the rotation parameter and gravity variation parameter.

It is also found that the scheme is more stable for category exponential, whereas it is more unstable for category parabolic.