The steady flow of a Second grade fluid through constricted tube for mild stenosis is modeled and analyzed theoretically. The governing equations are simplified by implying an order-of-magnitude analysis. Based on Karman Pohlhausen procedure polynomial solution for velocity profile is presented. Expressions for pressure gradient, shear stress, separation and reattachment points are also calculated. The effects of nondimensional parameters emerging in the model on the velocity profile, shear stress, pressure gradient are discussed and depicted graphically. The effect of non-Newtonian parameter on velocity profile, wall shear stress and pressure gradient is also analyzed. It is found that the Reynolds number strongly effect the wall shear stress, separation and reattachment points.

New exact solutions for unsteady magnetohydrodynamic (MHD)flows of a generalized Second-grade fluid due to uniform accelerating plate are derived. The generalized Second-gradefluid saturates the porous space.Fractional derivative is used in the governing equation. The analytical expressions for velocity and shear stressfields are obtained by using Laplace transform technique for the fractional calculus. The obtained solutions are expressed in series form in terms of Fox H-functions. Similar solutions for ordinary Secondgrade fluid passing through a porous space are also recovered. Moreover, several figures are sketched for the pertinent parameters to analyze the characteristics of velocityfield and shear stress.

This study attempts to analyze the effect of diverse parameters of the peristaltic flow of Second grade dusty fluid through a curved configuration. Stream function conversions are used to model the separate system of equations for the dust particles and fluid. The Perturbation technique is used to get the analytical solutions and the results are verified through graphs. It is noticeable that the trapped bolus, compresses both the dust particles and fluid with an increase in `the Second grade parameter'. Moreover, a surge in `the Reynolds number' Re effects the bolus trapped in the lower portion of the channel for fluid. Decrement in the velocity is observed with a rise in `the wave number' \delta and `the Second grade parameter' \alpha_1.

The importance of the slip flow over the no-slip condition is widely accepted in microscopic scaled domains with the direct impact on microfluidic and nanofluidic systems. The popular Navier Stoke’ s (N-S) flow model is largely utilized with the slip flow phenomenon. In the present study, the finite integral transform scheme along with the shift of variables is implemented to solve the equation of motion of Second grade fluid having thirdorder mixed partial derivative term. The velocity over the flow regime is studied with both the slip and no-slip boundary conditions for Newtonian and non-Newtonian characteristics by considering the generalized Couette flow. The impact of the pressure gradient and flow time on the velocity is investigated analytically. The output of the present work reveals that due to the slip flow velocity randomly varies at the vicinity of wall surface and such nature hasn’ t been found for the no-slip condition. The validation of the present work was done by comparison with the published work and the numerical values, and it shows well verified.

Transmission of heat and mass in boundary layer flows over stretching surfaces play a significant role in metallurgy and polymer industry. In Current article the assisting and opposing flow of a Second grade fluid towards a stretching sheet is analyzed to examine the heat and mass transfer in stagnation point boundary layer flow. Different flow parameters such as concentration, surface temperature and stretching velocity are supposed to variate linearly. The basic transport equations are transformed into non-linear ordinary differential equations by means of boundary layer approximation and similarity transmutations, which are then solved by employing nonlinear shooting (NLS) and Keller-box methods (KBM). These techniques are very useful for solving boundary-layer problems and are applicable to other general situations than that presented current study. The outcomes of velocity, temperature, concentration profile, skin-friction coefficient, heat and mass transfer coefficients are analyzed briefly in graphical and tabular formats. The mass transmission rate was found to be in direct relation with Schmidt number. Moreover, we predict that a rise in Prandtl number leads to a decline in temperature and thermal layer of boundary thickness for both supporting and contrasting flows. The outcomes of this article are important for the analysts in the field of Second grade fluids. We believe that the article is very well prepared and the results are original and useful from both theoretical and application point of views.

This study investigates the combined heat mass transport features in steady Magneto-Hydro-Dynamic (MHD) viscoelastic fluid ow through stretching walls of channel. The channel walls were considered porous. The analysis of heat transport was carried out with the help of Cattaneo-Christov heat diffusion formula and generalized Fick's theory was developed for the study of mass transport. The system of partial differential expressions was changed into an ordinary differential set by introducing suitable variables. The homotopic scheme was employed for solving the resultant equations and then, validity of the results was veri ed by various graphs. Moreover, an extensive analysis was performed on the influence of involved constraints on liquid velocity, concentration, and temperature pro les. It was observed that the normal component of velocity decreased by increasing Reynolds number or the viscoelastic constraint. Both temperature and concentration pro les were enhanced by increasing combined parameter and Reynolds number. The presence of thermal relaxation number and concentration relaxation number decreased temperature and concentration pro les, respectively.

The aim of this paper is to determine the time-dependent MHD fractionalized three-dimensional flow of viscoelastic fluid in porous medium with heat transfer by traveling wave solution. The governing nonlinear partial differential equations are altered by utilizing the wave parameter β ( ) ξ = lx +my+nz +ω t Γ β +1 into ordinary differential equations. The exact solutions are attained by applying a traveling wave method for two different cases. Here we discuss some precise cases, the solution of MHD Newtonian fluid in porosity can be obtained by substituting α → 1 0 in general solution. The impact of important governing parameters on the movement of a fluid is examined as well as the comparison of Newtonian and non-viscous fluids have been made by 2D and 3D graphical analysis.

The velocity field and the adequate shear stress, corresponding to the flow of a generalized Second grade fluid in an annular region, due to a quadratic time-dependent shear stress, are determined by means of the Laplace and the finite Hankel transforms. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. For b®1 or b®1 and a1®0, the corresponding solutions for a Second grade fluid, respectively, for the Newtonian fluid, performing the same motion, are obtained from general solutions. Finally, the influence of the material and fractional parameters on the shear stress as well as a comparison between models is drawn by graphical illustrations.

The dynamical analysis of MHD Second grade fluid based on their physical properties has stronger resistance capabilities, low-frequency responses, lower energy consumption, and higher sensitivities; due to these facts externally applied magnetic field always takes the forms of diamagnetic, ferromagnetic and paramagnetic. The mathematical modeling based on the fractional treatment of governing equation subject to the temperature distribution, concentration, and velocity field is developed within a porous surfaced plate. Fractional differential operators with and without non-locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. The fractionalized analytical solutions have been traced out separately through Atangana-Baleanu and Caputo-Fabrizio fractional differential operators. Our results suggest that the velocity profile decrease by increasing the value of the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.