A class of exact solutions of second grade fluid

Steady circulatory flow of a second grade fluid about a rotating porous cylinder

Helical flows of second grade fluid due to constantly accelerated shear stresses

We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.

The investigation is to explore the transportation of a viscoelastic fluid with fractional second grade model by peristalsis through a cylindrical tube under the assumptions of long wavelength and low Reynolds number. Analytical solution of problem is obtained by using Caputo?s definition. It is assumed that the cross-section of the tube varies sinusoidally along the length of tube. The effects of fractional parameter, material constant and amplitude on the pressure and friction force across one wavelength are discussed numerically with the help of illustrations. It is found that pressure decreases with increase in fractional parameter whereas increases with increase in magnitude of material constant or time. The pressure for the flow of second grade fluid is more than that for the flow of Newtonian fluid.

In the present investigation, a numerical study of the flow and heat transfer analysis of viscoelastic second grade fluid due to heated, continuous stretching of a vertical sheet has been carried out. The stretching velocity is assumed to vary linearly with the distance measured from the leading edge. The surface heat flux is assumed to be varied in power of distance measured from the leading edge. The governing differential equations are transformed by introducing proper non-similarity variables and solved numerically using two different methods, namely, the local non-similarity method with second level of truncation and the implicit finite difference method for values of ξ (=Grx/Rex2) ranging from 0 to 10. The comparisons of the results obtained by the aforementioned methods are found in excellent agreement. Effects of the viscoelastic parameter, λ (Deborah number) on the skin-friction and the heat transfer coefficients have been shown graphically for the fluid with Prandtl number equal to 0.7, 7.03 and 15.0. Keywords: Mixed convection, second grade fluid, stretching flat surface and variable surface heat flux.

In the present study we have explored the effects of thermal buoyancy on flow of a viscoelastic second grade fluid past a vertical, continuous stretching sheet of which the velocity and temperature distributions are assumed to vary according to a power-law form. The governing differential equations are transformed into dimensionless form using appropriate transformations and then solved numerically. The methods here employed are (1) the perturbation method together with the Shanks transformation, (2) the local non-similarity method with second level of truncation and (3) the implicit finite difference method for values of ξ ( = Grx/Rex2, defined as local mixed convection parameter) ranging in [0, 10]. The comparison between the solutions obtained by the aforementioned methods found in excellent agreement. Effects of the elasticity parameter λ on the skin-friction and heat transfer coefficients have been shown graphically for the fluids having the values of the Prandtl number equal to 0.72, 7.03 and 15.0. Effects of the viscoelastic parameter and the mixed convection parameter, ξ, on the temperature and velocity fields have also been studied. We notice that with the increase in visco-elastic parameter λ, velocity decreases whereas temperature increases and that velocity gradient is higher than that of temperature.

Oscillatory flow of second grade fluid in a straight rectangular duct

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.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Dumitru Vieru, Corina Fetecau, Mehwish Rana; Starting solutions for the flow of second grade fluids in a rectangular channel due to an oscillating shear stress. AIP Conference Proceedings 22 May 2012; 1450 (1): 45–54. https://doi.org/10.1063/1.4724116 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

The aim of this article is to investigate the exact solution by using a new approach for the thermal transport phenomena of second grade fluid flow under the impact of MHD along with exponential heating as well as Darcy’s law. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.

Unsteady free convection slip flow of second grade fluid over an infinite heated inclined plate is discussed. The effects of mass diffusions in the flow are also eligible. Caputo-Fabrizio fractional derivative is used in the constitutive equations of heat and mass transfer respectively. Laplace transform is utilized to operate the set of fractional governing equations for both ramped and stepped wall temperature. Expression for Sherwood number and Nusselt number with non-integer order are found by differentiating the analytical solutions of fluid concentration and temperature. Numerical results of Sherwood number, Nusselt number and skin friction are demonstrated in tables. Solutions are plotted graphically to analyze the impact of distinct parameters i.e. Caputo-Fabrizio fractional parameter, second grade parameter, slip parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number to observe the physical behavior of the flow.

Rotating effects and magnetohydrodynamic (MHD) free convection flow of second grade fluids in a porous medium is considered in this paper. It is assumed that the bounding infinite inclined plate has ramped wall temperature with the presence of heat and mass diffusion. Based on Boussinesq approximation, the analytical expressions for dimensionless velocity, temperature and concentration are obtained by using the Laplace transform method. All the derived solutions satisfying the involved differential equations with imposed boundary and initial conditions. The influence of various parameters on the velocity has been analyzed in graphs and discussed.

Analysis of an unsteady two-dimensional magnetohydrodynamic stagnation point flow of second-grade fluid is carried out in this article. It is supposed that the fluid is incompressible and impinges over the oscillatory stretching surface obliquely. The governing PDEs for second-grade fluid have been derived and then transfigured into a system of nonlinear coupled ODEs via appropriate similarity mappings. The BVP arrangement technique in Maple programming is used for the numerical arrangements of these subsequent nonlinear coupled equations. The outcomes are graphically represented and tabulated with the aim of illustrating the physical impacts of governing parameters on the temperature, concentration, and velocity profiles. The skin friction coefficient, Sherwood number, and Nusselt number are also analyzed by computational results, where it is reported that these physical quantities enhance with increment in Hartmann number and diminish with increment in the local second-grade parameter.

We have considered heat and mass transfer on the MHD free convection flow of second grade fluid through porous medium bounded by an infinite vertical porous rotating plate taking hall current into account. The analytical solutions for the governing equations are found by utilization of Laplace transformation methodology. The velocity, temperature and concentration is analysed graphically, and computational results for the skin friction, and Sherwood number are also obtained.

Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts