Symmetry analysis for steady boundary-layer stagnation-point flow of Rivlin–Ericksen fluid of second grade subject to suction

An analysis for the steady two-dimensional boundary-layer stagnation-point flow of Rivlin–Ericksen fluid of second grade with a uniform suction is carried out via symmetry analysis. By employing Lie-group method to the given system of nonlinear partial differential equations, the symmetries of the equations are determined. Using these symmetries, the solution of the given equations is found. The effect of the viscoelastic parameter k and the suction parameter R on the tangential and normal velocities, temperature profiles, heat transfer coefficient and the wall shear stress, have been studied. Also, the effect of the Prandtl number Pr on the temperature and the heat transfer coefficient has been studied

Further results on nonlinearly stretching permeable sheets: analitic solution for MHD flow and mass transfer

The steady magnetohydrodynamic (MHD) flow and mass transfer of an incompressible, viscous, and electrically conducting fluid over a permeable flat surface stretched with nonlinear (quadratic) velocity u(w)(x) = ax + c(0)x(2) and appropriate wall transpiration is investigated. It is shown that the problem permits an analytical solution for the complete set of equations with magnetic field influences when a fictitious presence of a chemical reaction is considered. Velocity and concentration fields are presented through graphs and discussed. The results for both skin friction coefficient f ''(0) and mass transfer gradient c'(0) agree well with numerical results published in the literatureCortell Bataller, R. (2012). Further results on nonlinearly stretching permeable sheets: analitic solution for MHD flow and mass transfer. Mathematical Problems in Engineering. 2012:1-18. doi:10.1155/2012/743130S1182012Cortell, R. (2011). Heat transfer in a fluid through a porous medium over a permeable stretching surface with thermal radiation and variable thermal conductivity. The Canadian Journal of Chemical Engineering, 90(5), 1347-1355. doi:10.1002/cjce.20639Sakiadis, B. C. (1961). Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE Journal, 7(1), 26-28. doi:10.1002/aic.690070108Crane, L. J. (1970). Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP, 21(4), 645-647. doi:10.1007/bf01587695Gupta, P. S., & Gupta, A. S. (1977). Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering, 55(6), 744-746. doi:10.1002/cjce.5450550619Vleggaar, J. (1977). Laminar boundary-layer behaviour on continuous, accelerating surfaces. Chemical Engineering Science, 32(12), 1517-1525. doi:10.1016/0009-2509(77)80249-2Hayat, T., Qasim, M., & Abbas, Z. (2010). Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space. Communications in Nonlinear Science and Numerical Simulation, 15(9), 2375-2387. doi:10.1016/j.cnsns.2009.09.013Cortell, R. (2005). Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing. Fluid Dynamics Research, 37(4), 231-245. doi:10.1016/j.fluiddyn.2005.05.001Cortell, R. (2007). Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet. Chemical Engineering and Processing - Process Intensification, 46(10), 982-989. doi:10.1016/j.cep.2007.05.022Ishak, A., Nazar, R., Bachok, N., & Pop, I. (2010). Melting heat transfer in steady laminar flow over a moving surface. Heat and Mass Transfer, 46(4), 463-468. doi:10.1007/s00231-010-0592-8Cortell, R. (2011). Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a power-law fluid past an infinite porous plate. Chemical Engineering Research and Design, 89(1), 85-93. doi:10.1016/j.cherd.2010.04.017Takhar, H. S., Raptis, A. A., & Perdikis, C. P. (1987). MHD asymmetric flow past a semi-infinite moving plate. Acta Mechanica, 65(1-4), 287-290. doi:10.1007/bf01176888Kumaran, V., & Ramanaiah, G. (1996). A note on the flow over a stretching sheet. Acta Mechanica, 116(1-4), 229-233. doi:10.1007/bf01171433Weidman, P. D., & Magyari, E. (2009). Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities. Acta Mechanica, 209(3-4), 353-362. doi:10.1007/s00707-009-0186-zMagyari, E., & Kumaran, V. (2010). Generalized Crane flows of micropolar fluids. Communications in Nonlinear Science and Numerical Simulation, 15(11), 3237-3240. doi:10.1016/j.cnsns.2009.12.013Cortell, R. (2007). Flow and heat transfer in a moving fluid over a moving flat surface. Theoretical and Computational Fluid Dynamics, 21(6), 435-446. doi:10.1007/s00162-007-0056-zPalani, G., & Kim, K. Y. (2011). On the diffusion of a chemically reactive species in a convective flow past a vertical plate. Journal of Applied Mechanics and Technical Physics, 52(1), 57-66. doi:10.1134/s0021894411010093Muhaimin, I., & Kandasamy, R. (2010). Local Nonsimilarity Solution for the Impact of a Chemical Reaction in an MHD Mixed Convection Heat and Mass Transfer Flow over a Porous Wedge in the Presence Of Suction/Injection. Journal of Applied Mechanics and Technical Physics, 51(5), 721-731. doi:10.1007/s10808-010-0092-0Abdel-Rahman, G. M. (2010). Thermal-diffusion and MHD for Soret and Dufour’s effects on Hiemenz flow and mass transfer of fluid flow through porous medium onto a stretching surface. Physica B: Condensed Matter, 405(11), 2560-2569. doi:10.1016/j.physb.2010.03.032Rohni, A. M., Ahmad, S., & Pop, I. (2012). Note on Cortell’s non-linearly stretching permeable sheet. International Journal of Heat and Mass Transfer, 55(21-22), 5846-5852. doi:10.1016/j.ijheatmasstransfer.2012.05.080Cortell, R. (2007). Viscous flow and heat transfer over a nonlinearly stretching sheet. Applied Mathematics and Computation, 184(2), 864-873. doi:10.1016/j.amc.2006.06.077Cortell, R. (2008). Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Physics Letters A, 372(5), 631-636. doi:10.1016/j.physleta.2007.08.005Akyildiz, F. T., & Siginer, D. A. (2010). Galerkin–Legendre spectral method for the velocity and thermal boundary layers over a non-linearly stretching sheet. Nonlinear Analysis: Real World Applications, 11(2), 735-741. doi:10.1016/j.nonrwa.2009.01.018Bataller, R. C. (2008). Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface. Journal of Materials Processing Technology, 203(1-3), 176-183. doi:10.1016/j.jmatprotec.2007.09.055Prasad, K. V., & Vajravelu, K. (2009). Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet. International Journal of Heat and Mass Transfer, 52(21-22), 4956-4965. doi:10.1016/j.ijheatmasstransfer.2009.05.022Raptis, A., & Perdikis, C. (2006). Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field. International Journal of Non-Linear Mechanics, 41(4), 527-529. doi:10.1016/j.ijnonlinmec.2005.12.003Kelson, N. A. (2011). Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet. International Journal of Non-Linear Mechanics, 46(8), 1090-1091. doi:10.1016/j.ijnonlinmec.2011.04.025Ahmad, A., & Asghar, S. (2011). Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field. Applied Mathematics Letters, 24(11), 1905-1909. doi:10.1016/j.aml.2011.05.016Cortell, R. (2007). MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species. Chemical Engineering and Processing: Process Intensification, 46(8), 721-728. doi:10.1016/j.cep.2006.09.008Andersson, H. I., Bech, K. H., & Dandapat, B. S. (1992). Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. International Journal of Non-Linear Mechanics, 27(6), 929-936. doi:10.1016/0020-7462(92)90045-9Vajravelu, K., Prasad, K. V., & Prasanna Rao, N. S. (2011). Diffusion of a chemically reactive species of a power-law fluid past a stretching surface. Computers & Mathematics with Applications, 62(1), 93-108. doi:10.1016/j.camwa.2011.04.055Akyildiz, F. T., Bellout, H., & Vajravelu, K. (2006). Diffusion of chemically reactive species in a porous medium over a stretching sheet. Journal of Mathematical Analysis and Applications, 320(1), 322-339. doi:10.1016/j.jmaa.2005.06.095Andersson, H. I., Hansen, O. R., & Holmedal, B. (1994). Diffusion of a chemically reactive species from a stretching sheet. International Journal of Heat and Mass Transfer, 37(4), 659-664. doi:10.1016/0017-9310(94)90137-6Makinde, O. D. (2010). On MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition. The Canadian Journal of Chemical Engineering, 88(6), 983-990. doi:10.1002/cjce.2036

Effect of temperature-dependent viscosity on entropy generation in transient viscoelastic polymeric fluid flow from an isothermal vertical plate

A numerical investigation of the viscosity variation effect upon entropy generation in time-dependent viscoelastic polymeric fluid flow and natural convection from a semi-infinite vertical plate is described. The Reiner-Rivlin second order differential model is utilized which can predict normal stress differences in dilute polymers. The conservation equations for heat, momentum and mass are normalized with appropriate transformations and the resulting unsteady nonlinear coupled partial differential equations are elucidated with the well-organized unconditionally stable implicit Crank-Nicolson finite difference method subject to suitable initial and boundary conditions. Average values of wall shear stress and Nusselt number, second-grade fluid flow variables conferred for distinct values of physical parameters. Numerical solutions are presented to examine the entropy generation and Bejan number along with their contours. The outcomes show that entropy generation parameter and Bejan number both increase with increasing values of group parameter and Grashof number. The present study finds applications in geothermal engineering, petroleum recovery, oil extraction and thermal insulation, etc

Free Convection Flow and Heat Transfer of Tangent Hyperbolic past a Vertical Porous Plate with Partial Slip

This article presents the nonlinear free convection boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a vertical porous plate with velocity slip and thermal jump effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Velocity slip (Sf), Thermal jump (ST), Prandtl number (Pr) and dimensionless tangential coordinate () on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, skin friction and heat transfer rate (Nusselt number) is increased with increasing Weissenberg number (We), whereas the temperature is decreased. Increasing power law index (n) enhances velocity and heat transfer rate but decreases temperature and skin friction. An increase in Thermal jump (ST) is observed to decrease velocity, temperature, local skin friction and Nusselt number. Increasing Velocity slip (Sf) is observed to increase velocity and heat transfer rate but decreases temperature and local skin friction. An increasing Prandtl number, (Pr), is found to decrease both velocity and temperature. The study is relevant to chemical materials processing applications

Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative

This thesis investigates analytically the magnetohydrodynamics (MHD) transport of Newtonian and non-Newtonian fluids flows inside a circular channel. The flow was subjected to an external electric field for the Newtonian model and a uniform transverse magnetic field for all models. Pressure gradient or oscillating boundary condition was employed to drive the flow. In the first model Newtonian fluid flow without stenotic porous tube was considered and in the second model stenotic porous tube was taken into account. The third model is concerned with the temperature distribution and Nusselt number. The fourth model investigates the non-Newtonian second grade fluid velocity affected by the heat distribution and oscillating walls. Last model study the velocity, acceleration and flow rate of third grade non-Newtonian fluid flow in the porous tube. The non-linear governing equations were solved using the Caputo-Fabrizio time fractional order model without singular kernel. The analytical solutions were obtained using Laplace transform, finite Hankel transforms and Robotnov and Hartley’s functions. The velocity profiles obtained from various physiological parameters were graphically analyzed using Mathematica. Results were compared with those reported in the previous studies and good agreement were found. Fractional derivative and electric field are in direct relation whereas magnetic field and porosity are in inverse relation with respect to the velocity profile in Newtonian flow case. Meanwhile, fractional derivative and Womersely number are in direct relation whereas magnetic field, third grade parameter, frequency ratio and porosity are in inverse relation in third grade non-Newtonian flow case. In the case of second grade fluid, Prandtl number, fractional derivative and Grashof number are in direct relation whereas second grade parameter and magnetic field are in inverse relation. The fluid flow model can be regulated by applying a sufficiently strong magnetic field

Stagnation Point Flow of Thixotropic Fluid over a Stretching Sheet with Mass Transfer and Chemical Reaction

The stagnation point flow of thixotropic fluid towards a linear stretching surface is investigated. Mass transfer with first order chemical reaction is considered. The resulting partial differential equations are reduced into the ordinary differential equations. Dimensionless velocity and concentration fields have been computed. Graphical plots are presented to illustrate the details of flow and mass transfer characteristics and their dependence upon the physical parameters. Numerical values of surface mass transfer are first computed and then analyzed

Recent Trends in Coatings and Thin Film–Modeling and Application

Over the past four decades, there has been increased attention given to the research of fluid mechanics due to its wide application in industry and phycology. Major advances in the modeling of key topics such Newtonian and non-Newtonian fluids and thin film flows have been made and finally published in the Special Issue of coatings. This is an attempt to edit the Special Issue into a book. Although this book is not a formal textbook, it will definitely be useful for university teachers, research students, industrial researchers and in overcoming the difficulties occurring in the said topic, while dealing with the nonlinear governing equations. For such types of equations, it is often more difficult to find an analytical solution or even a numerical one. This book has successfully handled this challenging job with the latest techniques. In addition, the findings of the simulation are logically realistic and meet the standard of sufficient scientific value

Computational Fluid Dynamics 2020

This book presents a collection of works published in a recent Special Issue (SI) entitled “Computational Fluid Dynamics”. These works address the development and validation of existent numerical solvers for fluid flow problems and their related applications. They present complex nonlinear, non-Newtonian fluid flow problems that are (in some cases) coupled with heat transfer, phase change, nanofluidic, and magnetohydrodynamics (MHD) phenomena. The applications are wide and range from aerodynamic drag and pressure waves to geometrical blade modification on aerodynamics characteristics of high-pressure gas turbines, hydromagnetic flow arising in porous regions, optimal design of isothermal sloshing vessels to evaluation of (hybrid) nanofluid properties, their control using MHD, and their effect on different modes of heat transfer. Recent advances in numerical, theoretical, and experimental methodologies, as well as new physics, new methodological developments, and their limitations are presented within the current book. Among others, in the presented works, special attention is paid to validating and improving the accuracy of the presented methodologies. This book brings together a collection of inter/multidisciplinary works on many engineering applications in a coherent manner