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

Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source

The paper considers the flow of a power-law fluid past a vertical stretching sheet. Effects of variable thermal conductivity and non-uniform heat source/sink on the heat transfer are addressed. The thermal conductivity is assumed to vary linearly with temperature. Similarity transformation is used to convert the governing partial differential equations into a set of coupled, non-linear ordinary differential equations. Two different types of boundary heating are considered, namely Prescribed power-law Surface Temperature (PST) and Prescribed power-law Heat Flux (PHF). Shooting method is used to obtain the numerical solution for the resulting boundary value problems. The effects of Chandrasekhar number, Grashof number, Prandtl number, non-uniform heat source/sink parameters, wall temperature parameter and variable thermal conductivity parameter on the dynamics are shown graphically in several plots. The skin friction and heat transfer coefficients are tabulated for a range of values of the parameters. Present study reveals that in a gravity affected flow buoyancy effect has a significant say in the control of flow and heat transfer. © 2008 Elsevier Ltd. All rights reserved

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers

Variable Conductivity and Partial Slip on Flow over a Nonlinear Radiated Stretching Sheet

The heat and mass transfer effects on hydrodynamic slip flow past a non-linear stretching sheet is considered. For improving the thermal moment we also considered the thermal radiation and variable thermal conductivity. The condition of slip is one of the core concepts of the Navier – Stokes theory. The sheet is placed horizontally, so that buoyancy forces are less and negligible and the plate is stretching nonlinearly. The partial velocity slip may occur on the stretching boundary when the fluid is particulate such as emulsions, suspensions, foams and polymer solutions. It has significant in biological and medicinal treatments such as controlling the heart attacks, improving the blood pumping, controlling high pressure etc. The thermal radiation is also significant in various treatments such as endoscopy, radiation treatment cancer, scanning and DNA checkup etc. The governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) by using similarity transformation and solutions are carried out with help of the Runge-Kutta based shooting technique. The effects of various material parameters on the velocity, temperature, concentration of the flow field as well as the skin-friction coefficient, heat and mass transfer rates are inspected in detail. It is found that the effects of slip parameter decelerates the fluid velocity, while raises the fluid temperature. Keywords: Non-linear stretching sheet; variable conductivity; partial slip; thermal radiation.

Numerical study of radiative Maxwell viscoelastic magnetized flow from a stretching permeable sheet with the Cattaneo–Christov heat flux model

In this article, the Cattaneo-Christov heat flux model is implemented to study non-Fourier heat and mass transfer in the magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) fluid over a permeable stretching sheet under a transverse constant magnetic field. Thermal radiation and chemical reaction effects are also considered. The nonlinear partial differential conservation equations for mass, momentum, energy and species conservation are transformed with appropriate similarity variables into a system of coupled, highly nonlinear ordinary differential equations with appropriate boundary conditions. Numerical solutions have been presented for the influence of elasticity parameter (), magnetic parameter (M2), suction/injection parameter (λ), Prandtl number (Pr), conduction-radiation parameter (Rd), sheet stretching parameter (A), Schmidt number (Sc), chemical reaction parameter (γ_c), modified Deborah number with respect to relaxation time of heat flux (i.e. non-Fourier Deborah number) on velocity components, temperature and concentration profiles using the successive Taylor series linearization method (STSLM) utilizing Chebyshev interpolating polynomials and Gauss-Lobatto collocation. The effects of selected parameters on skin friction coefficient, Nusselt number and Sherwood number are also presented with the help of tables. Verification of the STSLM solutions is achieved with existing published results demonstrating close agreement. Further validation of skin friction coefficient, Nusselt number and Sherwood number values computed with STSLM is included using Mathematica software shooting quadrature

E-store management using bell-lapadula access control security model

Generally, the existing store management system does not provide any access control mechanism in order to manage resources. All levels of user have the same right to access the store and borrow the equipment. Therefore, the E-Store management system using Bell- LaPadula access control model was proposed. The prototyping methodology was used to develop the system because methodology model is quickly constructed to test or illustrate design features and ideas, in order to gather user feedback. Moreover, the system is built using hypertext processor (PHP) language. The E-Store system has three types of users, which are known as top management of Welding Department, lecturers and students. The user’s access control is divided by high-level privilege to lower-level privilege. Therefore, each user will have different login interface according to their role and access right to the system. Through the system, high-level user manages in and out equipment flow, manages authorization, view history log in activity and verify complaint report. Lower-level user can view list of equipment, report complaint and damage equipment and borrow equipment. The E-Store management system is expected to manage the store effectively and reduced redundancy issues of equipment requested. The user access right has been assigned based on their access leve