Journal of Marine Science and Technology

Journal of Marine Science and Technology

Numerical steady stream moving boundary layer on a plate and in the presence of thermal radiation Using Lie group

Document Type : Original Manuscript

Authors
amin ghaemian 1
mohsen sadeghian kerdabadi 2
Manuchehr Manouchehr Fadavi Ardestani 1
1 Mechanical Engineering Amirkabir University of Technology
2 Faculty of Marine Engineering Amirkabir University of Technology
10.22113/jmst.2017.47002
Abstract
In this study ahead to solve the equations of the boundary layer on a plate Mthrkprdakhth is steady. It takes into account the energy equation, heat transfer components also be considered. The solution method used to solve nonlinear equations, the method is Lie group. The initial conditions using an iterative algorithm for solving differential equations with relatively good accuracy estimates. Then, the fourth-order Runge-Kutta method to solve environmental values ​​across functions to be obtained. Using the results of the numerical solution of the boundary layer heating speed and simulate the effects of radiation coefficient, the speed and suction factor to be considered in the boundary layer. Finally, to assess the results of the numerical solution methods Lie group, the results of earlier shooting method is used. A comparison of numerical solution methods and techniques shooting show Lie group Lie group method convergence addition to high speed, good accuracy as well.
Keywords
By Lai Group
the boundary layer equations
Thermal radiation

Subjects

Mukhopadhyay, S., Bhattacharyya, K., Layek, G.C., “Steady boundary layer flow and heat transfer over a porous moving plate in presence of thermal radiation”, International Journal of heat and mass transfer, Vol. 54, pp.2751-2757, 2011
Cao, L., Si, X., Zheng, L., “The flow of a micro polar fluid through a porous expanding channel: A Lie group analysis”, Applied Mathematics and Computation, Vol. 270, pp.242-250, 2015
Abd-el-Malek, M., Amin, A., “New exact solution for solving the initial-value-problem of the KdV-KP equation via the Lie group method”, Applied Mathematics and Computation, Vol. 261, pp.408-418, 2015
Uddin, M.J., Kabir, M.N., Alginahi, Y.M., “Lie group analysis and numerical solution of magnetohydrodynamic free convective slip flow of micro polar fluid over a moving plate with heat transfer”, Computers and Mathematics with Applications, 2015
Liu, Ch., “Lie-group differential algebraic equations method to recover heat source in a Cauchy problem with analytic continuation data”, International Journal of Heat and Mass Transfer, Vol. 78, pp.538-547, 2014
Liu, Ch., “Elastoplastic models and oscillators solved by a Lie-group differential algebraic equations method”, International Journal of Non-linear Mechanics, 2014
Liu, Ch., “A new sliding control strategy for nonlinear system solved by the Lie-group differential algebraic equation method”, Commun Nonlinear SciNumerSimulat, Vol. 19, pp. 2012-2038, 2014
Liu, Ch., “The Lie-group shooting method for boundary-layer problems with suction/injection/reverse flow conditions for power-law fluids”, International Journal of Non-linear Mechanics, Vol. 46, pp. 1001-1008, 2011
Celledoni, E., Marthinsen, H., Owren, B., “An introduction to Lie group integrators-basics, new developments and applications”, Journal of Computational Physics, 2013
Blasius, H., “Grenzschichten in FlussigkeitenmitkleinerReibung”, Z.math.Phys, Vol. 56, pp. 1-37, 1908
Han, Z., “Nanofluids with Enhanced Thermal Transport Properties”, University of Maryland at College Park, 2008
Liu, Ch., “An SL(3,R) shooting method for solving the Falker-Skan boundary layer equation”, International Journal of Non-linear Mechanics, Vol. 49, pp. 145-151, 2013
Liu, Ch, “Developing an SL(2,R) Lie-group shooting method for a singular φ-Laplacian in a nonlinear ODE”, Commun Nonlinear SciNumerSimulat, Vol. 18, pp.2327-2339, 2013

  • Receive Date 11 January 2017
  • Revise Date 01 June 2017
  • Accept Date 19 June 2017
  • Publish Date 21 November 2020