This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers＇ fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The mo...This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers＇ fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The momentum equation is formulated with multi-term fractional derivatives, and by means of viscous dissipation, the fractional derivative is considered in the energy equation. A finite difference scheme is established based on the Gl-algorithm, whose convergence is confirmed by the comparison with the analytical solution in an example. Meanwhile the numerical solutions of velocity, temperature and shear stress are obtained. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Increasing the fractional derivative parameter a, the velocity and temperature have a decreasing trend, while the influences of fractional derivative parameter ,8 on the velocity and temperature behave conversely. Increasing the absolute value of the first order slip parameter and the second order slip parameter both cause a decrease of velocity. Furthermore, with the decreasing of the magnetic parameter, the shear stress decreases.展开更多
The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterativ...The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.展开更多
基金Supported by the National Natural Science Foundations of China under Grant Nos.21576023,51406008the National Key Research Program of China under Grant Nos.2016YFC0700601,2016YFC0700603the BUCEA Post Graduate Innovation Project(PG2017032)
文摘This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers＇ fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The momentum equation is formulated with multi-term fractional derivatives, and by means of viscous dissipation, the fractional derivative is considered in the energy equation. A finite difference scheme is established based on the Gl-algorithm, whose convergence is confirmed by the comparison with the analytical solution in an example. Meanwhile the numerical solutions of velocity, temperature and shear stress are obtained. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Increasing the fractional derivative parameter a, the velocity and temperature have a decreasing trend, while the influences of fractional derivative parameter ,8 on the velocity and temperature behave conversely. Increasing the absolute value of the first order slip parameter and the second order slip parameter both cause a decrease of velocity. Furthermore, with the decreasing of the magnetic parameter, the shear stress decreases.
文摘The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.
