Abstract
In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.
Highlights
Nonlinear equations play an important role in applied mathematics, physics and issues related to engineering due to their role in describing many real world phenomena
Numerical methods give discontinuous points of a curve and it is very time consuming to obtain a complete curve of results
The goal of the present study is to develop similarity transformations via one parameter linear group of transformations and the corresponding similarity solutions for mixed convection flow of viscous incompressible fluid past a moving vertical flat plate with thermal convective and hydrodynamic slip boundary conditions and to solve the transformed coupled ordinary differential equations using the differential transform method
Summary
Nonlinear equations play an important role in applied mathematics, physics and issues related to engineering due to their role in describing many real world phenomena. The importance of obtaining exact or approximate solutions of nonlinear partial differential equations is still a big problem that compels scientists and engineers to seek different methods for exact or approximate solutions. A variety of numerical and analytical methods have been developed to obtain accurate approximate and analytic solutions for problems. There are some analytic techniques for nonlinear equations Some of these analytic methods are Lyapunov’s artificial small parameter method [1], d-expansion method [2], perturbation techniques [3,4], variational iteration method (VIM) [5,6] and homotopy analysis method (HAM) [7,8]
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