Natural Heat Convection through Vertical Flat Plates by Volume of Parameter Method
Keywords:
Natural heat convection, Variation of Parameters Method (VPM), vertical parallel flat plates, third-grade fluid, non-Newtonian fluids.Abstract
Natural heat convection for the flow of a third-grade fluid through two parallel vertical infinite flat plates is investigated. As the nonlinear differential equation which governs the flow model can be obtained by using the conversation of laws, the Variation of Parameters Method (VPM) is then applied to solve the aforementioned differential equation. The VPM is used to determine the semi-exact solution to the problem. The proposed VPM is applied without any discretization, perturbation, transformation or restrictive assumptions and is free from round off errors and calculation. A numerical solution is also sought using Runge-Kutta method. The results show that the Runge-Kutta numerical solution and the VPM has an excellent agreement. Effects of flow parameters β, Eckert number, Ec and Prandtl number, Pr on the velocity profile and temperature distribution were demonstrated graphically with comprehensive discussions. Numerical results reveal the complete reliability of the proposed VPM.
