Analysis of fully developed flow and heat transfer in a vertical channel with prescribed wall heat fluxes by the homotopy analysis method

Abstract

SUMMARYThe model of combined forced and free convection in a vertical parallel-plate channel with prescribed wall heat fluxes was presented by considering a fully developed flow and by taking into account the effect of viscous dissipation. In this paper, homotopy solution for the model is obtained. Convergent region of the homotopy analysis method solution is presented. Residual error for the HAM solution is presented graphically.

Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method

“…To know the internal mechanism of complex physical phenomena exact solutions of nonlinear fractional differential equations is very much important. As a result, recently some useful methods have been established and enhanced for obtaining exact solution to the fractional evolution equations such as, the extended direct algebraic function method [3] [4], the F-expansion method [5], the Adomian decomposition method [6], the homotopy perturbation method [7] [8] [9] [10], the tanh-function method [11], the Sine-Cosine method [12], the Jacobi elliptic method [13], the finite difference method [14], the variational iteration method [15] [16], the variational method [17], the Fourier transform technique [18], the modified decomposition method [19], the Laplace transform technique [20], the operational calculus method in [21], the exp-function method [22] [23], the ( ) G G ′ -expansion method [24] [25] [26], the modified simple equation method (MSE) [27]- [34], the ( ) ( ) exp ϕ η − -expansion method [35], the sub equation method [36], the multiple exp-function method [37] [38], the simplest equation method [39], the direct algebraic function method [40] [41] [42] [43], the extended auxiliary equation method [44] etc.…”