This article is dedicated to analyzing the heat transfer in the flow of water-based nanofluids in a channel with non-parallel stretchable walls. The magnetohydrodynamic (MHD) nature of the flow is considered. Equations governing the flow are transformed into a system of nonlinear ordinary differential equations. The said system is solved by employing two different techniques, the variational iteration method (VIM) and the Runge-Kutta-Fehlberg method (RKF). The influence of the emerging parameters on the velocity and temperature profiles is highlighted with the help of graphs coupled with comprehensive discussions. A comparison with the already existing solutions is also made, which are the special cases of the current problem. It is observed that the temperature profile decreases with an increase in the nanoparticle volume fraction. Furthermore, a magnetic field can be used to control the possible separation caused by the backflows in the case of diverging channels. The effects of parameters on the skin friction coefficient and Nusselt number are also presented using graphical aid. The nanoparticle volume fraction helps to reduce the temperature of the channel and to enhance the rate of heat transfer at the wall.

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.