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.

We have investigated a two-dimensional radiative flow of a boundary layer nature. The fluid under consideration is carbon nanotube (CNT)-based nanofluid and it flows over a curved surface. The heat transfer through the flow is analyzed under the influence of internal heat generation. Water (base fluid) along with single or multi-walled carbon nanotubes is taken to compose the nanofluid. After introducing the suitable similarity variables, the consequent equations are reduced to a system of nonlinear ordinary differential equations. The solution to the system is computed by using the shooting method accompanied by Runge–Kutta–Fehlberg algorithm. Various parameters, emerging in the governing equations, influences the flow and heat transfer distribution. These changes are captured and portrayed in the form of graphs. The changes in local rate of heat transfer and skin friction coefficient are also enlisted. To ensure the correctness of applied numerical scheme, the results are compared with some already existing studies.

An innovative concept of water-based Cu–Al₂O₃ hybrid nanofluid has been employed to investigate the behavior of flow and heat transfer inside a rectangular channel whose permeable walls experiences dilation or contraction in height. The transformed set of ordinary differential equations is then solved by a well-known Runge–Kutta–Fehlberg algorithm. The analysis also includes three different shapes of copper nanocomposites, namely, platelet, cylinder and brick- shaped. The impact of various embedded parameters on the flow and heat transfer distributions have been demonstrated through the graphs. All the flow properties, temperature profile and rate of heat transfer at the walls are greatly influenced by the presence of copper nanoparticles. Furthermore, it was observed that the platelet shaped nanocomposites provide a better heat transfer ability as compared to the other shapes of nanoparticles.

The colloidal analysis for H₂O and EG (Ethylene Glycol) by considering the influence of radiative heat flux and viscous dissipation is not performed so far. This study is performed to fill up this gap. Therefore, the flow of water and ethylene glycol functionalized magnetite nanoparticles over a moving wedge is examined. For thermal enhancement, two different magnetite nanoparticles, namely ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ (Cobalt ferrite) and $\mathrm{Mn}-{\mathrm{ZnFe}}_2{\mathrm{O}}_4$ ( $\mathrm{Mn}-\mathrm{Zn}$ ferrite), diluted in the base fluids. Self-similar flow model of a nonlinear nature, containing the volume fraction of nanoparticles is obtained by using compatible similarity variables. For mathematical treatment of the model, the Runge-Kutta scheme is utilized, coupled with shooting techniques. The results for flow characteristics and significant physical parameters are graphically examined. A comprehensive comparative analysis has been made, which proved the reliability of the study.

The modification of the expansion method, namely, the New Modified Simple Equation Method is presented and subsequently implemented on nonlinear partial differential equations. The implementation of the new modification is demonstrated by solving Landau-Ginburg-Higgs equation and Cahn-Allen equation, as a result many new and more general multiple wave solution consisting of Hyperbolic function solutions, trigonometric function solutions and rational function solutions are obtained. Also double solitary wave solutions are found by substituting the different values for some parameters. The method appears to be straightforward and powerful by means of symbolic computational system. Keywords: New Modified Simple Equation Method, Multiple wave solutions, Landau-Ginburg-Higgs equation, Cahn-Allen equatio