Abstract
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.
Highlights
Flow through non-parallel walls is an important area of research due to its many practical, industrial, physical and biological applications, such as flows through rivers and canals
In the study under consideration, we examined a further extended form of the same problem dealing with the nanofluid flow under the influence of magnetohydrodynamic forces
The Maxwell-Garnett model for the effective thermal conductivity of nanofluids is used in this problem as [14]: knf kf
Summary
Flow through non-parallel walls is an important area of research due to its many practical, industrial, physical and biological applications, such as flows through rivers and canals. Several researchers from all over the world have used the said problem to formulate and present the various properties of flows over the stretching/shrinking surfaces that can be seen in [6,7,8] and some of the references therein. The experimental results have proven that the thermal properties of traditional fluids can be enhanced appreciably by using the said technique After this groundbreaking idea, many models were presented by various researchers that had incorporated the Brownian motion and thermophoresis effects. Turkyilmazoglu [38] extended the traditional Jeffery-Hamel flow problem to a case incorporating stretching/shrinking walls. He studied the heat transfer effects on the flow. A comprehensive graphical description of the effects of the various parameters on the velocity and temperature profiles is presented coupled with some detailed discussions
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