Least square study of heat transfer of water based Cu and Ag nanoparticles along a converging/diverging channel

Abstract

Present study is devoted to analyze the flow and heat transfer of water-based metallic nanoparticles along a converging/diverging channel with non-parallel walls. In order to control the random motion of nanoparticles, MHD effects are also incorporate for present mechanism. The governing equations are obtained in the form of coupled nonlinear PDEs. This system is first transformed into the coupled nonlinear ODEs and then tackled through least square method. The effects of the emerging parameters on temperature and velocity profile are analyzed through graphs and tables and then comprehensive analysis is presented in results and discussion section. A detailed evaluation of outcomes is obtained via least square method (LSM), RK (order-4) and already existing results are provided. Moreover, graphical representation, the error, convergence and comparison analysis of outcomes endorsing that the least square method is extremely effective. It is observed that by increasing the nanoparticle volume fraction a significant increase in the temperature profile. Additionally, for divergent channels, wit can control the possible separation effects by the backflows via a magnetic field. The rate of heat transfer at the wall has been enhanced due to increase of nanoparticle volume fraction. The skin friction coefficient reduced due to nanoparticle volume fraction for all of the cases. Shrinking channels have greater skin friction values than stretching channels.