Entropy analysis of Hall current and thermal radiation influenced by cilia with single- and multi-walled carbon nanotubes

The present investigation explores the significance of creeping viscous nanofluids in an axi-symmetric channel influenced by metachronal waves containing magnetohydrodynamics and Hall current. Heat transport analysis is also performed to derive the impact of thermal radiation on internal heat source phenomena. The use of mathematical formulation resulted in a set of nonlinear coupled partial differential equations. The governed differential system is transformed into an ordinary differential system by considering similar variables. Exact solutions in the closed form have been derived for the temperature, momentum and pressure gradient. Moreover, entropy generation due to heat transfer, thermal radiation and magnetic effects has been measured. The graphical results have been presented to interpret sundry parameters of interest. Streamlines and isotherms are also plotted against the multi-walled carbon nanotube. For the validation of our results, a comparison table is presented. It is also seen that entropy of the system increases and the Bejan number decreases with an increase in the Brinkman number.