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

Abstract

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.

Peristaltic heat transport analysis of carbon nanotubes in a flexible duct due to metachronal waves of cilia

“…\end{equation}$$Following transformation are useful to transform the flow from unsteady $$(\bar{R}, \bar{Z})$$ to steady $$(\bar{r},. \bar{z})$$ flow [14]. $$$$\begin{equation} \bar{Z}=\bar{z}+c\bar{t},\quad \bar{R}=\bar{r}, \quad \bar{U}=\bar{u},\quad \bar{W}=\bar{w}+c, \quad \bar{P}(\bar{Z},\bar{R},\bar{t})=\bar{p}(\bar{z},\bar{r},\bar{t}), \end{equation}$$$$The foundational system of equations are of the form [15]: $$$$\begin{align} \frac{\partial \bar{u}}{\partial \bar{r}}+\dfrac{\bar{u}}{\bar{r}}+\dfrac{\partial \bar{w}}{\partial \bar{z}}=0, \end{align}$$$$ …”

“…Following transformation are useful to transform the flow from unsteady ( R, Z) to steady ( r, . z) flow [14].…”

“…where ū and w are the velocity components in the radial r and axial z directions, respective. Thermal properties of the nanofluid are defined as follows [14]:…”

“…Iqbal et al [13] investigates the boundary layer flow of MHD fluid influenced by transverse and applied magnetic field over a stretching sheet. Recently, impact of magnetic field on nanofluid along with the heat transfer mechanism has been investigated by several authors [14][15][16][17][18][19].…”

Entropy Generation Analysis and Radiated Heat Transfer in MHD (Al2O3-Cu/Water) Hybrid Nanofluid Flow

“…Results showed that entropy generation amplifies significantly for diffusive variable, Brinkman number, and concentration ratio parameter whereas Bejan number decreases for all these parameters. In this regard, some investigations on entropy generation analysis for different flows and geometries under various physical aspects are reviewed (see articles [ 34 , 35 , 36 ]). Moreover, use of an analytical technique for the solution of the mathematical model is aimed by using homotopy analysis method (HAM).…”