Entropy Production in Electroosmotic Cilia Facilitated Stream of Thermally Radiated Nanofluid with Ohmic Heating

Abstract

No thermal process, even the biological systems, can escape from the long arms of the second law. All living things preserve entropy since they obtain energy from the nutrition they consume and gain order by producing disorder. The entropy generation in a biological and thermally isolated system is the main subject of current investigation. The aim is to examine the entropy generation during the convective transport of a ciliated nano-liquid in a micro-channel under the effect of a uniform magnetic field. Joint effects of electroosmosis and thermal radiation are also brought into consideration. To attain mathematical simplicity, the governing equations are transformed to wave frame where the inertial parts of the transport equations are dropped with the use of a long-wavelength approximation. This finally produces the governing equations in the form of ordinary differential equations which are solved numerically by a shooting technique. The analysis reports that the cilia motion contributes to enhance the flow and heat transfer phenomena. An enhancement in the flow is observed near the channel surface for higher cilia length and for smaller values of the electroosmotic parameter. The entropy generation in the ciliated channel is observed to be lessened by intensifying the thermal radiation and decreasing the Ohmic heating. The extended and flexible cilia structure contributes to augment the volumetric flow rate and to drop the total entropy generation in the channel.

Keywords: Carreau nanofluid; Joule heating; electroosmotic ciliary flow; entropy analysis; magnetic field; thermal radiation.

Figure 1

Schematic diagram of flow through the electroosmotic ciliated pump.

Figure 6

Pressure gradient at varying ε.

Figure 7

Pressure gradient at varying K.

Figure 8

Pressure gradient at varying We.

Figure 9

Pressure-rise per wavelength at varying ε.

Figure 10

Effect of variation in K on pressure rise per wavelength.

Figure 11

Temperature profile at various Pr.

Figure 12

Temperature profile at various R_n.

Figure 13

The temperature field for various values of S_p.

Figure 14

The temperature field for various values of K.

Figure 15

Entropy generation number for different values of R_n.

Figure 16

Entropy generation number for different values of S_p.

Figure 17

Entropy generation number for different values of ε.

Figure 18

Entropy generation number for different values of α.

Figure 19

The Bejan number at various Ha.

Figure 20

The Bejan number at various R_n.

Figure 21

The Bejan number for different values of S_p.

Figure 22

The Bejan number for different values of Pr.

Figure 23

The entropy number when Br = 5, ε = 0.2, α = 0.3, We = 0.01, β = 0.1, K = 2, R_n = 3, Ha = 1, n = 0.2, and Ec = 0.05.

Figure 24

The Bejan number when Br = 5, ε = 0.2, α = 0.3, We = 0.01, β = 0.1, K = 2, R_n = 3, Ha = 1, n = 0.2, and Ec = 0.05.

Figure 25

Streamlines for variation in K when n = 0.2 We = 0.05, α = 0.45, ε = 4, β = 0.1, U_HS = 2, Ha = 1, Q = 0.4. (a) K = 2; (b) K = 4.

Figure 26

Streamlines for variation in Ha when n = 0.2 We = 0.05, α = 0.45, ε = 4, β = 0.1, U_HS = 2, K = 2, Q = 0.4. (a) Ha = 0.5; (b) Ha = 1.2.

Figure 27

Streamlines for variation in ε when n = 0.2 We = 0.05, α = 0.45, Ha = 1, β = 0.1, U_HS = 2, K = 2, Q = 0.4. (a) ε = 0.4; (b) ε = 0.6.

Figure 2

Axial velocity u(y) for various Ha.

Figure 3

Axial velocity u(y) for various U_HS.

Figure 4

Axial velocity u(y) for various K.

Figure 5

Axial velocity u(y) for various ε.