## THERMAL SCIENCE

International Scientific Journal

### ENTROPY ANALYSIS IN CILIATED INCLINED CHANNEL FILLED WITH HYDROMAGNETIC WILLIAMSON FLUID FLOW INDUCED BY METACHRONAL WAVES

**ABSTRACT**

This study reveals the entropy analysis of hydromagnetic pumping flow of Williamson fluid through a 2-D symmetric channel carrying cilia. Propulsive metachronal waves are mobilized by whipping and beating of uniformly distributed cilia which follow elliptic trajectory movements in the parallel direction of flow. The flow is resisted by a uniform transverse magnetic field. The entire study is carried out in wave frame of reference. After implying lubrication approximations, the governing equations of the present flow problem are solved by perturbation method. Effects of physical parameters of interest on various flow quantities, the total entropy generation number and the Bejan number are plotted and discussed. It is observed that fluid velocity and temperature is enhanced in the core channel region for small values of Hartmann number and cilia length. It is also noticed that the entropy generation and the Bejan number are decreasing function of magnetic field. Near the channel center, irreversibility due to fluid friction is dominant but at the channel wall heat transfer irreversibility effects are observed to be substantial. The confined bolus reduces in size for small values of cilia length parameter and large values of Hartmann number.

**KEYWORDS**

PAPER SUBMITTED: 2019-10-06

PAPER REVISED: 2020-05-08

PAPER ACCEPTED: 2020-05-13

PUBLISHED ONLINE: 2020-06-07

**THERMAL SCIENCE** YEAR

**2021**, VOLUME

**25**, ISSUE

**Issue 5**, PAGES [3687 - 3699]

- Pablo, J. L., et al., Progress in ciliary ion channel physiology, Journal of General Physiology, 149 (2017), 1, pp. 37-41
- Satir, P. and Christensen, S. T., Structure and Function of Mammalian Cilia, Histochem Cell Biol., 129 (2008), 6, pp. 687-693
- Eddy, C. A. and Pauerstein, C. J., Anatomy and Physiology of the Fallopian Tube, Clinical Obstetrics and Gynecology, 23 (1980), 4, pp. 1177-1194
- Gahazal, S., et al., Egg Transport and Fertilization, in, The Global Library of Women's Medicine (ISSN: 1756-2228), 2009, DOI 10.3843/GLOWM.10317
- Lehti, M. S. and Sironen, A., Formation and Function of Sperm Tail Structures in Association with Sperm Motility Defects, Biology of Reproduction, 97 (2017), 4, pp. 522-536
- Wheway, G., Signaling Through the Primary Cilium, Front Cell Dev Biol., 6 (2018), 8, pp. 1-13
- Brennen, C., An Oscillating-boundary-layer Theory for Ciliary Propulsion, J. Fluid Mech., 65 (1974), 4, pp. 799-824
- Qiu. T., et al., Swimming by Reciprocal Motion at low Reynolds Number, Nature Communications, 5 (2014), 1, pp. 5119
- Eytan, O. and Elad, D., Analysis of Intra-uterine Fluid Motion Induced by Uterine Contractions, Bull. Math. Biol., 61 (1999), 2, pp. 221-238
- Farooq, A. A., et al., On the Propulsion of Micropolar Fluid Inside a Channel Due to Ciliary Induced Metachronal Wave, Appl. Math. Comput., 347 (2019), pp. 225-235
- Farooq, A. A. and Siddiqui, A. M., Mathematical Model for the Ciliary-induced Transport of Seminal Liquids Through the Ductuli Efferentes, Int. J. Biomath., 10 (2016), 03, pp. 1750031
- Ponalagusamy, R., Mathematical Analysis of Flow of Non-Newtonian Fluid Due to Metachronal Beating of Cilia in a Tube and ts Physiological Applications, Appl. Math. Comput., 337 (2018), pp. 545-561
- Ezzati, M., et al., Tubal Transport of Gametes and Embryos: A Review of Physiology and Pathophysiology, J Assist Reprod Genet., 31 (2014), 10, pp. 1337-1347
- Stud, V. K., et al., Pumping action on blood by a magnetic field, Bull. Math. Biol., 39 (1977), 3, pp. 385-390
- Maqbool, K., et al., Exact Solution of Cilia Induced Flow of a Jeffrey Fluid in an Inclined Tube, Springerplus, 5 (2016), 1, pp. 1379
- Hayat, T., et al., Magnetohydrodynamic Flow of a Carreau Fluid in a Channel with Different Wave Forms, Zeitschrift für Naturforschung A, 66 (2011), 3-4, pp. 215-222
- Prakash, J., et al., Non - linear Blood Flow Analysis on MHD Peristaltic Motion of a Williamson Fluid in a Micro Channel, AIP Conference Proceedings, 2112 (2019), 1, 020048
- Abou-Zeid, M., Homotopy Perturbation Method for MHD Non-Newtonian Nanofluid Flow through a porous medium in Eccentric Annuli With Peristalsis , Thermal Science, 21 (2017), 5, pp. 2069-2080
- Saleem, N. and Munawar, S., A Mathematical Analysis of MHD Blood Fow of Eyring-Powell Fluid Through a Constricted Artery, Int. J. Biomath., 09 (2015), 02, pp. 1650027
- Bejan, A., Study of Entropy Generation in Fundamental Convective Heat Transfer, J. Heat Transf.-Trans. ASME, 101 (1979), 4, 718-725
- Bejan, A., Entropy Generation Minimization, Boca Raton, 1996, New York, CRC Press
- Munawar, S. and Saleem, N., Thermal Analysis of an Eyring-Powell Fluid Flow Through a Constricted Channel, Thermal Science, 24 (2020), 2, pp. 1207-1216
- Mehmood, A. et al., Entropy Analysis in Moving Wavy Surface Boundary-Layer, Thermal Science, 23 (2019), 1, pp. 233-241
- Munawar, S., Thermal analysis of the flow over an oscillatory stretching cylinder, Phys. Scr., 86 (2012), 6, pp. 065401
- Souidi, F., et al., Entropy Generation Rate for a Peristaltic Pump, J. Non-Equilib. Thermodyn., 34 (2009), 2, pp. 171-194
- Akbar, N. S., Entropy Generation and Energy Conversion Rate for the Peristaltic Flow in a Tube with Magnetic Field, Energy, 82 (2015), pp. 23-30
- Munawar, S., et al., Second-law Analysis in the Peristaltic Flow of Variable Viscosity Fluid, Int. J. Exergy, 20 (2016), 2, pp. 170-185
- Saleem, N., Entropy Production in Peristaltic Flow of a Space Dependent Viscosity Fluid in Asymmetric Channel, Thermal Science, 22 (2018), 6, pp. 2909-2918
- Munawar, S. and Saleem, N., Entropy analysis in cilia driven pumping flow of hyperbolic tangent fluid with magnetic field effects, Fluid Dyn. Res., 52 (2020), pp. 025503
- Ramesh, K., et al., Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids. J Propul. Power., 8 (2019), pp. 221-233
- Bejan, A., Second law analysis in heat transfer, Energy, 5 (1980), pp. 720-723
- Adesanya, S.O. and Makinde, O.D., Thermodynamic analysis for a third grade fluid through a vertical channel with internal heat generation. J. Hydrodyn. 27 (2015), pp. 264-272
- Munawar, S. and Saleem, N., Entropy Analysis of an MHD Synthetic Cilia Assisted Transport in a Microchannel Enclosure With Velocity and Thermal Slippage Effects, Coatings., 10 (2020), pp. 414