## THERMAL SCIENCE

International Scientific Journal

### HEAT AND MASS TRANSFER EFFECTS ON THE PERISTALTIC FLOW OF SISKO FLUID IN A CURVED CHANNEL

**ABSTRACT**

In the present study heat and mass transfer phenomena in flow of non-Newtonian Sisko fluid induced by peristaltic activity through a curved channel have been investigated numerically using an implicit finite difference scheme. The governing equations are formulated in terms of curvilinear co-ordinates with appropriate boundary conditions. Numerically solution is carried out under long wavelength and low Reynolds number assumptions. The velocity field, pressure rise per wavelength, stream function, temperature, and concentration fields have been analyzed for the effects of curvature parameter, viscosity parameter, and power law index. Additionally, the computation for heat transfer coefficient and Sherwood number carried out for selected thermophysical parameters. The main results that are extracted out this study is that for strong shear-thinning biofluids (power-law rheological index, n < 1) the flow exhibits the boundary-layer character near the boundary walls. Both temperature and mass concentration are found to increase with increasing the generalized ratio of infinite shear rate viscosity to the consistency index. The amplitude of heat transfer coefficient and Sherwood number is also an increasing function of generalized ratio of infinite shear rate viscosity to the consistency index.

**KEYWORDS**

PAPER SUBMITTED: 2016-10-18

PAPER REVISED: 2017-04-07

PAPER ACCEPTED: 2017-04-11

PUBLISHED ONLINE: 2017-05-06

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**1**, PAGES [331 - 345]

- Bandopadhyay, A., Tripathi, D. and Chakraborty, S., Electroosmosis-modulated peristaltic transport in microfluidic channel, Phy. of Fluids., 28 (2016) pp. 052002.
- Tripathi, D., Bhushan, S. and Bég, O.A., Transverse magnetic field driven modification in unsteady peristaltic transport with electrical double layer effects, Colloid Surface A, 506 (2016) pp. 32-39.
- Latham, T.W., Fluid motion in peristaltic pump, MS Thesis, MIT Press, Cambridge, MA, 1966.
- Shapiro, A.H., Jaffrin, M.Y. and Weinberg, S.L., Peristaltic pumping with long wavelength at low Reynolds number, J. of Fluid Mech., 37 (1969) pp. 799-825.
- Fung, Y.C. and Yih, C.S., Peristaltic transport, Trans. ASME Journal of App. Mech., 33 (1968) pp. 669-675.
- Barton, C. and Raynor, S., Peristaltic flow in tubes, The Bulletin of Math. Biophy., 30 (1968) pp. 663-680.
- Jaffrin, M.Y., Inertia and streamline curvature effects in peristaltic pumping, Int. J. of Eng. Sci., 11 (1973) pp. 681-699.
- Jaffrin, M.Y., Shapiro, A.H., Peristaltic pumping, Annual Review of Fluid Mech., 3 (1971) pp. 13-37.
- Mittra, T.K. and Parsad, S.N., Interaction of peristaltic motion with Poiseuille flow, The Bulletin of Math. Bio., 36 (1974) pp. 127-141.
- Srivastava, L.M. and Srivastava, V.P., Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube, J. of Biomech., 18 (1985) pp. 247-253.
- Brown, T.D., Hung, T.K., Computational and experimental investigations of two-dimensional nonlinear peristaltic flows, J. of Fluid Mech., 83 (1977) pp. 249-272.
- Takabatake, S., Ayukawa, K., Numerical study of two-dimensional waves, J. of Fluid Mech., 122 (1982) pp. 439-465.
- Takabatake, S., Ayukawa, K., Mori, A., Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency, J. of Fluid Mech., 193 (1988) pp. 267-283.
- Raju, K.K., Devanathan, R., Peristaltic motion of non-Newtonian fluid, Acta, 11 (1972) pp. 170-178.
- Raju, K.K., Devanathan, R., Peristaltic motion of non-Newtonian fluid II, Viscoelastic Fluid Rheol, Acta, 13 (1974) pp. 944-948.
- Siddiqui, A.M., Provost, A., Schwarz, W.H., Peristaltic pumping of second order fluid in a planar channel, Rheol. Acta, 30 (1991) pp. 249-262.
- Siddiqui, A.M., Schwarz, W.H., Peristaltic flow of second order fluid in tubes, J. of Non-Newtonian Fluid Mech., 53 (1994) pp. 257-284.
- Hayat, T., Wang, Y., Siddiqui, A.M., Hutter, K., Asghar, S., Peristaltic transport of third order fluid in a cylindrical tube, Math. Models and Methods in App. Sci., 12 (2002) pp. 169-176.
- Hayat, T., Wang, Y., Siddiqui, A.M., Hutter, K., Peristaltic motion of Johnson-Segalman fluid in a planar channel, Math. Problems in Eng., 1 (2003) pp. 1-23.
- Hayat, T., Wang, Hutter K, Asghar, S., Siddiqui, A.M., Peristaltic transport of an Oldroyd-B fluid in a planar channel, Math. Problems in Eng., 4 (2004) pp. 347-376.
- Srinivasacharya, D., Mishra, M., Rao, A.R., Peristaltic pumping of a micropolar fluid in a tube, Acta Mech., 161 (2003) pp. 165-178.
- Mekheimer, Kh.S., Peristaltic transport of a Newtonian fluid through a uniform and non-uniform annulus, The Arabian J. of Sci. and Eng., 30 (2005) pp. 71-83.
- Haroun, M.H., Nonlinear peristaltic flow of a fourth grade fluid in an inclined asymmetric channel, Comp. Material Sci., 39 (2007) pp. 324-333.
- Vajravelu, K., Radhakrishnamacharya, G., Radhakrishnamurty, V., Peristaltic flow and heat transfer in a vertical porous annulus with long wavelength approximation, Int. J. of Nonlinear Mech., 42 (2008) pp. 754-759.
- Tripathi, D., Bég, O.A., A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping, Proceedings of the Institution of Mechanical Engineers, Part H, J. of Eng. in Med., 226 (2012) pp. 631-644.
- Tripathi, D. and Bég, O.A., Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic flood bolus through the human esophagus, Int. J. of Thermal Sci., 70 (2013) pp. 41-53.
- Tripathi, D. and Bég, O.A., Mathematical modelling of peristaltic propulsion of viscoplastic bio-fluids, Proceedings of the Institution of Mechanical Engineers, Part H, J. of Eng. in Med., 228 (2014) pp. 67-88.
- Nabil T. M. El-dabe, Sallam N. S., Mona A. A., Mohamed Y. A., Assmaa A. H., Effects of chemical reaction with heat and mass transfer on peristaltic flow of Jeffrey fluid through porous medium in an inclined asymmetric channel with Hall currents. International Journal of Applied Mathematics and Physics, 3(2) (2011), pp. 155-167.
- Tanveer A., Hina S., Hayat T., Mustafa M., Ahmed B., Effects of the Cattaneo-Christov heat flux model on peristalsis. Engineering applications of computational fluid mechanics, 10 (2016), pp. 373-383.
- Walker, S.W. and Shelley, M.J., Shape optimization of peristaltic pumping, J. of Comp. Phy., 229 (2010) pp. 1260-1291.
- Ceniceros, H.D. and Fisher, J.E., Peristaltic pumping of a viscoelastic fluid at high occlusion ratios and large Weissenberg numbers, J. of Non-Newtonian Fluid Mech., 171, (2013) 31-41.
- Böhme, G. and Müller, A., Analysis of non-Newtonian effects in Peristaltic pumping, J. of Non-Newtonian Fluid Mech., 201 (2013) pp. 107-119.
- Shit, G.C. and Roy, M., Hydromagnetic effect on inclined peristaltic flow of a couple stress fluid, Alex. Eng. J., 53 (2014) pp. 949-958.
- Abbas M.A., Bai Y.Q., Bhatti M.M. and Rashidi M.M., Three dimensional peristaltic flow of hyperbolic tangent fluid in non-uniform channel having flexible walls, Alexandria Engineering Journal 55 (2016) pp. 653-662.
- Abbas M.A., Bai Y.Q., Rashidi M.M. and Bhatti M.M., Application of drug delivery in magnetohydrodynamics peristaltic blood flow of nanofluid in a non-uniform channel, Journal of Mechanics in Medicine and Biology, 16 (2016)1650052.
- Abbas M.A., Bai Y.Q., Rashidi M.M. and Bhatti M.M., Analysis of entropy generation in the flow of peristaltic nanofluids in channels with compliant walls, Entropy (2016) 18 (3), 90.
- Sato, H., Kawai, T., Fujita, T. and Okabe, T.M., Two dimensional peristaltic flow in curved channels, The Japan Society of Mechanical Engineers, 66 (2000) pp. 679-685.
- Ali, N., Sajid, M. and Hayat, T., Long wavelength flow analysis in a curved channel, Zeitschrift für Naturforsch, 65a (2010) pp. 191-196.
- Hayat, T., Abbasi, F.M., Ahmed, B. and Narla, V.K., Peristaltic Transport of Carreau-Yasuda Fluid in a Curved Channel with Slip Effects, PLos One, (2011) pp. 5126-5136.
- Ramanamurthy, J.V., Prasad, K.M. and Narla, V.K., Unsteady peristaltic transport in curved channels, Phy. of Fluids, 25 (2013) pp. 091903-091920.
- Kalantari, A., Sadeghy, K. and Sadeqi, S., Peristaltic flow of non-Newtonian fluids through curved channels: a Numerical Study, Annual Transactions of the Nordic Rheo. Society, 21 (2013) pp. 163-170.
- Ali, N., Sajid, M., Javed, T. and Abbas, Z., Heat transfer analysis of peristaltic flow in a curved channel, Int. J. of Heat and Mass Trans., 53 (2010) pp. 3319-3325.
- Hayat, T., Hina, S., Hendi, A.A. and Asghar, S., Effect of wall properties on the peristaltic flow of a third grade fluid in a curved channel with heat and mass transfer, Int. J. of Heat and Mass Trans., 54 (2011) pp. 5126-5136.
- Hina, S., Hayat, T. and Asghar, S., Heat and mass transfer effects on the peristaltic flow of Johnson-Segalman fluid in a curved channel with compliant walls, Int. J. of Heat and Mass Trans., 55 (2012) pp. 3511-3521.
- Wang, Y., Hayat, T., Ali, N. and Oberlack, M., Magneto hydrodynamic peristaltic motion of a Sisko fluid in a symmetric or asymmetric channel, Phy. A, 387 (2008) pp. 347-362.
- Ali, N., Wang, Y., Hayat, T. and Oberlack, O., Slip effects on the peristaltic flow of a third grade fluid in a circular cylindrical tube, J. of App. Mech., 76 (2009) pp. 1-10.
- Ali, N., Javid, K., Sajid, M. and Hayat, T., New concept about existence of Hartmann boundary layer in peristalsis through Curved Channel-Asymptotic solution, Meccanica, 51 (2016) pp. 1783-1795.