Impacts of Hall and heat transfer on peristaltic blood flow of a MHD Jeffrey fluid in a vertical asymmetric porous channel. (English) Zbl 1468.76080

Asha, S. K.; Deepa, C. K.

Int. J. Adv. Appl. Math. Mech. 6, No. 4, 55-63 (2019).

Summary: In this paper, we investigate the effects of hall and heat transfer on peristaltic blood flow of a MHD (Magneto hydrodynamic) Jeffrey fluid in a porous asymmetric channel. The flow is analysed by long wavelength and low Reynolds number approximations. The reduced equations are solved by using the Adomian Decomposition Method and the expressions for velocity, stream function and pressure gradient are obtained. The effect of pertinent parameters are illustrated graphically.

MSC:

76Z05	Physiological flows
76W05	Magnetohydrodynamics and electrohydrodynamics
76A05	Non-Newtonian fluids
76S05	Flows in porous media; filtration; seepage
76M99	Basic methods in fluid mechanics
80A19	Diffusive and convective heat and mass transfer, heat flow
92C35	Physiological flow

Keywords:

long wavelength approximation; low Reynolds number approximation; Adomian decomposition method; stream function; pressure gradient

References:

[1]	T. Hayat, N. Ali, and S. Asghar, Hall effects on peristaltic flow of a Maxwell fluid in a porous medium, Physics Letters A, 363 (2007) 397—403. · Zbl 1197.76126
[2]	E. M. Abo-Eladahab, E. I. Barakat and K. I. Nowar,Effects of Hall and ion-slip currents on peristaltic transport of a couple stress fluid, International Journal of Applied Mathematics and Physics, 2 (2010) 145—157.
[3]	E. M. Abo-Eldahab, E.I. Barakat and K. I. Nowar, Hall currents and ion-slip effects on the MHD peristaltic transport, International Journal of Applied Mathematics and Physics, 2 (2010) 113-123. · Zbl 1264.76137
[4]	M. H. Haroun,A mathematical study of Hall effects on peristaltic transport of hydromagnetic flow through a porous medium,Journal of Porous Media, 10 (2007) 687-700.
[5]	E. Abo-Eladhab, E. Barakat and Kh.Nowar,Hall Currents and Heat Transfer Effects on Peristaltic Transport in a Vertical Asymmetric Channel through a Porous Medium, Mathematical Problems in Engineering, 10 (2012) 2043. · Zbl 1264.76137
[6]	Kh. S Mekheiimer, and M. A. El-Kot, Influence of magnetic field and Hall currents on blood flow through a stenotic artery, Applied Mathematics and Mechanics (English Edition), 29, (2008) 1093-1104. · Zbl 1148.76363
[7]	S. Srinivas and M. Kothandapani, Peristaltic transport in an asymmetric channel with heat transfer A note, Int. Commun. Heat Mass Transfer, 35 (2008) 514-522. · Zbl 1217.76105
[8]	B. Prabhakar Reddy, MHD flow over a vertical moving porous plate with viscous dissipation by considering double diffusive convection in the presence of chemical reaction, Int. J. Adv. Appl. Math. and Mech. 2(4) (2015) 79-83. · Zbl 1359.76281
[9]	T. W. Latham, Fluid motion in a peristaltic pump, M.S. Thesis. MIT. Cambridge, MA, (1966).
[10]	A. H. Shapiro, M. Y. Jaffrin and S. L. Weinberg, Peristaltic pumping with long wavelength and low Reynolds number, J. Fluid Mech, 37 (1969) 799-825.
[11]	Y.C. Fung and C.S. Yih Peristaltic transport, Journal of Applied Mechanics, 35 (1968) 669-675. · Zbl 0182.59302
[12]	Kh. S Mekheimer, Peristaltic transport of blood under the effect of magnetic field in non-uniform channels, Appl. Math. Comput, 153 (2004) 763-777. · Zbl 1041.92006
[13]	V.P. Rathod and Laxmi Devindrappa, Peristaltic transport in an inclined asymmetric channel with heat and mass transfer by Adomian decomposition method Adv in Applied Sci and Research, 7 (2016) 83-100.
[14]	Hayman Thabet and Subhash Kender New modification of Adomian decomposition method for solving a system of nonlinear fractional partial differential equations, Int. J. Adv. Appl. Math. and Mech. 6(3) (2019) 1-13. · Zbl 1472.65115
[15]	M. Kothandapani and S. Srinivas, Peristaltic transport of a Jeffery fluid under the effect of magnetic field in an asymmetric channel, Int. J. Non-Linear Mech. 43 (2008) 915-924.
[16]	K. Vajravelu, S. Sreenadh, G. Sucharitha. and P. Lakshminarayana., Peristaltic transport of a conducting Jeffrey fluid in an inclined asymmetric channel, International Journal of Biomathematics, 7 (2014) 145-164. · Zbl 1305.76009
[17]	T Hayat. and N. Ali. “Peristaltic motion of a Jeffrey fluid under the effect of magnetic field in tube”.Commun Nonlinear Sci Numer Simul, 313 (2008) 43-52. · Zbl 1221.76016
[18]	K. Vajravelu, S. Sreenadh and P. Lakshminarayana, The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum, Commu. in Nonlin. Sci and Num Sim, 16 (8) (2011) 3107-3125. · Zbl 1343.76073
[19]	A. Ebaid, E. F. Elshehawey, N. T. Eldabe, and E. M. Elghazy, Peristaltic transport in an asymmetric channel through a porous medium, Applied Mathematics and Computation, 182(1) (2006) 140-150. · Zbl 1149.76670
[20]	M. Kothandapani and S. Srinivas, Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium, Phys. Lett. A, 372 (2008) 1265-1276. · Zbl 1217.76105
[21]	S. R. Mahmouda, N. A. S. Afifib and H. M. Al-Isedec Effect of Porous Medium and Magnetic Field on Peristaltic Transport of a Jeffrey Fluid, Int. Journal of Math. Analysis, 5 (2011) 1025 - 1034. · Zbl 1243.76101
[22]	Santosh Nallapu and G Radhakrishnamacharya, Jeffrey fluid flow through porous medium in the presence of magnetic field in narrow tubes, International Journal of Engineering Mathematics, (2014) http://dx.doi.org/10.1155/2014/713-831. · Zbl 1381.76345
[23]	N.D. Patel and Ramakanta Meher, Analytical investigation of Jeffery-Hemal flow with magnetic field by differential transform method, Int. J. Adv. Appl. Math. and Mech. 6(1) (2018) 1-9. · Zbl 1469.76149