Sains Malaysiana 49(5)(2020): 1175-1190

http://dx.doi.org/10.17576/jsm-2020-4905-23

Hall Current and Joule Heating Effects on Peristaltic Flow of a Sisko Fluid with Mild Stenosis through a Porous Medium in a Tapered Artery with Slip and Convective Boundary Conditions

(Arus Hall dan Kesan Pemanasan Joule pada Aliran Peristalsis Bendalir Sisko dengan Stenosis Lembap melalui Medium Berliang dalam Arteri Tirus dengan Syarat Gelinciran dan Syarat Sempadan Olakan)

 NABIL T.M. EL-DABE & DOAA R. MOSTAPHA*

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Received: 11 July 2019/Accepted: 15 January 2020

ABSTRACT

This work is arranged to investigate the Hall current and Joule heating effects on peristaltic flow of a Sisko fluid through a porous medium. The streaming is through tapered artery with mild stenosis. The influences of radiative heat transfer and chemical reactions are taken in consideration. Convective conditions are considered for heat and mass transfer. However, the slip conditions are adopted for the velocity distribution. The combined effects of viscous dissipation and radiation in energy expression are presented. Soret and Dufour features produce the coupled differential systems. The presumptions of the long wavelength and low Reynolds number are adopted to examine the governing equations of motion. The analytical solutions of these equations are given by two methods. The first one uses regular perturbation technique, which based on small wave number for small artery. The second one is based on utilizing the Homotopy perturbation technique. The approximate analytical solutions of the pressure rise and friction force are predestined along a numerical integration. The influences of various physical parameters of the problem are debated and depicted graphically through a set of figures. It is found that the axial velocity increases with the increase of Hall current parameter and with the decrease of Hartmann number. Also, it can be observed that the Brickmann number and Dufour number give rise to the fluid temperature. Meanwhile, reverse effect is observed towards concentration for both Schmidt number and chemical reaction number. Furthermore, the stream lines are graphically shown.

Keywords: Hall current; Joule heating; peristaltic flow; porous medium; Sisko model

ABSTRAK

Kajian ini mengkaji arus Hall dan kesan pemanasan Joule terhadap aliran peristalsis bendalir Sisko melalui medium berliang. Aliran adalah melalui arteri tirus dengan stenosis lembut. Pengaruh pemindahan haba sinaran dan tindak balas kimia dipertimbangkan. Syarat perolakan dipertimbangkan bagi pemindahan haba dan jisim. Walau bagaimanapun, syarat gelinciran digunakan dalam taburan halaju. Kesan gabungan lesapan likat dan radiasi dalam ungkapan tenaga dipersembahkan. Ciri-ciri Soret dan Dufour menghasilkan sistem persamaan pembezaan terganding. Andaian panjang gelombang dan nombor Reynolds yang rendah digunakan untuk mengkaji persamaan yang mengawal gerakan. Penyelesaian beranalisis persamaan ini diberikan oleh dua kaedah. Yang pertama menggunakan teknik usikan biasa, yang berdasarkan nombor gelombang kecil untuk arteri kecil. Yang kedua adalah berdasarkan teknik usikan homotopi. Penyelesaian analisis anggaran kenaikan tekanan dan daya geseran ditentukan menggunakan kamiran berangka. Pengaruh pelbagai parameter fizikal bagi masalah ini dibahas dan digambarkan secara grafik. Didapati bahawa halaju bertambah dengan peningkatan parameter arus Hall dan dengan penurunan nombor Hartmann. Juga, boleh diperhatikan bahawa nombor Brickmann dan nombor Dufour meningkatkan suhu bendalir. Sementara itu, kesan bertentangan diperhatikan terhadap kepekatan untuk kedua-dua nombor Schmidt dan nombor tindak balas kimia. Juga, garis arus ditunjukkan secara grafik.

Kata kunci: Aliran peristalsis; arus Hall; pemanasan Joule; medium berliang; model Sisko  

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*Corresponding author; email: doaaroshdy@edu.asu.edu.eg