Sains Malaysiana 51(2)(2022): 619-632

http://doi.org/10.17576/jsm-2022-5102-25

Bödewadt Flow and Heat Transfer in Nanofluid over a Permeable and Radially Stretching Disk

(Aliran Bödewadt dan Pemindahan Haba dalam Nanobendalir terhadap Cakera Telap dan Meregang secara Jejarian)

ANIS ANISAH MAHYUDDIN¹, LOK YIAN YIAN¹* & SYAKILA AHMAD²

¹Mathematics Section, School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

²School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Received: 10 March 2021/Accepted: 2 June 2021

ABSTRACT

A Bödewadt boundary layer flow and heat transfer problem in nanofluid was investigated in this study for suction/injection as well as combined effects of suction/injection and radial stretching disk. Similarity variables were introduced to transform the three-dimensional flow into a system of ordinary differential equations. Moreover, similar to the Bödewadt heat transfer problem in a viscous fluid, adequate suction is also required so that similarity solutions exist for nanofluid problems with no other boundary effects such as a partial slip or stretching disk. Both the suction and stretching disk effects can suppress the natural oscillatory behavior of flow apart from reducing the momentum and thermal boundary layer thicknesses. As expected, injection acts oppositely. However, the skin friction coefficient and heat transfer rate for Bödewadt flow increase with the increasing suction and stretching parameters. As for stagnant disk, increasing the nanoparticle volume fraction can enhance the wall shear stress, whereas nanofluid can only enhance the heat transfer when both the suction and nanoparticle volume fraction are sufficiently small. For radially stretching disk, both the local skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction increases. However, for larger suction, a smaller volume fraction of nanoparticles yielded enhanced heat transfer than the larger volume fraction of nanoparticles.

Keywords: Bödewadt flow; nanofluid; numerical solutions; radial stretching; suction/injection

ABSTRAK

Penyelidikan ini mengkaji masalah aliran sempadan Bödewadt dan pemindahan haba dalam nanobendalir bagi kes sedutan/semburan dan juga gabungan kes sedutan/semburan dan regangan jejari cakera. Pemboleh ubah keserupaan telah diperkenalkan untuk menjelmakan aliran tiga dimensi kepada sistem persamaan pembezaan biasa. Sama seperti kes pemindahan haba Bödewadt dalam cecair likat, tenaga sedutan yang mencukupi juga diperlukan agar penyelesaian keserupaan wujud untuk masalah nanobendalir tanpa kesan sempadan lain seperti slip separa atau regangan cakera. Kedua-dua kes sedutan dan regangan mempunyai kesan untuk menekan perilaku aliran berayun semula jadi dan dapat mengurangkan ketebalan lapisan sempadan momentum dan termal. Seperti yang dijangkakan, semburan bertindak sebaliknya. Pekali geseran kulit dan kadar pemindahan haba untuk aliran Bödewadt meningkat dengan peningkatan parameter penyedutan dan regangan. Untuk kes cakera statik yang tiada regangan tetapi berlakunya sedutan, peningkatan pecahan isi padu nanozarah meningkatkan geseran dinding. Walau bagaimanapun, peningkatan pemindahan haba hanya berlaku ketika nilai sedutan dan pecahan isi padu nanozarah cukup kecil. Untuk kes cakera regangan jejari, kedua-dua parameter iaitu pekali geseran kulit tempatan dan nombor Nusselt tempatan meningkat apabila pecahan isi padu nanozarah meningkat. Namun, untuk nilai sedutan yang besar, pecahan isi padu nanozarah yang lebih kecil memberikan peningkatan pemindahan haba yang lebih baik daripada pecahan isi padu nanozarah yang lebih besar.

Kata kunci: Aliran Bödewadt; nanobendalir; penyelesaian berangka; regangan jejari; sedutan/semburan

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*Corresponding author; email: lokyy@usm.my