Heat transfer and velocity in the squeezing flow between two parallel disks by Gegenbauer Wavelet Collocation Method

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O R I G I NA L

˙ Ibrahim Çelik

· Harun Kemal Öztürk

Heat transfer and velocity in the squeezing flow between two parallel disks by Gegenbauer Wavelet Collocation Method

Received: 30 January 2020 / Accepted: 11 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract In this study, the squeezing flows between parallel disks, which one disk is impermeable and the other is porous, in the presence of magnetic field are investigated by Gegenbauer Wavelet Collocation Method (GWCM). Appropriate similarity transformations may be used to convert the governing non-linear partial differential equations into non-linear ordinary differential equations. The resultant non-linear ordinary differential equations are transformed into a sequence of linear differential equations by quasilinearization technique. Velocity and temperature fields of squeezing flows between parallel disks have been obtained by Gegenbauer Wavelet Collocation Method. The effects of squeeze number (S), Hartman number (Ha), Prandtl number (Pr), and Eckert number (Ec) and suction/blowing parameter (A) are analysed through graphs for the velocity and temperature profiles. GWCM is generalized form of the Legendre, Chebyshev and second kind Chebyshev wavelets. The basic advantage of the proposed method (GWCM) is to reduce the computational work. From the numerical results, it is observed that present method is convergent even in the case of a small number of grid points. The obtained results are in good agreement with the results in literature. Keywords Heat transfer · Gegenbauer wavelets · Squeezing flow · Magnetic field · Quasilinearization technique 1 Introduction The unsteady squeezing flow of a viscous fluid stimulated significant interest among the researchers. Squeezing flow has various applications in the industrial, biological and engineering applications such as flow through arteries, food processing, polymer processing, compression, transient loading of mechanical components, injection modelling, squeezed film in power transmission, moving pistons, chocolate filler and bearings with liquid metal lubrication. Magnetohydrodynamic (MHD) fluid may be use a lubricant to prevent the unexpected variation of lubricant viscosity with temperature under certain extreme operating conditions. First study on squeezing flow under lubrication approximate was given by Stefan [1]. Rashidi et al. [2] discussed two dimensional axisymmetric squeezing flows between parallel plates. Siddiqui et al. examined effects of magnetic field in the squeezing flow between infinite parallel plates in [3]. Domairry and Aziz [4] discussed MHD effects on squeezing flow of viscous fluid between parallel disks with suction or blowing. The work in [4] was extended by Hayat et al. [5] to the squeezing flow of non-Newtonian fluids by taking second grade fluids. The characteristics of heat transfer in squeezed flow through a porous surface were studied by Mahmood et al. [6]. Duwairi et ˙I. Çelik (B) Department of Mathematics, Faculty of Arts and Sciences, Pamukka