Computational Analysis of Unsteady Swirling Flow Around a Decelerating Rotating Porous Disk in Nanofluid
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RESEARCH ARTICLE - MECHANICAL ENGINEERING
Computational Analysis of Unsteady Swirling Flow Around a Decelerating Rotating Porous Disk in Nanofluid Talat Rafiq1 · M. Mustafa1 Received: 21 September 2019 / Accepted: 15 November 2019 © King Fahd University of Petroleum & Minerals 2019
Abstract Here, we analyze the unsteady nanofluid flow triggered around a decelerating (permeable) rotating disk immersed in an otherwise calm environment. The present model assumes that disk angular velocity follows inversely linear time dependency. By following a similarity approach, the distributions of velocity and thermal fields above the disk are estimated numerically for six nanoparticle materials, namely Ag, Cu, CuO, Fe3O4, TiO2 and Al2O3. The solutions involve a dimensionless parameter S measuring the decay rate of the disk angular velocity. We primarily focus on how solid volume fraction affects the key physical attributes, namely resisting torque, volumetric flow rate and cooling rate when unsteady action of the disk is present. Similar to pure fluid flow, there exists a critical unsteady parameter S = S∗ which corresponds to the free disk requiring no torque. For some range of S , flow field surrounding the disk revolves faster than the disk itself. Similar to the steady-state case, suction seems to contribute vitally toward heat transfer enhancement of nanoparticle working fluid. Radial and circular motions around the disk diminish, and axial velocity becomes uniform when disk is subjected to sufficient amount of suction. Keywords Decelerating disk · Rotating disk · Nanoparticle · Time-dependent suction · Resisting torque
1 Introduction Von Karman’s problem [1] of infinite rotating disk represents one of the few flows for which an explicit exact solution of Navier–Stokes equations can be sought. This is the prime reason why it has been receiving continued attention of the research community. The problem is immensely important in applications involving rotating disk electrodes, viscometers, flow between a rotor and a stator and centrifugal pumps. The centrifugal effect around the disk induces a radially outward flow which is compensated by vertically downward motion toward the disk. Von Karman’s work has led to the publication of numerous research articles in this domain. Cochran [2] revisited von Karman’s work with a view to obtain more accurate solution via power series method. An extension to the von Karman’s work was made by Benton [3] for the flow starting impulsively from rest. Benton also proposed a simple analytical–numerical method that furnished more * M. Mustafa [email protected] 1
School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan
accurate solution than the one derived by Cochran. Properties of equations, such as existence and uniqueness, were explored by McLeod [4]. Watson and Wang [5] introduced unsteadiness in von Karman’s work by assuming that angular velocity of the disk reduces as time progresses. They were able to convert full Na
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