Thermophoretic particle deposition in time-dependent flow of hybrid nanofluid over rotating and vertically upward/ downward moving disk
Introduction
The fluids that are capable of transferring heat are widely used in industries. These fluids are considered to be functioning fluid in electronic devices, machinery systems and have numerous applications involving the elimination and accumulation of thermal energy from one part of machine to another. However, the low thermal conductivity of these fluids is the main complexity facing in heat transfer phenomenon. But, in some particles the thermal conductivity is higher than base liquids. These particles with size less than 100 nm are suspended in base fluids which exhibits high thermal behavior and comes under special category of fluids that helps in obtaining efficient energy during transfer of heat called as nanofluids. Hybrid nanofluids provides highly efficient thermal energy compared to that of ordinary nanofluids. This is prepared by the process of adding two or more diverse nanoparticles in a single base fluid. Recently, Ramesh et .al [1] scrutinised the mathematical model for the hybrid nanofluid flow. The foremost characteristics of the base fluid and nanoparticles are tabulated in this paper. The impact of several physical parameters on both nanofluid and hybrid nanofluid was represented through graphically by Kumar et .al [2]. Babazadeh et .al [3] scrutinized the heat transportation phenomenon in hybrid nanofluid with magnetic effect. Muhammad et .al [4] considered hybrid nanofluid with suspended copper oxide nanoparticle and Carbon nanotubes in the base fluid water. Here, they discussed the thermophysical features of nanoparticles and water. By using single and dual phase nanofluid models Turkyilmazoglu [5] scrutinised the slip flow in concentric annuli. Waini et .al [6] used a cylinder having the property of stretching and shrinking to study the flow of hybrid nanofluid. Turkyilmazoglu [7] deliberated the hydrodynamic linear stability on nanofluid flow. Radhika et .al [8] explored the hybrid nanofluid flow with dust particles suspension on taking account of melting effect. Several researchers used ferrite nanoparticle suspension in different base fluids to analyze the thermal behaviour of these nanoparticles in the fluid flow through different surfaces [9], [10], [11].
Thermophoresis mechanism notices to the system that micron-sized elements achieve speed in the direction of diminishing the thermal gradients and are suspended in non-isothermal gas. The theoretical and experimental understanding of thermophoretic particle deposition is significant, because of its wide range of industrial and laboratory applications. In recent years, many research articles involving thermophoretic particle deposition have been published. Recently, Rahman [12] imposed magnetic effect on the nanofluid flow over the rotating system and enunciated the thermophoretic particle deposition. Doh and Muthtamilselvan [13] deliberated the flow of micropolar fluid through rotating disk with deposition of thermophoretic particle. Alam et .al [14] meticulously depicted the heat and mass transfer of a fluid flow through disk. Hafeez et .al [15] considered a rotating disk to elucidate the Oldroyd-B liquid flow in the occurrence of thermophoretic particle deposition. Shehzad et .al [16] examined the fluid flow with the help of a rotating disk in the occurrence of thermophoretic particle deposition..
The study of fluid flow through a rotating disk has been a topic of major research for the past decade. This geometrical shaped disk has been related with heat transfer characteristics which is the main applications in lots of engineering processes. The flow of magnetized fluid through a disk which is spinning with an angular velocity Ω was analysed by Turkyilmazoglu [17]. Turkyilmazoglu [18] deliberated the impact of unvarying centrifugal electric field on the MHD liquid flow caused by a rotating disk. Prasannakumara et .al [19] explained the transfer of heat and fluid flow with the help of a rotating disk. The transfer of heat over a rotating disk which moves vertically during the fluid flow was analysed by Turkyilmazoglu [20]. Hafeez et .al [21] determined the flow pattern of Oldroyd-B liquid caused due to a rotating disk on taking account of modified Fourier heat flux model with chemical reaction. Khan et .al [22] scrutinized the flow of Maxwell liquid with magnetic field through an expansion/contraction rotating disk. The flow model in various mechanical equipment cannot be described by an ordinary equation. The viscous property not only depend on the shear rate but it also depends on time in which the fluid has been exposed to shearing. Recently, Hamid et .al [23] utilized a plate to analyse the impact of natural convective phenomenon on the MHD time dependent Prandtl fluid flow. Ahmad et .al [24] used two plates that are placed parallel to each other and demonstrated the time dependent fluid flow. The mixed convective heat transfer on the Maxwell fluid flow which is depending on time was reported by Haider et .al [25]. Hashim et .al [26] proposed a research which determines the heat transfer process on the time dependent Williamson nanofluid flow. The nature of second grade nanofluid which is time dependently flowing in three dimensions was illustrated by Ahmad et .al [27].
In this paper, we investigated the three-dimensional hybrid nanofluid flow past an expansion/contraction moving rotating disk with thermophoretic particle deposition, which constitutes a novelty of the present work. The pertinent nonlinear problem is solved numerically and results discussed comprehensively. Such model for fluid flow with hybrid nanoparticle suspension and thermophoretic particle deposition has not been described in the works earlier to our knowledge. It very well may be trusted that the investigation of fluid with suspension of two nanoparticles is useful in electronic devices, machinery systems, disease treatment and in various medical equipment's.
Section snippets
Mathematical formulation
Consider the thermophoretic particle deposition on fluid flow instigated by a rotating disk in up and down motion, which is thought to be made immeasurable. The disk rotates at an angular velocity Ω(t), which is a major cause of fluid flow. The axisymmetric flow thinking leads to the removal of the available azimuthal elements. The surface of the rotating disk is sustained at the constant temperature Tw(t) and the temperature of the free stream is T∞ such that, T∞ > Tw(t). The filtering of disk
Physical concern parameters
Velocity of thermophoretic particle deposition, Velocity of thermophoretic and Stanton number are the visible parameters from an engineering point of view. Thermophoretic cycles associated with horizontal and axial directions on the surface of the disk are calculated as Rahman and Postelnicu [30].
The axial thermophoretic dimensionless velocity is given by
The thermophoretic velocity of particle deposition at disk surface is demarcated by
Results and discussions
The modelled PDEs are converted to ODEs with consideration of similarity variables. The reduced set of ODEs are coupled and nonlinear, makes difficulties in closed form solutions. To sidestep the difficulties, reduced ODEs with boundary constraints have been numerically solved by using RKF-45 method by adopting shooting technique. We discarded the equation containing the pressure term from the system as it can be utilized to calculate pressure when F and H are known in other expressions. Here,
Final remarks
Deposition of thermophoretic particles are basic processes for the transfer of small particles through a temperature gradient and are of great importance in aerosol and electronics technology. Here, we examined the model of three-dimensional fluid flow through expansion/contraction moving rotating disk with thermophoretic particle deposition. The complete investigation is achieved by considering two distinctive nanoparticles of ferrites in particular, manganese zinc ferrite (MnZnFe2O4) and
Author statement
R. J. Punith Gowda and R. Naveen Kumar conceived of the presented idea (Thermophoretic particle deposition in time-dependent flow of hybrid nanofluid). They developed the theory and B.C. Prasannakumara and Mohammad Rahimi-Gorji helped them to perform the computations. They verified the applied methods. During revision, some comments of the reviewers were very difficult. Ali Aldalbahi, Alibek Issakhov and Mostafizur Rahaman are expert in nanofluids, materials science, fluid mechanics and
Declaration of Competing Interest
There is not any conflict of interest for all authors of this manuscript.
Acknowledgement
We acknowledge King Saud University, Riyadh, Saudi Arabia, for funding this work through Researchers Supporting Project number (RSP-2020/30).
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