Analysis of Von Kármán Swirling Flows Due to a Porous Rotating Disk Electrode

• Published in: Micromachines (Basel) Vol. 14; no. 3; p. 582
• Main Authors: Visuvasam, James, Alotaibi, Hammad
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 28.02.2023; MDPI
• Subjects: Biofuels; Boundary conditions; Differential equations; Electrodes; Equipment and supplies; Fluid flow; Food processing; Heat exchangers; Heating; homotopy analysis method; Homotopy theory; Incompressible flow; Incompressible fluids; Investigations; Linear equations; Liquid metals; Magnetic fields; mathematical modeling; Methods; non-linear differential equations; Nonlinear differential equations; Nonlinear equations; Ordinary differential equations; Parameters; Partial differential equations; Porosity; rotating disk electrodes; Rotating disks; Rotating fluids; Rotating liquids; Slip; Swirling; Velocity; Velocity distribution; Wholesale industry; mathematical modeling; non-linear differential equations; homotopy analysis method; rotating disk electrodes
• ISSN: 2072-666X; 2072-666X
• DOI: 10.3390/mi14030582

The study of Von Kármán swirling flow is a subject of active interest due to its applications in a wide range of fields, including biofuel manufacturing, rotating heat exchangers, rotating disc reactors, liquid metal pumping engines, food processing, electric power generating systems, designs of multi-pore distributors, and many others. This paper focusses on investigating Von Kármán swirling flows of viscous incompressible fluid due to a rotating disk electrode. The model is based on a system of four coupled second-order non-linear differential equations. The purpose of the present communication is to derive analytical expressions of velocity components by solving the non-linear equations using the homotopy analysis method. Combined effects of the slip λ and porosity γ parameters are studied in detail. If either parameter is increased, all velocity components are reduced, as both have the same effect on the mean velocity profiles. The porosity parameter γ increases the moment coefficient at the disk surface, which monotonically decreases with the slip parameter λ. The analytical results are also compared with numerical solutions, which are in satisfactory agreement. Furthermore, the effects of porosity and slip parameters on velocity profiles are discussed.