Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform vertical magnetic field

• Published in: Acta mechanica Vol. 218; no. 3-4; pp. 237 - 245
• Main Author: Turkyilmazoglu, M.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.05.2011; Springer; Springer Nature B.V
• Subjects: Approximation; Ariel; Asymptotic properties; Boundary layer; Boundary layer flow; Classical and Continuum Physics; Control; Dynamical Systems; Engineering; Engineering Thermodynamics; Exact sciences and technology; Exact solutions; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Heat and Mass Transfer; Laminar boundary layers; Laminar flows; Magnetic fields; Mathematical analysis; Mathematical models; Physics; Rotating disks; Solid Mechanics; Theoretical and Applied Mechanics; Vibration; Convergence Region; Analytic Approximate Solution; Wall Shear Stress; Secular Term; Homotopy Analysis Method; Rotating disk; Homotopy; Electrical conduction; Modelling; Asymptotic approximation; Conducting fluid; Viscous fluids; Boundary layers
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-010-0416-4

The present paper is concerned with the analytical solution of the boundary layer flow of a steady, laminar, incompressible, viscous and electrically conducting fluid due to a rotating disk. Within this purpose, the recently popular homotopy analysis method is employed, making it possible to obtain explicitly analytic expressions for Lighthill’s coordinate straining parameter c in terms of the magnetic field parameter m , first used in Ackroyd (J Eng Phys 12:207–220, 1978 ) for the nonmagnetic case and recently studied to get the small perturbation and large asymptotic representations in Ariel (Z Angew Math Mech 82:235–246, 2001 ) for the magnetic case. Making use of the outlined approach, the mean velocity profiles corresponding to a wide range of magnetic strength parameters are computed, and also explicit formulas are derived for several quantities of physical significance.