Journal of Applied Mechanical Engineering

The modification of Ekman-Hartmann layer by the imposition of axial velocity

3^rd International Conference on Fluid Dynamics & Aerodynamics

October 25-26, 2018 | Berlin, Germany

Satyanarayana Badeti, Somaraju Vempaty and S Srinivas

VIT - AP University, India
GVP-LIAS College of Engineering, India

Scientific Tracks Abstracts: J Appl Mech Eng

Abstract:

The effect of normal blowing on a linear, steady, axisymmetric Ekman-Hartmann boundary layer on an infinite flat insulating plate is analyzed. The problem is governed by three parameters, namely the Ekman number 2 E L ? ?? ? =? ? ? ? ?, the magnetic interaction parameter 2 2 ?? B0 ? ? ? ? ? = ? ? ? ? ? ? and the injection Rossby number R U L ? ? =? ? ?? ? In the parametric range E 1/2? ??? 1 << R >> E 1/2? and E 1/2 << R << 1 , the viscous Ekman-Hartmann layer is blown up by the injection of the fluid, and it becomes inviscid to the lowest order. Injection and magnetic terms balance each other giving rise to a new boundary layer of thickness 2 O R ? ? ? ? ? ? ?, which may be called linear resistive layer. Since, the resistive layer is thicker than the Ekman-Hartmann layer, it can support more electric and mass flux, thus signifying a possible faster spin-up compared to conventional hydromagnetic case. The electric current increases with magnetic interaction parameter ? beyond the saturation value, and finally approaches the saturation value as R??? E 1/2? The vertical mass flux into the resistive layer decreases with magnetic field as expected because of the stiffening effect of the magnetic field. This resistive layer, characterized by dispersive and diffusive length scales for ? 2 < O(1) merges with the interior and becomes a resistive region in the parameter range E 1/3 << R >> E 1/2? ???1 and R >>? 2 . The other parameter ranges are clearly identified wherein the resistive 2 R ? layer merges smoothly into the Ekman layer, the R3 E injection layer that occurs when? = 0 , the Ekman- Hartmann layer and the E 1/2 ? Hartmann layer. In addition to exact solutions, asymptotic solutions are also given for? 2 ??? O(1) and ? 2 < O(1) to understand the problem more systematically and physically. Recent Publications 1. Satyanarayana Badeti, Somaraju Vempaty and Suripeddi Srinivas (2018) A unified linear theory of rotating hydromagnetic floe between two parallel infinite plates subject to imposition of axial velocity. Journal of Applied Mathematics and Mechanics DOI: 10.1002/zamm.201700174. 2. Satyanarayana Badeti, Somaraju Vempaty and Suripeddi Srinivas (2018) A heuristic method to solve nonlinear vibration problems, National Academy Science Letters 41(4):225-231.

Biography :

Satyanarayana Badeti completed his PhD from VIT University, India under the guidance of Dr. Somaraju Vempaty. Presently he is an Assistant Professor at VIT-AP University, Amaravati, Andhra Pradesh, India in the Department of Mathematics.

E-mail: satyabadeti1980@hotmail.com