Electronic edition ISSN 1574-0579

Momentum and heat transfer in MHD unsteady Dean flow between two arbitraty cylinders with transient pressure gradient: Laplace transform and finite difference approach

P. Dash^1, - K. L. Ojha^1, - B. K. Swain^2, - G. C. Dash¹

¹ Department of Mathematics, Siksha `O' Anusandhan University, Bhubaneswar, 751030, India }
² Department of Mathematics, Agarpara College, Bhadrak, 756115, India

Abstract
In the present investigation, the combined effect of an exponentially growing/decaying azimuthal pressure gradient and an electromagnetic body force on Dean flow is of current interest. The flow domain is an annular region formed by two stationary electrically non-conducting cylinders, with the outer cylinder being arbitrarily placed. The azimuthal rotational flow is initiated by the exponentially growing/decaying pressure gradient along with the external resistive body force due to the applied magnetic field interacting with the electrically conducting flowing fluid. The vortex formation and flow reversal in the flow domain are consequences of rotational motion and curvature of the inner and outer cylinders. Another aspect of the present study is to establish the accuracy of solution, i.e. semi-analytical (Laplace transform with Riemann sum approximation) and numerical method (finite difference method). The following suggestive and remedial measures are the outcomes for end-users: (i) the transverse applied magnetic field regulates the machining in production; (ii) it is essential to ascertain the position of the outer cylinder to avoid flow reversal by reducing skin friction; (iii) the variation of Dean vortex is independent of the intensity of the applied magnetic field in the middle of the annular region, which is an epoch-making outcome that ensures the flow phenomenon reversibility. The above outcomes are of immense use, particularly, in industrial and biological systems. The specific examples are mentioned in the paper. Key words: Axial magnetic field; Azimuthal pressure gradient; Laplace transform; Finite difference; Riemann-sum approximation; Bessel function; Stationary cylinders. Tables 1, Figs 9, Refs 27.