Numerical study of fluid flow and heat transfer in a backward facing step with a rotating cylinder

A. Anguraj; J. Palraj

doi:10.26637/MJM0602/0022

Abstract

The present study analyzes the laminar flow and heat transfer over a backward-facing step with an adiabatic rotating cylinder in a channel. The governing Navier-Stokes and energy equations are solved using finite element method. The effect of Reynolds number, cylinder rotation angle and various cross-stream positions of the cylinder on the fluid flow and heat transfer characteristics of the backward-facing step flow have been studied numerically. The working fluid is assigned a Prandtl number of 0.71 throughout this investigation. The flow and thermal fields have been explained by streamline and isotherm profiles respectively. It is observed that the flow field and heat transfer rate are influenced by the variations of these parameters. Furthermore, the length and size of the wake zones can be controlled with cylinder rotation angles.

Keywords:

Navier-Stokes equations, Rotating obstacle, Backward facing step, finite element method, Recirculation length, Heat transfer

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

A. Anguraj Department of Mathematics, PSG College of Arts and Science, Tamil Nadu, India.
J. Palraj Department of Mathematics, PSG College of Technology, Tamil Nadu, India.

Pages: 435-442
Date Published: 01-04-2018
Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)

B.F. Armaly, A. Li, J.H. Nie, Measurements in threedimensional laminar separated flow, Int. J. Heat Mass Transfer 46 (19) (2003) 3573-3582.

H. Stuer, A. Gyr, W. Kinzelbach, Laminar separation on a forward facing step, European Journal of Mechanics-B/Fluids 18 (1999) 675-692.

B.F. Armaly, F. Durst, J.C.F. Pereier, B. Schonung, Experimental and theoretical investigation of backward-facing step flow, Journal of Fluid Mechanics 127 (1983) 473-496.

M. Sherry, D.LoJacono, and J.Sheridan, An experimental investigation of the recirculation zone formed downstream of a forward facing step, J. Wind Eng.Ind.Aerodyn., 98(2010) 888-894.

A. Anguraj and J. Palraj, Comparison of four different obstacle models of fluid flow with a slip-like boundary condition. Malaya J. Mat. 2(4)(2014) 517-526.

H. Abu-Mulaweh, A review of research on laminar mixed convection flow over backward-and forward facing steps, Int. J. Therm. Sci. 42 (2003) 897-909.

J. Nie, B. Armaly, Three-dimensional convective flow adjacent to backwardfacing step-effects of step height, Int. J. Heat Mass Transfer 45 (2002) 2431-2438.

Barbosa-Saldana JG, Anand NK. Flow over a threedimensional horizontal forward-facing step. Numer Heat Transfer A 53 (2008) 1-17.

F. Rehimi, F. Aloui, S. Ben Nasrallah, L. Doubliez, J. Legrand, Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls, J. Fluids Struct. 24 (2008) 855-882.

S.H. Hussain, A.K. Hussein, Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations, Int. Commun. Heat Mass Transf. 38 (2011) 263-274 .

Selimefendigil F, Oztop H. Control of laminar pulsating flow and heat transfer in backward facing step by using a square obstacle. ASME-J Heat Transf 136 (2014)081701.

H.F. Oztop, K.S. Mushatetb, I. Yilmaz, Analysis of turbulent flow and heat transfer over a double forward facing step with obstacles, International Communications in Heat and Mass Transfer 39 (2012) 1395-1403.

A. Kumar, A.K. Dhiman, Effect of a circular cylinder on separated forced convection at a backward-facing step, Int. J. Therm. Sci. 52 (2012) 176-185.

J.T. Lin, B.F. Armaly, T.S. Chen, Mixed convection in buoyancy-assisting vertical backward-facing step flows, Int. J. Heat Mass Transfer 10 (1990) 2121-2132.

S. Acharya, G. Dixit, Q. Hou, Laminar mixed convection in a vertical channel with a backstep: a benchmark study, ASME HTD 258 (1993) 11-20.

R. Cochran, R. Horstman, Y. Sun, A. Emery, Benchmark solution for a vertical buoyancy-assisted laminar backward-facing step flow using finite element, finite volume and finite difference methods, ASME HTD 258 (1993) $37-47$

B. Dyne, D. Pepper, F. Brueckner, Mixed convection in a vertical channel with a backward-facing step, ASME HTD 258 (1993).

A. Logg, K.A. Mardal, G.N. Wells, et al., Automated Solution of Differential Equations by the Finite Element Method, Springer, 2012.

R. Eymard, T. Gallouet and R. Herbin, Finite Volume Methods, Handbook of Numerical Analysis, 7 (2003) 713 1020. Edited by P.G. Ciarlet and J.L. Lions (North Holland).