Time-Dependent Flow with Convective Heat Transfer through a Curved Square Duct with Large Pressure Gradient

Rabindra Nath Mondal^1*, Md. Nurul Amin Helal², Poly Rani Shaha¹, Nayan Kumar Poddar¹

¹Department of Mathematics, Jagannath University, Dhaka, Bangladesh.
²Additional Director (Education), Training Directorate, BGB Head Quarter, Pilkhana, Dhaka, Bangladesh.

DOI: 10.4236/ojfd.2015.53026                

Abstract

A numerical study is presented for the fully developed two-dimensional laminar flow of viscous incompressible fluid through a curved square duct for the constant curvature δ = 0.1. In this paper, a spectral-based computational algorithm is employed as the principal tool for the simulations, while a Chebyshev polynomial and collocation method as secondary tools. Numerical calculations are carried out over a wide range of the pressure gradient parameter, the Dean number, 100 ≤ Dn ≤ 3000 for the Grashof number, Gr, ranging from 100 to 2000. The outer wall of the duct is treated heated while the inner wall cooled, the top and bottom walls being adiabatic. The main concern of the present study is to find out the unsteady flow behavior i.e. whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn or Gr is increased. It is found that the unsteady flow is periodic for Dn = 1000 at Gr = 100 and 500 and at Dn = 2000, Gr = 2000 but steady-state otherwise. It is also found that for large values of Dn, for example Dn = 3000, the unsteady flow undergoes in the scenario “periodic→chaotic→periodic”, if Gr is increased. Typical contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of single-, two-, three- and four-vortex solutions. The present study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal force in a curved square passage that stimulates fluid mixing and consequently enhance heat transfer in the fluid.

Keywords

Curved Square Duct, Secondary Flow, Time-Evolution, Periodic Solution, Chaos

Conflicts of Interest

The authors declare no conflicts of interest.

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