Flow and Heat Transfer Through Constricted and Obstructed Channel

The steady, symmetric and two-dimensional flow of viscous, incompressible, and Newtonian fluid through a constricted and obstructed channel is investigated numerically. The constriction is in the form of a step while the obstructions are in the form of periodically placed sharp edged baffles as shown in figure 1. The plane Poiseuille flow is considered far from upstream and downstream of the step. This numerical experiment consists of three geometry parameters α, β, γ and a flow parameter Reynolds number R. The parameters α, β control the obstructions while γ controls the constriction. The numerical scheme which we use have two main parts, namely parts A and B. Part A is related to flow when R lies in the range 0 ≤ R ≤ 10³ while part B is related to flow when R lies in the range 10³ < R ≤ 10⁸. Both the parts are solved by special finite-difference methods but Fourier series and boundary layer methods are used as initial estimation for parts A and B respectively. This numerical scheme transforms the governing equations to system of finite-difference equations. This system is solved by S.O.R. iterative method. Moreover, the results obtained are further refined and upgraded by Richardson Extrapolation method. This scheme yields the sixth order accurate solution. The results are compared with parabolic velocity profile when there is no constriction and obstruction (i.e. α = β = 0, γ = 1). The results are also compared with those of Dennis [5], when there is no obstruction (i.e. α = β = 0). In both cases, the comparison is very well.