Numerical Simulation of Reciprocating Flow Forced Convection in Two-Dimensional Channels

Abstract

Numerical simulations of laminar, forced convection heat transfer for reciprocating, two-dimensional channel flows are performed as a function of the penetration length, Womersley (α) and Prandtl (Pr) numbers. The numerical algorithm is based on a spectral element formulation, which enables high-order spatial resolution with exponential decay of discretization errors, and second-order time-accuracy. Uniform heat flux and constant temperature boundary conditions are imposed on certain regions of the top surface, while the bottom surface is kept insulated. Periodicity of velocity and temperature fields is imposed on the side boundaries, while the flow is driven by an oscillating pressure gradient. These sets of boundary conditions enable time-periodic solution of the problem. Instantaneous and time-averaged surface and bulk temperature distributions, and Nusselt number variations are presented. For high α flows, the temperature field is significantly affected by the Richardson’s annular effect. Overall, forced convection increases by increasing the penetration length, α and Pr. Corresponding steady-flow simulations are performed by matching the volumetric flowrate. For the limited parameter space investigated in this paper, steady unidirectional forced convection is more effective than the reciprocating flow forced convection.

Forced convection with laminar pulsating flow in a channel or tube

“…However, our literature survey revealed only a score of papers on the problem where the applied pressure gradient, and hence the velocity, is pulsating harmonically about a non-zero mean. Experimental work has been reported in [1][2][3][4] and numerical solutions have been presented in [5][6][7][8][9][10][11][12][13].…”

Lattice Boltzmann simulations of conjugate heat transfer in high-frequency oscillating flows

“…Heat transfer enhancements with oscillating flows were also presented by Walsh et al (1993), Qiu and Simon (1994), Liao et al (1994Liao et al ( , 1995, Cheng (1995, 1996), Li and Yang (2000), Herman and Kang (2001), Yang (2003), Iwai et al (2004) and Bouvier et al (2005). Sert and Beskok (2003) presented numerical simulations for laminar oscillating flow and heat transfer in a two-dimensional channel based on a spectral element formulation. The results show that the convection heat transfer in a steady flow with the same volumetric flow rate is higher than the heat transfer in an oscillating flow.…”

Heat Transfer Characteristics of Reciprocating Flows in Channels Partially Filled with Porous Medium

“…Alternatively, one can select the desired heat flux (q * ), and calculate T * to find the maximum surface temperature. This normalization makes it easier to utilize dynamic similarity for obtaining the dimensional temperature and heat flux values (Sert and Beskok 2003).…”

“…Since then, additional results dealing with oscillatory flows are reported by Zhao and Cheng (1995), and Liao et al (1995), which all show significant heat transfer enhancement in ducts and enclosures. Sert and Beskok (2003) have studied the effect of frequency on flow pattern and heat transfer in two-dimensional channels with reciprocating fluid.…”