## 1 Introduction and Literature Review
It is important to highlight that most numerical modelling work presented in this review applies a simplified model whereby a thin plate or a pair of adjacent plates with an implementation of periodic boundary conditions to replicate the array of plates is considered. In modelling, a periodic boundary condition means that the flows at the matching periodic boundary are linked so that flow conditions are shared at this boundary. As a result the flow will be duplicated for all other channels in a periodic manner [12]. While this has advantages in terms of computational cost, it must be carefully applied as  
Figure 1: Schematic of a simple thermoacoustic cooler arrangement (**top**). The acoustically induced compression and expansion of fluid elements causes heat pumping effects along the stack (**bottom**). it might give misleading information pertaining to the flow structure. This has been demonstrated experimentally by [PERSON] and [PERSON] [PERSON] and [PERSON] (2013). Their experimental results were later compared to a numerical model developed using commercial software, Fluent Fluent (2014), using the same number of plates as in the experiment. Their works show that, for a structure with an array of plates, the flow structures at the end and in the middle of the plates are influenced by the adjacent plates. The Strouhal number (the ratio of a product of a characteristic length and the frequency of the vortex shedding to a reference velocity) is reported to have changed in magnitude when a comparison was made between the two arrangements. It is important to highlight here that the investigations reported in [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013) were carried out in steady flow and might not be directly applicable to the oscillatory condition, but they do give an idea of possible sources of discrepancy if investigations of an array of plates are carried out using single plate approximation. The observation of asymmetry and non-periodic development of vortex structures at the end of a plate array was also reported by [PERSON] et al. [PERSON] et al. (2013). This suggests that a physical periodic structure (array of plates) does not guarantee that the flow structures are periodic. Hence modelling a single plate may not be adequate to describe the physics of flow around a structure with an array of plates. Similarly, considering a single plate, the flow structures at two ends may not be identical in practice for reciprocating flows. Most investigations (cf., [PERSON] (1990); [PERSON] (1990); [PERSON] and [PERSON] (2013)) assumed that flows at the two ends are actually symmetrical and therefore the analysis was mainly focused on just one end. This seems reasonable for investigations that do not involve a temperature gradient (adiabatic stack). However, the presence of a temperature gradient on solid boundaries is necessary for the thermoacoustic effect to take place. Temperature effects must be considered to account for additional phenomena such as temperature-driven buoyancy [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013) and non-linear effects [PERSON] et al. (2013) that could affect the flow symmetry. Experimental studies often reveal signs of nonlinearities that are insufficiently addressed by the linear model [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013). In most numerical studies (cf. [PERSON] (1990); [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013)) the natural convection effect was neglected. This effect however was observed in many experimental works [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013); [PERSON] and [PERSON] (2013). Current computational fluid dynamics (CFD) study aims to improve the understanding of physical processes involved in the phenomena reported in the earlier experimental work of [PERSON] et al. [PERSON] et al. (2015). However, bearing in mind more complex operating conditions (e.g., tilted-angle solar powered systems [PERSON] et al. (2015); [PERSON] et al.