## 1 Introduction  
Particle-Based Concentrating Solar Power (PBCSP) is one of the promising technologies that has the potential to minimize the dependency on fossil fuels. This technology offers several advantages over those in the same category. A PBCSP system can operate at higher temperatures than other CSP systems [1], permitting the integration with high-efficiency power cycles. Moreover, PBCSP systems can provide a cost-effective energy storage [2], which other CSP systems and solar photovoltaic (PV) systems currently lack. PBCSP systems do not have issues like freezing, corrosion, or flux limits. Additionally, the US Department of Energy (DOE) has selected the solid-particle pathway, over the other CSP competitors, as a way to develop highly efficient CSP plants which can achieve a levelized cost of electricity of $0.05/kWh [3]. The first pilot PBCSP plant was built at the campus of King Saud University (KSU), Riyadh, Saudi Arabia [4; 5]. A typical PBCSP plant is composed of a heliostat field, a particle heating receiver (PHR), a thermal energy storage (TES), a particle-based heat exchanger (PBIX), and a power block. Solid particles serve as an energy carrier, transferring and storing heat medium; the particles are allowed to freely fall in the PHR to become irradiated by sunlight reflected from the heliostat field. The hot particles are then stored in a high-temperature TES bin that continuously feeds the PBHX which, in turn, transfers the thermal energy from the hot particles to the working fluid of a power cycle to generate electricity. The cooled particles are then collected in a low-temperature TES bin to be circulated, thus completing the particle loop. The PBHX stands as one of the most critical components that requires extensive experimental and theoretical investigations towards commercializing the PBCSP technology. Developing an effective PBHX will greatly improve the overall efficiency of the plant and reduce the fuel consumption. Various designs (mainly categorized as direct and indirect-contact) are being investigated, including, but not limited to, moving packed-bed, fluidized-bed, and falling cloud direct-contact PBHXs [6]. To date, the indirect-contact moving packed-bed heat exchangers (ICMPBHXs), either the shell-and-tube or the shell-and-plate design, are attractive options to transfer thermal energy from solar-heated particles to the working fluid of the power cycle. ICMPBHXs offer several advantages, compared to the other designs, such as no parasitic load requirements, simpler in design, gravity-driven, no risk of contaminating the working fluid, and commercial availability. Although these heat exchangers have inherently low overall heat transfer coefficients and are costly because of the large amounts of expensive alloys needed, research is going on to develop designs that mitigate such limitations. Several studies have been conducted to investigate the particle flow kinematics and performance of a shell-and-tube design in which particles move around tubes on a shell-side. [PERSON] [7] used X-ray video films to visualize the flow of particles around a circular tube of several types of tube arrangements including a single tube, a single row of tubes, two rows of tubes, and three rows of tubes; staggered formation was used in the last two cases. The author found that the flow pattern and, thus, the local heat transfer coefficient depends greatly on the tube arrangement. Three zones were observed around the tube of staggered banks, namely, a stagnant zone on top of the tube, a void zone below the tube, and a moving bed region along both sides of the tube. The size of stagnant zone is affected by the tube pitch, as the pitch increases the stagnant zone flattens; on the other hand, the particle velocity has no effect on the stagnant zone. The existence of stagnant and void zones has a negative effect on the heat exchange process. The local heat transfer coefficient was found to be between 25 and 120 W/m\({}^{2}\)-K for the two-row arrangement when particles velocities range from 0.4 to 6.7 mm/s.