**1. Introduction**

Granular beds are extensively used in the metallurgical industry, environmental protection, and other fields given their simple structure, convenient operation, and strong environmental adaptability. The reaction heat inside the bed can be moved out e ffectively by using buried tubes. Heat transfer process is complex and a ffects the normal operation of granular beds importantly. Numerous studies have been conducted on the heat transfer process in granular beds.

Nasr et al. [1] used air as the working medium to study the influence of filling particle diameter and heat transfer coe fficient of the heat transfer process in granular beds. Their results showed that small particles indicate improved heat transfer performance of a granular bed. Pivem et al. [2] used a granular layer as a porous medium to establish a model and studied the influence of porosity, Reynolds number, and other factors on the heat transfer process by using a two-energy equation model. In engineering practice, the random accumulation of particles explains the di fference in bed porosity in various locations. Zumbrunnen et al. [3] designed an equipment to measure thermal

conductance for several packed beds over a wide temperature range, and the thermal conductance of packed beds increased with the temperature di fference across the bed thickness. Ram et al. [4] developed a simple numerical method to determine the interparticle radiation heat transfer in granular bed, which can handle large numbers of surfaces without involving matrix inversion and independent of coordinate system. Shen et al. [5] studied the heat transfer performance of a parallel flow heat exchanger. Their results showed that the heat transfer e fficiency of a parallel flow heat exchanger is between 95% and 98% and is a ffected by a pulsation phenomenon caused by a small tube diameter. Thus, further research is required to determine the appropriate heat transfer tube diameter to eliminate the influence of the pulsation phenomenon. Zhang et al. [6] studied the influence of vertical buried tubes on heat transfer in a large-particle fluidized bed. Their results showed that the average heat transfer coe fficient in the circumferential direction of the vertical buried tube remains stable after the fluidization speed reaches the bubble speed, and the heat transfer coe fficient in the lateral direction of the horizontal buried tube with the same diameter is approximately 20% higher than that under the same condition. Royston [7] conducted experiments to investigate the heat transfer of gas–solid two-phase mixtures flowing through a column granular bed vertically under the adiabatic wall conditions. The experimental results showed a significant enhancement of heat transfer in comparison with single gas phase conditions. Doherty et al. [8] conducted experiments to investigate the heat transfer coe fficient of a horizontal smooth tube immersed in a gas–liquid bed and the results showed that the heat transfer coe fficient of the gas and liquid phase decreases at first as the outer diameter of tube is increased but increases as the diameter is further increased. Zhang and Wang [9] studied the heat transfer for a fluidized granular bed air receiver experimentally and numerically with a non-uniform energy flux and the fluidization occurs inside cylindrical metal and quartz glass tubes and a numerical model was established to study the fluidized heat transport inside the quartz tube. Cong et al. [10] obtained the total heat transfer coe fficient through logarithmic mean temperature di fference method and conducted an experimental study on the heat transfer of a gas–solid two-phase mixture. Grewal and Saxena [10] analyzed the e ffects of particle size, shape, density, and specific heat; tube size; bed depth; heat flux density; and distributor design on the heat transfer coe fficient by measuring serval particles. The experimental results showed that the heat transfer coe fficient increases with the increasing of gas velocity and decreases with the further increase and the turning point is 0.5 m/s. Yin et al. [11] conducted an experimental study on the heat transfer characteristics of dusty gas through buried tubes in a granular bed. Their study utilized a solid corundum ball as the filtration medium and analyzed the influence of dust concentration and flue gas velocity on the bed temperature distribution through a comprehensive heat transfer coe fficient of the bed. The experimental correlations between the bed heat transfer coe fficient and dust concentration and flue gas velocity were proposed. Yin et al. [12] proposed an ammonia absorption cooling and heating dual-supply system based on off-peak electricity heat storage. This system can use the waste heat of flue gas for heating and cooling instead of o ff-peak electricity. Chen et al. [13] studied the collection mechanism and heat-transfer characteristics of a packed granular filter by using a three-dimensional randomly packed granular filter model.

In the present work, vertical heat exchange tubes were arranged in a granular bed with 3–5-mm hollow corundum balls as filler particles to reduce heat storage. The total heat transfer coe fficient of the granular bed was used to characterize the heat transfer capability of the particle bed, and the heat transfer experimental equipment was built. The experiments were conducted at 1073.15 K, and the influence of inlet gas temperature and cooling water flow rate on the heat transfer process was studied. The temperature distribution in the bed was simulated through the computational fluid dynamics' (CFD) method, and the simulation results were compared with the experimental results.
