## 1 Introduction  
Drying plays an important role in post-processing of agricultural products and is a highly energy-intensive operation [1]. According to some open literature [2; 3; 4], the energy consumed by drying operations accounts for about 10-20% of the national industrial energy consumption every year in some developed countries. With the development of global industries and economics, the steep rise in energy consumption has become one of the common concerns all over the world. In this regard, the development of energy-saving as well as environment-friendly drying technologies has been strongly encouraged around world [5]. In the last few decades, researchers have done a lot of work on grain-drying technologies and processes from a multi-scale (nano [6], micro [7] and macro [8]) perspective. Few works have been focused on industrial-scale grain drying, while industrial grain-drying production is the most effective way to satisfy the steep rise in grain consumption. Moreover, although a number of innovative drying technologies arising from all over the world have been applied in grain-drying production, hot air drying is still one of the most effective methods, owing to its advantages of feasibility, efficiency and being economical [9]. For example, [PERSON] et al. introduced an industrial-scale 5 HFS-10-type automatic control grain dryer with a drying capacity of 27.35 t/h, drying temperature of hot air of 127 \({}^{\circ}\)C and drying cycle of 5.25 h. The results showed that energy consumption was reduced by more than 20% compared with a traditional positive-pressure air-supply dryer [10]. [PERSON] et al. proposed a SHP-3.5 hot-air circulation dryer with a loading capacity of 31 t; energy performance under a constant drying temperature of 78 \({}^{\circ}\)C was investigated, and the results showed that thermal efficiency of the drying chamber varied from 17.14% to 97.83% [11]. Although hot-air drying technology has been widely applied in industrial grain-drying production, few works have focused on the variable temperature of the drying process. Moreover, drying is a typical heat- and mass-transfer process, and during the hot-air drying process, different fluxes (e.g., material flux, flue gas flux, hot air flux) flow throughout the whole system. The match between different fluxes is a key issue for designing the variable temperature of the drying process as well as optimizing the drying system. Accordingly, it is necessary to have a fundamental understanding of the allocation among different fluxes for the purpose of energy-saving and efficient grain drying. Heat recirculation is one of the most common approaches used to save energy in an energy-consuming system and is also widely used in the agricultural-product drying field. For example, [PERSON] and [PERSON] focused on waste-heat recovery from the exhaust air of a grain spray dryer. More specifically, during the drying process, the exhaust air was separated from the material flux and further mixed with fresh air in the drying chamber; the experimental results showed that the methodology effectively improved the energy efficiency of the spray dryer [12]. [PERSON] et al. introduced a grain heat-pump drying system with an outlet air-waste heat-recovery function; the exhaust air was exhausted to the cold-water chamber, and the water was heated up to 30 \({}^{\circ}\)C and further used to prepare the hot water (60-80 \({}^{\circ}\)C); the results showed that almost 18% of the total energy consumption was recovered [13]. [PERSON] et al. studied waste-heat recovery from a tractor exhaust; their results showed that the recovered energy could be used to dehydrate 3-6% of moisture from wet grains [14]. According to the analysis above, recovery of waste heat from exhaust drying air is an effective way to save energy; however, few works have focused on waste-heat recovery from exhaust flue gas, while there is huge heat-recirculation potential in exhaust flue gas of the heat exchanger.