# An Economical and Precise Cooling Model and Its Application in a Single-Cylinder Diesel Engine
## 1 Introduction  
The cooling system performance is important for engine performance [1]. The purpose of the cooling is to maintain the temperature of the engine components and the temperature gradient at appropriate levels (for example, at 180-200 \({}^{\circ}\)C for aluminum alloys and 380 \({}^{\circ}\)C for cast iron). At present, most cooling systems are designed with mechanical fans, water pumps, and max thermostats. Since the fan and water pump are driven by the crankshaft at fixed speed ratios, their speed changes with that of the crankshaft but it does not change with the engine load which results in the problems of undercooling or overcooling [2]. Undercoiled engines may suffer from several problems, including loss of material strength, high thermal strain, lubricant oil degradation, overheating and abrasion of the power cylinder components, heating the intake air, and lower volumetric efficiency. At part loads or in cold climates, the engine coolant can become excessively cold, which adversely affects engine combustion and performance. Overcooled engines may worsen the combustion and fuel economy and result in excessive heat rejection, high wear of piston rings and liners, and excessive friction and noise. Both overcooling and undercooling have adverse effects on engine performance. Undercooling, which results in damage to the engine, should be avoided. [PERSON] et al. [3] estimated that engines with mechanical cooling system are overcooled for about 95% of their operating time. Mechanical cooling systems (the speed of the fan or water pump connected to the crankshaft) are not capable of regulating the temperature precisely [4]; therefore, they should be decoupled from the crankshaft so the speed can be controlled independently. The fan, water pump, and thermostat can be controlled electrically and can be regulated upby an electronic control unit (ECU); this controllable system has potentiality to realize the target temperature. Recently, many researchers have investigated this topic. [PERSON] et al. [5] discovered the benefits of such systems. In the past two decades, great progress has been made with regard to precise cooling [6], cooling mechanisms [7], engine cooling system design and optimization by [PERSON] et al. [8], and cooling system simulations by [PERSON] et al. and [PERSON] et al. [9; 10]. As the demand for higher fuel economy and stricter emission regulations has increased [11; 12; 13], the engine operating parameters are falling into a smaller range, which highly depends on the speed, load, atmospheric parameters, and other factors. Therefore, the operating parameters should be tuned precisely [2; 14; 15]. For example, the fuel injection timing, injection pressure, and pressure ratio of the supercharger should be controlled by the ECU of engine. In this study, we focus on the control of the engine coolant temperature. Many studies [16; 17; 18; 19; 20] have examined this topic in passenger and commercial vehicle engines, some of which were equipped with an electric cooling system. In general, this system utilizes feedback control strategies, including the electric pump, electric fan, electric thermostat, and controllers as well as various sensors. The system is complex, costly, and easily fails in harsh environments. Single-cylinder diesel engines and applications in tractors are widely used in underdeveloped and developing countries. Statistics have shown that more than 12 million single-cylinder diesel engines are used in China and Southeast Asia. These engines are commonly operated in poor working environments and their cost should be as low as possible. In fact, in order to save costs, manufacturers have not comprehensively updated their product in the past 50 years, even though the emission characteristics of these engines are lower than the EPA Tier 1 [21]. For these reasons, the electric cooling systems used in commercial vehicles cannot be directly applied to single-cylinder engines. Therefore, innovations are required, especially with regard to the cost-effective cooling systems.