This research introduces a novel framework integrating stochastic finite element analysis (FEA) with advanced circular statistical methods to optimize heat pump efficiency under material uncertainties. The proposed methodologies and optimization focus on balancing the mean efficiency and variability by adjusting the concentration parameter of the Von Mises distribution, which models directional variability in thermal conductivity. The study highlights the superiority of the Von Mises distribution in achieving more consistent and efficient thermal performance compared to the uniform distribution. We also conducted a sensitivity analysis of the parameters for further insights. The results show that optimal tuning of the concentration parameter can significantly reduce efficiency variability while maintaining a mean efficiency above the desired threshold. This demonstrates the importance of considering both stochastic effects and directional consistency in thermal systems, providing robust and reliable design strategies.

This research introduces a novel framework integrating stochastic finite element analysis (FEA) with advanced circular statistical methods to optimize heat pump efficiency under material uncertainties. By modeling directional variability in thermal conductivity using both uniform and Von Mises distributions, the study highlights the superiority of the Von Mises distribution in providing consistent and efficient thermal performance. The Von Mises distribution, known for its concentration around a mean direction, demonstrates a significant advantage over the uniform distribution, resulting in higher mean efficiency and lower variability. The findings underscore the importance of considering both stochastic effects and directional consistency in thermal systems, paving the way for more robust and reliable design strategies.

Due to the short cost-effective heat transportation distance, the existing geothermal heating technologies cannot be used to develop deep hydrothermal-type geothermal fields situated far away from urban areas. To solve the problem, a new multi-energy source coupling a low-temperature sustainable central heating system with a multifunctional relay energy station is put forward. As for the proposed central heating system, a compression heat pump integrated with a heat exchanger in the heating substation and a gas-fired water/lithium bromide single-effect absorption heat pump in the multifunctional relay energy station are used to lower the return temperature of the primary network step by step. The proposed central heating system is analyzed using thermodynamics and economics, and matching relationships between the design temperature of the return water and the main line length of the primary network are discussed. The studied results indicate that, as for the proposed central heating system, the cost-effective main line length of the primary network can approach 33.8 km, and the optimal design return temperature of the primary network is 23 ℃. Besides, the annual coefficient of performance and annual energy efficiency of the proposed central heating system are about 3.01 and 42.7%, respectively.

The direct expansion heat pump with solar energy is an energy conversion system used for water heating applications, air heating for air conditioning buildings, water desalination, solar drying, among others. This paper reviews the main designs and analysis of experiments in order to identify the fundamental objectives of any experiment which may be: to determine the factors that have a significant influence, to obtain a mathematical model and/or to optimize performance. To achieve this task, the basic and advanced configuration of this system is described in detail in order to characterize its thermal performance by means of energy analysis and/or exergy-based analysis. This review identifies possible lines of research in the area of design and analysis of experiments to develop this water heating technology for industrial applications.

The heat collection evaporator was modeled based on equilibrium homogeneous theory, and the Runge-Kutta calculation method was used to analyze and solve the flow in the heat collection evaporator. The influence of environmental factors such as solar irradiance, ambient temperature and wind speed on the variation of refrigerant pressure in two kinds of heat collecting evaporator was analyzed under the set working conditions. The results show that the solar energy irradiance has a great influence on the pressure drop in the tube of serpentine heat collecting evaporator, and the maximum pressure drop of the refrigerant in the tube is 16.3%, minimum pressure drop is 7.8%. However, it has little influence on the pressure drop of the tube sheet evaporator. The maximum pressure drop in the refrigerant tube of the tube sheet evaporator is 4.8%, minimum pressure drop is 1.8%. When the irradiance reaches 800 W/m², the refrigerant in the serpentine-tube evaporator has been completely vaporized at 6 m, it’s completely vaporized at 3 m.

The CO₂  heat pump air conditioning system of new energy vehicle is designed, and the vehicle model of CO₂  heat pump module and heat management system is established based on KULI simulation. The effects of refrigerant charge, running time and compressor speed on the heat pump air conditioning system is studied, and the energy consumption is compared with the PTC heating system and the CO₂ heat pump air conditioning system without waste heat recovery. The results show that the optimal charge for full-service operation is 750 g; increasing the compressor speed can increase the cooling capacity, so that the refrigerant temperature in the passenger compartment and battery inlet can quickly reach the appropriate temperature, but the COP_h, COP_c are reduced by 2.5% and 1.8% respectively. By comparing it with PTC heating and CO₂ heat pump air conditioning systems without waste heat recovery, it is found that the energy consumption of this system is only for the PTC heating systems 42.5%, without waste heat recovery carbon dioxide heat pump air conditioning system of 86.6%. It greatly saves energy, but also increased the waste heat recovery function, so that the system supply air temperature increased by 26%, improve passenger cabin comfort. This  provides a reference for the future experimental research of CO₂ heat pump air conditioning and heat management system.