## 1 Introduction
The thermal energy is determined by obtaining a temperature measurement at the back surface of the element, and the rate of change of the temperature provides the heat flux of the exposed surface. Different types of calorimeter gauges, such as thin-wall calorimeters [14], slug calorimeters [27], and null-point calorimeters [28; 29], have been developed by researchers to address the requirements of unique testing environments. Slug and null-point calorimeter gauges are generally developed for long test time measurements (such as a plasma wind tunnel), whereas a thin-wall calorimeter is more suitable for transient hypersonic facilities with testing durations on the order of milliseconds. Previous thin-wall calorimeters usually have copper as the calorimeter material and a thermocouple on the back of the calorimeter to measure the temperature rise. However, they have the same disadvantage--namely, low sensitivity--as coaxial thermocouples. [PERSON] [30] proposed a new design method that used an aluminum sheet as the calorimeter. In addition, the back was anodized for electrical insulation and plated with a platinum film. The back temperature of the aluminum sheet was measured by the platinum film to improve the output sensitivity of the calorimeter. However, this design was only reported in a few articles in 1960s, and there is no literature of relevance in the following years. The main reason was that cavities remained on the surface of the aluminum sheet after oxidation in the actual production process. The secondary coating resulted in conduction between the platinum film and the base material, and the platinum film did not provide insulation from the aluminum sheet. The thermal conductivity of the aluminum oxide after oxidation was also poor, adversely affecting the heat flux measurements. The above improved design of the calorimeter can greatly improve the output sensitivity of the calorimeter, but it is necessary to find a new calorimeter material with high thermal conductivity and resistance. The thermal conductivity of natural diamonds is about 2200 W/m K, which is five times that of copper. Additionally, the resistivity is more than \(10^{14}\)\(\Omega\cdot\)cm, which meets the requirements of high thermal conductivity and resistance. Thus, diamonds may be an ideal calorimetric material. Natural diamonds are expensive, but chemical vapor deposition (CVD) diamonds are relatively mature due to the development of synthetic materials [31]. Although the thermal conductivity of CVD diamonds does not reach the level of natural diamonds, it is still much higher than that of conventional metals, and the production cost is much lower. If CVD diamonds can be used to fabricate a calorimeter, the thermal response would be very fast because of the high thermal conductivity of CVD diamonds. Due to the advantages of this new type of transient calorimeter, researchers investigated potential applications. [PERSON] [32] fabricated a diamond calorimeter heat transfer gauge with a diameter of 3.9 mm. The filling material of the bottom lining was glue, and experiments were conducted in an X2 expansion wind tunnel. [PERSON] [33] used CVD diamonds to create a novel heat transfer calorimeter with a diameter of 20 mm and air as the bottom lining material. The author performed validation experiments in a shock wind tunnel. [PERSON] and [PERSON] obtained promising results. However, the effective test time in the X2 expansion tube was short (in the order of microseconds), and the heat dissipation effect may not be serious. Although [PERSON] used air as the back-filling material to reduce the heat dissipation effect, the sensor size was large, which was not conducive to easy installation. As the sensor scale was reduced, the effects of transverse heat transfer and bottom heat dissipation due to the structure of the calorimeter could not be ignored, which would lead to the measurement deviation. Few studies have investigated these problems. Thus, it is necessary to perform more in-depth research.