## 1 Introduction  
Oil shale is a lamellar and impermeable sedimentary rock, which contains large amounts of kerogen that can be decomposed into smaller molecules to produce oil, gas, and carbonaceous coke by pyrolysis or retorting [1]. The development of oil-shale resources has attracted increasing interest due to the tremendous increase in global energy demand and rapid depletion of conventional oil resources [2]. Traditionally, the shale oil is produced aboveground by mining the oil shale and then post-treating it in proceeding facilities [3]. However, opencast mining occupies much land and produces a large amount of polluted gas, acidic water, and waste residues. In the past few decades, the in situ resorting technologies for the production of hydrocarbons from oil shale have been developed significantly, including conductive heating [4], convective heating [5], combustion [6], and the radiant heating [7]. Among these technologies, the downhole electric resistive heaters are still believed to be the optimal method for oil-shale in situ resorting, as they have been widely used in the exploitation of shale oil in various fields. Shell developed the in situ conversion process for oil-shale exploitation [4] by heating the oil-shale deposit by using the electric resistive heaters. Due to the limited heat-transfer area, the heating conduction efficiency of the bare electric heater is pretty low, which takes over one year to heat the oil shale before mass production [8]. Thus, recent studies focus on expanding the heat-transfer area of the electric resistive heater by adding various kindsof enhanced fins [9; 10; 11; 12; 13; 14; 15; 16]. [PERSON] et al. [9] proposed a double-shell-structured downhole electric heater with continuous helical baffles, which improved the heating efficiency of the downhole electric heaters effectively. Later, [PERSON] et al. [10] claimed that the electric heater with the axial separation helical baffle schemes showed better comprehensive index and temperature uniformity than those of the segment baffle ones. [PERSON] et al. [11] also found that the heater with continuous helical baffles was more suitable for downhole heating than that with segmental baffles in terms of the long-term working stability by simulation and experiments. [PERSON] et al. [12] studied the downhole unilateral-ladder-type helical baffle heat exchangers with folded baffles and found that the shell-side heat-transfer coefficients were larger, but the comprehensive indexes were smaller than those of the corresponding plane ones. [PERSON] et al. [13] proposed the trisection-helical-baffled electric heaters to overcome the defects in conventional segmental-baffled ones. [PERSON] et al. [14] designed a novel configuration of the axial-separation helical-baffle heat exchangers and solved the problem in the seriation of the helical-baffle angles to reduce the fabrication cost. All the electric resistive heaters with enhanced fins are mineral insulated to preserve and protect the purity and electrical properties of the core heating elements. Generally, the armored electric heaters are filled with high-quality electrical-grade magnesium oxide (MgO) powder due to its high dielectric and thermal conductivities. However, due to the rapid degradation of the electrical resistivity of MgO powder when the operating temperature is above 800 \({}^{\circ}\)C [17], the high nickel alloy sheath, MgO dielectric insulation, and resistance wire construction allow the tracing of heater temperature up to 600 \({}^{\circ}\)C for the armored electric heaters, much smaller than that of the bare electric heaters (-1000 \({}^{\circ}\)C). Note that the pyrolysis temperature of oil shale may range from 350 \({}^{\circ}\)C to 560 \({}^{\circ}\)C [18]. The lower operating temperature of the armored electric heaters requires complex fin structures to expand the heat transfer area.