## 1 Introduction  
Manufacturers are currently under pressure to improve the efficiency of internal combustion engines in terms of fuel consumption and exhaust emissions [1]. In fact, the combustion of fossil fuels is a primary source of harmful gases, such as CO\({}_{2}\) and NOx [2]. Diesel engines, in fact, are among the most significant polluters due to their widespread applications. Most of the heat wasted in internal combustion engines comes from exhaust gases [3]. In fact, only 30 to 40% of fuel energy is converted into useful work [4]. To harness this wasted energy, waste heat recovery technologies can be integrated. Recently, organic Rankine cycle (ORC) as a waste heat recovery technology has received great attention among scholars and in the industry sector due to the availability of components, its simplicity, and reliability [5, 6]. Moreover, ORC systems exhibit great thermal efficiency in comparison to other WHR technologies under a variety of operating situations [7]. The organic Rankine cycle is simply a Rankine cycle operating with organic fluids instead of steam. Due to the low boiling point of some organic fluids, they can be utilized in low to medium heat source applications [8, 9]. In addition, the densities of organic fluids are relatively high, which results in smaller systems compared to steam;hence, there are lower costs [10]. Typical Rankine cycles consist of four main components, namely, an evaporator, turbine, condenser, and pump. The turbine is one of the most important components in the system since this is the medium where power production takes place [11]. Variable geometry turbines are of valuable interest especially in internal combustion engines in order to cope with the transient operating conditions in the engine. Conventional radial turbines (fixed geometry turbines) suffer from low efficiencies at part-load conditions [12]. A variable geometry radial turbine is simply a radial turbine that has movable stator vanes which provide a quick response to the change in engine load/speed [13]. In addition, by utilizing variable geometry vanes, it is possible to adjust the mass flow rate and to balance the volume of the working fluid [13]. The concept of variable geometry turbines is not new and has been extensively studied for turbocharging. However, applying such a technology in ORC systems is an area in which little available literature exists. Therefore, the investigated literature is limited to applications of the ORC with variable geometry turbines. The application of ORCs in internal combustion engines, covering different types of expansion machines, was extensively reviewed in the authors' study [14]. The authors also experimentally tested the potential of ORCs for waste heat recovery using fixed geometry turbines in several studies [15]. [PERSON] et al. [16] simulated a 1.25 L Zetec-SE DOHC engine model coupled with an organic Rankine cycle and a variable geometry turbine. The results showed that the variable geometry turbine can improve the thermal efficiency and net power by 5.59% and 3 kW, respectively. [PERSON] et al. [17] evaluated the performance of an ORC considering geothermal resources as the heat sources. Although a variable geometry turbine was considered, the authors did not point out the potential of the turbine. They concluded that the net power output is higher at low ambient temperatures than at warm ones. [PERSON] and [PERSON] [18] examined the decarbonization of marine transport using an ORC and a variable geometry turbine. The results showed that the highest system efficiency of 15% was achieved by utilizing the variable geometry turbine. [PERSON] et al. [19] investigated the thermodynamic optimization of organic Rankine cycles considering both fixed and variable geometry radial inflow turbines. The results proved the efficacy of variable geometry turbines when operating at off-design conditions. Other scholars integrated fixed geometry radial inflow turbines or other types of turbines, such as axial ones. [PERSON] et al.