## 1 Introduction  
Improving the performance and examination of diesel engine emissions is the main feature of much recent research. One of the most important measures addressed in this research regarding enhanced performance and reduced emissions is the introduction of nanotechnology as a fuel additive. It was noted that the quality of combustion was increased through the use of nanoparticles mixed with fuel, and as a result, the overall performance of the engine was improved [1]. To further achieve this goal, many different oxygenated additives have been used with biofuels by many researchers to study their effect under a wide range of engine operating conditions. For example, combustion characteristics and engine performance were improved by adding nanomaterial oxide particles to fuel mixtures, including AL\({}_{2}\)O\({}_{3}\), Fe\({}_{3}\)O\({}_{4}\), CuO, TiO\({}_{2}\), and others, as this addition proved to increase the heat release rate and thermal efficiency [2; 3]. The ability of oxide nanoparticles to donate oxygen atoms during the combustion process is a prominent feature of creating a high surface-to-volume ratio, making it a highly reactive medium that aids in combustion. More precisely, mixing nanoparticles with neat engine oil increases the kinematic viscosity; it raises the flash point temperature and increases the flash point temperature due to increases in thermal conductivity [4; 5; 6]. It is known that fossil fuels are the most used energy sources in industrial settings. The harmful effects of gases emitted from internal combustion engines on human and animal life, as well as crops, become clear. Unfortunately, these emissions contain substances that are harmful to human health, as these emissions contain more than 40 toxic pollutants that spread into the air surrounding these facilities. Environmental conservation organizations classify the compounds and derivatives found in internal combustion engine emissions as the most influential, as they include hydrocarbon (HC), particulate matter (PM), nitrogen oxide (NOx), carbon dioxide (CO\({}_{2}\)), and other gases, recording 600 million, an important factor resulting from these emissions [7]. The data also confirm the degree to which it directly affects climate change and causes the expansion of the outer layer of the ozone layer, as well as the negative effects on people who suffer from diseases, such as bronchitis, chronic lung disease, and others. In addition, harmful substances accumulate in agricultural crops and impact the economic security of the world [7]. These reports helped environmental specialists and researchers find many applied solutions [8; 9]. Many programs and plans have been prepared to avoid the problem of pollution, especially reducing emissions resulting from the combustion of fossil fuels through research in the field of fuel technology using many solutions, the most prominent of which is the use of additive technology by mixing traditional fuel with biofuel or the use of nano additives to reduce emissions [10; 11; 12], as well as the development of filtration systems for exhaust gases. Using biodiesel blends with nanomaterials, the detailed combustion mechanism was studied as a new process for developing diesel engines [13; 14]. The interaction between soot particles and NOx was described, and it was reported that both the radiation resulting from the thermal process as well as the reaction resulting from the chemical process help increase the influence of soot on nitrogen oxides [15; 16]. Many experiments on diesel engines were carried out, fueled by the biodiesel blends with nanomaterials. The results of these tests were compared with simulation results at the same conditions [17; 18; 19; 20]. Through numerical investigations, it is clear that adding nanomaterials to fuel contributes to increasing the ignition delay and heat release rate during the combustion operation, which in turn leads to a higher peak pressure as well as a higher exhaust temperature.