This study presents a novel fifth-order iterative method for solving nonlinear systems derived from a modified combination of Jarratt and Newton schemes, incorporating a frozen derivative of the Jacobian. The method is applied to approximate solutions of the nonlinear convection–diffusion equation. A MATLAB script function was developed to implement the approach in two stages: first, discretizing the equation using the Crank–Nicolson Method, and second, solving the resulting nonlinear systems using Newton’s iterative method enhanced by a three-step Jarratt variant. A comprehensive analysis of the results highlights the method’s convergence and accuracy, comparing the numerical solution with the exact solution derived from linear parabolic partial differential transformations. This innovative fifth-order method provides an efficient numerical solution to the nonlinear convection–diffusion equation, addressing the problem through a systematic methodology that combines discretization and nonlinear equation solving. The study underscores the importance of advanced numerical techniques in tackling complex problems in physics and mathematics.

Hybrid photovoltaic (PV) and thermoelectric generator (TEG) systems combine heat and light energy harvesting in a single module by utilizing the entire solar spectrum. This work analyzed the feasibility and performance of a hybrid photovoltaic–thermoelectric generator system with efficient thermal management by integrating heat pipe (HP), radiative cooling (RC), and heat sink (HS) systems. The proposed system effectively reduces the PV operation temperature by evacuating the residual heat used in the TEG system to generate an additional amount of electricity. The remaining heat is evacuated from the TEG’s cold side to the atmosphere using RC and HS systems. This study also analyzed the inclusion of two TEG arrays on both sides of the HP condenser section. This numerical analysis was performed using COMSOL Multiphysics 5.5 software and was validated by previous analysis. The performance was evaluated through an energy and exergy analysis of the TEG and PV systems. Enhancing the thermal management of the hybrid PV-TEG system can increase energy production by 2.4% compared to a PV system operating under the same ambient and solar radiation conditions. Furthermore, if the proposed system includes a second array of TEG modules, the energy production increases by 5.8% compared to the PV system. The exergy analysis shows that the enhancement in the thermal management of the PV operating temperature decreases the thermal exergy efficiency of the proposed system but increases the electricity exergy efficiency. Including TEG modules on both sides of the condenser section of the HP shows the system’s best thermal and electrical performance. These results may be helpful for the optimal design of realistic solar-driven hybrid systems for globally deserted locations.

Graphene oxide (GO) has garnered significant interest due to its exceptional and tunable properties, which make it a promising candidate for a wide range of engineering applications, including composite material fabrication and water treatment. In this study, GO was synthesized from graphite flakes using a modified Hummers method involving a reduced amount of sulfuric acid. The resulting material was characterized using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and X-ray photoelectron spectroscopy (XPS). These techniques enabled a clear differentiation between the morphology of the synthesized GO and that of the original graphite. The GO exhibited a substantially altered structure, with increased thickness likely due to the incorporation of oxygen-containing functional groups on its basal plane. FTIR analysis confirmed the presence of characteristic functional groups such as hydroxyl, carbonyl, and carboxyl. XPS analysis revealed that the elemental composition of the synthesized GO consisted of approximately 69.7% carbon and 29.9% oxygen, with a trace amount of sulfur attributed to the reagents used in the synthesis. The observed changes in morphology and composition suggest the successful synthesis of GO with potential for functionalization and application in diverse engineering contexts.

In the present investigation, carbon dioxide (CO₂), carbon monoxide (CO), hydrocarbons (HC), nitric oxides (NO_X), particulate matter (PM), and fuel consumption were measured in a compression ignition internal combustion engine on a road route cycle in Quito, Ecuador. We used premium diesel and a mixture of diesel and cerium oxide at a concentration of 250 ppm. This research aimed to investigate the impact of cerium oxide on fossil fuels in terms of CO₂, CO, HC, NOx, PM, and fuel consumption. Five repetitions were performed for each fuel, and the results obtained were statistically analyzed using control charts. The experimental results showed a 27.1% reduction in PM, a 24.9% increase in NOx, and a 24.2% increase in HC, along with a 1% decrease in fuel consumption compared to the premium diesel case. We observed that the reduction in PM was due to the catalytic action of CeO₂, which enhances carbon oxidation. On the other hand, the increase in NOx was related to the higher temperature in the combustion chamber resulting from the improved thermal efficiency of the engine. This study provides guidelines for controlling air pollutants originating from vehicle emissions in high-altitude (over 2000 masl) road operations using cerium oxide as an additive.