Panel tilt angles (0°–90°) need to be in a proper position and location to get maximum productivity from solar energy. Values used in solar energy applications are generally computed by (global, diffuse, and direct) variation on horizontal surfaces calculated using isotropic sky and a mean albedo method. Being parallel to the available literature concerning such applications, this study focuses on the optimum solar panel angle. In this study, optimum solar panel angle value by months was determined for three sample provinces (Antalya, Kayseri, and Trabzon) first and North Hemisphere then. Capacity calculation of sample provinces was performed based on monthly, seasonal, and annual angle values and horizontal situation. Monthly and annual optimum angle values for Northern Hemisphere by 1° increase for between the latitudes of 1° N and 65° N. While the panel angle is at the highest level in autumn and winter (November-December-January and February) in annual process, the lowest angle is observed in spring and summer (May-June-July-August). Several different mathematical models have been developed for the sample provinces and Northern Hemisphere. While the variable of 12 different models that were developed for provinces is the Declination (δ) coefficient, the variable of 7 different models that were developed Northern Hemisphere is the latitude (Ø). Regional values in literature with estimation results of models were analyzed based on NASA and PVGIS data color scale. There was created a possibility of comparison by aligning all the optimum solar panel angle values of related location via a scale whose values vary by 1 and 10. Moreover, all the models were verified by statistical analysis methods. R² (determination coefficient) in 19 different estimation equations is pretty close or equal to 1. However, the best among them is Eq. 32 (0.9979) for sample provinces and Eq. (33) (1) for the Northern Hemisphere; developed models are less-than-stellar. Other statistical data of these equations are MBE (−0.0616), RMSE (1.1176), t-sat (0.1830), Bias (1). For Eq. (32); MBE (1.96), RMSE (2.75), t-sat (8.13), MPE % (3.98), MAPE (5.87), SSRE (0.27), and RSE (0.06) for Eq. (33). The statistical analyzes indicate that all regression models are applicable in Turkey and Northern Hemisphere. Developed all correlations are recommended for academic and industrial users.

The importance of solar radiation for the body’s ability to synthesize Vitamin D₃ is well documented, yet the precise amount of sun exposure required to avoid Vitamin D insufficiency is less clear. To address this knowledge gap, this study sought to utilize the sun in a suitable period at the optimum dose by utilizing numerical simulations to determine the amount of Vitamin D₃ synthesis in the skin according to season, time of day, and geographical location in Turkey. The study was carried out in three stages; in the first stage, daily, monthly, and annual values were determined in cases where the solar zenith angle has the active UV-B wavelength. The second stage determined the level of Vitamin D that can be synthesized in all skin types at 25% solar radiation exposure. In the third stage, the sun exposure time required for 1000 International Units (IU) for all skin types was calculated. According to the analysis, the yearly period of active synthesis of D₃ on Earth lasts from the beginning of March to the third week of October. During the day, it is between 10:00 and 16:00. For 1000 IU/day, the average annual estimated times (minutes) are 5.05 for Type I, 6.3 for Type II, 7.6 for Type III, 11.35 for Type IV, 15.15 for Type V, and 25.25 for Type VI. The results of this paper will impact awareness for academic-medical users.

Insulating is the most effective method that is used to save energy in buildings. Samples from cities from different climatic zones from TS 825 (Turkey) first. Optimum insulation thickness ( $x_{opt}$) analysis is based on two types of insulating and four different fuels (natural gas, coal, fuel oil and electric) of related cities. Cost accounts, payback period and CO₂-SO₂ emission calculations were performed based on these analyses. Second of all, the relationship between a number of degree day (NDD) and optimum insulation thickness ( $x_{opt}$) was developed by linear, quadratic and cubic correlations. Thirty different mathematical correlations based on different fuel types by using XPS and EPS insulating materials. Twenty-four of these models that were developed were generated peculiar to the fuel type; six of them were generated based on average insulation thickness. R² values of related correlations are between 0.9989 most and 0.9952 at least as well as it is pretty close to (R ≤ 1) one value. The model among these models is the $x_{opt}=a+b\left(NDD\right)+c{\left(NDD\right)}^2+d{\left(NDD\right)}^3$ cubic mathematical model that gives the best average value. a = 0.0036, b = 5E-05, c = – 7E-09 and d = 6E-13 are the values for XPS material. Following values are for EPS material; a = 0.0028, b = 5E-13, c = – 7E-09 and d = 4E-05. R² determination coefficient of both two equations is pretty close to 0.9989 and 1; the models obtained are less-than-stellar. Optimum insulation thickness of the area can be known based on the type of material via the number of degree day without the need for long analyses. According to the R² values, the use of all models is recommended for academic and industrial users.

The current study depicts the effects of different insulation materials and fuel types on the cooling and heating performance of buildings situated in hot and dry, warm and humid, composite, and cold climatic conditions in India. Ten different locations chosen from diverse climatic regions were selected, and various potential parameters for expanded polystyrene and extruded polystyrene insulation materials were evaluated. Potential parameters, such as optimal insulation thickness, annual savings, and payback period, were computed for cooling and heating requirements and were found in the ranges of 0.0428–0.891 m, 10.83–19.19 $/m², and 1.49–2.36 years for cooling, as well as 0.0063–0.1522 m, 0.29–55.92 $/m², and 0.95–6.52 years for heating, respectively. An emission analysis was also carried out for the estimation of greenhouse gas (GHG) emissions by the engagement of optimal insulation thickness for heating. The GHG emissions from natural gas, coal, and diesel by the employment of various insulating materials were found in the ranges of 5.39–11.28, 9.47–32.68, and 2.26–4.51 kg/m²-year, respectively. A correlation formulation (power) for optimal insulation thickness was also carried out. For checking the preciseness of the developed mathematical models, statistical tools were utilized, and their obtained values in the satisfactory range signified the accurateness of the developed models.

Alternative fuels such as biodiesel and n-butanol offer environmental benefits but are limited by low energy density and combustion efficiency. This study examines the effects of multi-metal oxide nanoparticles on the combustion, performance, and emissions of B20 and B20But10 blends in a single-cylinder diesel engine. Experiments were conducted at four engine loads and nanoparticle concentrations ranging from 0 to 100 ppm. Response Surface Methodology was applied to optimize performance and emissions. The addition of 75 ppm Zn_0.5Mn_0.5Fe₂O₄ increased brake thermal efficiency by 1.5% for B20 and 2.6% for B20But10, while reducing brake specific fuel consumption by 2.52% and 1.47%, respectively. Both blends showed substantial reductions in CO, HC, and smoke emissions, although NOₓ emissions increased due to higher combustion temperatures. The ignition delay was reduced by 2°CA in both blends at the highest nanoparticle concentration, indicating earlier and more controlled combustion. The optimal nanoparticle concentration ranged from 68 to 89 ppm, and the optimal engine load from 0.46 to 3 bar. Enhanced atomization and combustion uniformity from the nanoparticles led to improved efficiency and cleaner combustion. The findings demonstrate that Zn_0.5Mn_0.5Fe₂O₄ is a promising additive for sustainable diesel engine operation using biodiesel–n-butanol blends. Graphical abstract