1 Vol.:(0123456789) Scientifc Reports | (2022) 12:13275 | https://doi.org/10.1038/s41598-022-15396-z www.nature.com/scientificreports Assessment of thermal distribution through an inclined radiative‑convective porous fn of concave profle using generalized residual power series method (GRPSM) R. S. Varun Kumar 1 , G. Sowmya 2 , M. C. Jayaprakash 3 , B. C. Prasannakumara 1 , M. Ijaz Khan 4,5 , Kamel Guedri 6 , Poom Kumam 7,8* , Kanokwan Sitthithakerngkiet 9 & Ahmed M. Galal 10,11* The thermal distribution in a convective‑radiative concave porous fn appended to an inclined surface has been examined in this research. The equation governing the temperature and heat variation in fn with internal heat generation is transformed using non‑dimensional variables, and the resulting partial diferential equation (PDE) is tackled using an analytical scheme, generalized residual power series method (GRPSM). Moreover, a graphical discussion is provided to examine the consequence of diverse non‑dimensional variables including the parameters of convection‑conduction, ambient temperature, radiation, heat generation, and porosity efect on the thermal feld of the fn. Also, a graph is plotted to analyze the variations in unsteady temperature gradient using the fnite diference method (FDM) and generalized residual power series method (GRPSM). The major result of this investigation unveils that as the convection‑conduction parameter scale upsurges, the distribution of temperature in the fn diminishes. For the heat‑generating parameter, the thermal distribution inside the fn increases. Abbreviations k Termal conductivity Nc Convection–conduction parameter α Angle of inclination OPEN 1 Department of Mathematics, Davangere University, Davangere, Karnataka 577002, India. 2 Department of Mathematics, M S Ramaiah Institute of Technology, Bangalore, Karnataka 560054, India. 3 Department of Information Technology, University of Technology and Applied Sciences, Al Mussanah, Sultanate of Oman. 4 Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad 44000, Pakistan. 5 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. 6 Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah 21955, Saudi Arabia. 7 Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. 8 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan. 9 Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), 1518, Wongsawang, Bangsue, Bangkok 10800, Thailand. 10 Mechanical Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University, Wadi ad-Dawasir 11991, Saudi Arabia. 11 Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, P.O. 35516, Mansoura, Egypt. * email: poom.kum@kmutt.ac.th; ahm.mohamed@psau.edu.sa