Abstract This study explores the unsteady three-dimensional forced convection flow of a Powell-Eyring nanofluid over a bidirectional stretching surface under the non-Fourier heat flux model. The analysis incorporates Joule heating, radiative heat and internal heat effects. Using similarity transformations, the governing equations are reduced to nonlinear ordinary differential equations and solved numerically via the shooting method. Two nanofluids-copper/kerosene oil ( Cu-KO ) and silicon carbide/kerosene oil ( SiC-KO ) are examined. The impact of various parameters on velocity, temperature, skin friction, heat transfer rate, and entropy generation is explored. In addition, statistical analysis based on response surface methodology and sensitivity analysis is carried out to quantify the relative influence of key physical parameters on the heat transfer performance. Results show that a rise in thermal relaxation time enhances heat transfer by 0.38 %–2.17 % for Cu-KO and 0.26 %–1.33 % for SiC-KO . A 60 % increase in the radiative heat boosts heat transfer by 17.55 % and 17.78 % for Cu-KO and SiC-KO , respectively. Entropy generation intensifies with the Reynolds and Brinkman numbers and is more pronounced in copper-based nanofluids. These findings provide valuable insights for high-temperature industrial and energy systems, including solar thermal collectors, microchannel heat exchangers, and other controlled heat transfer applications utilizing kerosene oil-based nanofluids.
Zafar et al. (Tue,) studied this question.