“…Cubic spline curves are piecewise polynomials consisting of adjacent segments. The most crucial engineering application for splines is path planning (Mahmood et al, 2019) in robotics (Ghafil and Jármai, 2019). The heat exchanger (Bouchenna et al, 2021) is a device used to heat transfer between two or more fluids for various applications, including power plants, nuclear reactors, refrigeration and air condition system, automotive industries, heat recovery system, chemical processing and food industries.…”