A fuzzy numerical solution of a one-dimensional steady-state heat conduction problem with a constant gradient

Fuzzy differential equations have been gaining popularity in recent years.  Traditional heat transfer models often rely on precise input parameters; however, real-world scenarios frequently involve uncertainty and imprecision.  With advancements in mathematical modeling, the heat transfer increasingly used to address real-world problems.  This paper presents a one-dimensional steady-state fuzzy heat transfer problem.  To solve this problem, the fuzzy Runge–Kutta Cash–Karp of the fourth–order method is employed, demonstrating its effectiveness.  The results are then compared to analytical solutions, revealing that the approximate solutions closely align with the analytical ones.