Numerical Simulation of Time Fractional Nonlinear Heat Transfer Equation With Predictor-Corrector Approach

This article enables the changing specific heat coefficient to solve two nonlinear heat transfer problems. With mechanical engineering at the cutting edge, efficient heat transmission is essential to the effectiveness, safety, and performance of many engineering systems. The transfer of heat occurs through multiple pathways, including conduction, convection, and radiation, each playing a vital role in shaping the thermal landscape of modern technologies. We propose a fractional-order approach to reduce the complexity of the study. Here, using the Caputo fractional derivative (CFD), we examine and evaluate the solutions of the considered problems using the Predictor-Corrector method (PCM). To verify the reliability of the considered approach, the present findings are compared with those of the variational iteration method (VIM), homotopy perturbation method (HPM), hermite wavelet method (HWM), differential transformation method (DTM) and the accurate solutions. The PCM is typically more advantageous for actual numerical calculations, particularly when flexibility, stability, and accessibility of implementation are needed. The outcomes suggest that the PCM can forecast the solution of such problems with more appropriate results.