Heat transfer modeling using fractional differential equations

This study looks into how fractional differential equations (FDEs) can be used to model heat transfer. FDEs are an extension of standard Fourier-based models that add memory and nonlocal effects. Fractional derivatives enable precise modelling of the anomalous diffusion observed in mixed, porous, or microscale materials. Various analytical methods, including Laplace transforms and variable separation, are employed to resolve fractional heat transfer equations. Numerical techniques, such as finite difference and spectral techniques, are also used. The results show that lowering the fractional order slows thermal diffusion. This captures the real non-Fourier behaviour in complex materials and improves the ability to predict what will happen in advanced thermal system modelling.

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