In view of the complex behaviors in the heat and fluid flow involving the different differential and integral operators, e. g., classical, fractional-order, local fractional (fractal), and other operators, our chief aims of the special issue is to propose the new methods for finding the approximate or exact, or analytical or, numerical solutions for the ODE and PDE for the descriptions of more reasonable models for the problems as well as the new computational technologies with the fractal dimension, and to present the new and novel operators as mathematical tools to handle the more reasonable models for the heat and fluid flow. This special issue, entitled Advanced Computational Methods for Linear and Non-linear Heat and Fluid Flow, consists of 44 papers.