Computational fluid dynamics and heat transfer has been advanced since the second half of the 20^th century, in parallel to computer hardware evolution, offering simulation tools for modern thermal and fluids engineering design. Nevertheless, classical analytical approaches for partial differential equations remained in use, along this same period, due to benchmarking and preliminary conceptual design needs. Analytical methods offer evident advantages in precision, robustness, and computational speed, but are very restricted by the complexity of the mathematical formulations. To narrow this gap, hybrid numerical-analytical methodologies have been proposed along the way to benefit from both the accuracy and robustness of an analytic-based solution path and the flexibility of numerical methods. One such hybrid approach is the so called Generalized Integral Transform Technique (GITT), which is a generalization of the classical integral transform method. The immediate gain was the expansion of the benchmarks database for the verification of numerical codes and the expansion on the classes of problems that can be dealt with in preliminary design. However, the GITT was progressively extended for about forty years, leading to a widely applicable computational-analytical approach that deals with nonlinear formulations, irregular domains, heterogeneous media, coupled problems, moving boundaries, boundary layer and Navier-Stokes equations. Also, in CPU-intensive simulations that require numerous evaluations of a partial differential system solution, which may include optimization, inverse problem analysis, simulation under uncertainty, and physically informed neural networks, the analytic nature behind the hybrid methodology leads to more evident advantages. The GITT is here reviewed and illustrated, emphasizing recent methodological developments, for two selected transport phenomena forward-inverse problem solutions.