An approximate solution for the complex heat transfer of external fluid heat loads in civil aircraft fuel systems is provided in this article, with the wing fuel tank serving as an example. The skin is treated as a large flat plate, and the aim is to investigate the one-dimensional unsteady complex heat transfer law along the thickness direction of the flat plate. The research process introduces the penetration depth, penetration time, and dimensionless parameters of heat transfer, and the concept of the temperature distribution function is combined with the calculation methods of heat balance integral and approximate time integral to solve the inner surface temperature of the skin. The analytical and numerical solutions obtained by previous scholars are verified. It is demonstrated that the approximate solution method can be competent for calculating the heating process, with the absolute error controlled within 0.05. However, a more significant error is observed in the cooling process, with the absolute error controlled within 0.07, except for large radiation Biot numbers. The solution method can be applied to calculate the external heat load heat transfer of fuel tanks made of different materials, which is especially valuable for the study of airworthiness certification of composite fuel tanks.
Yang et al. (2026) studied this question.