Mathematical Formulation and Numerical Study of Parameter‐Performance Relationships for Thermal Protective Clothing Under Windy Conditions

ABSTRACT This study focuses on developing a coupled heat transfer model in the Environment‐Clothing‐Human body system under realistic firefighting conditions, which shows how ambient temperature, wind velocity, and perspiration rate influence skin‐burn injury. The model, consisting of a three‐layer fabric, a single air gap and a double‐layer skin structure, is derived based on Darcy's law and the Bernoulli equation for airflow. The existence of weak solutions to the resulting nonlinear PDE system is mathematically proved via the Galerkin approximation, energy estimates, and compactness arguments. Uniqueness is established using the classical energy method combined with Grönwall's inequality. Numerical simulations are performed with a mixed explicit‐implicit finite difference scheme, and Henriques' burn integral is employed to evaluate skin burn injury and predict the longest safe working time. The numerical simulation results indicate that burn injury increases with higher wind velocities and meanwhile decreases with greater perspiration rates when the parameters are chosen from engineering applications. These results provide a scientific basis for the design of firefighting protective clothing and enhance the interpretability of the model.