Variational formulation for a fractional heat transfer model in firefighter protective clothing

We propose a fractional heat transfer model to simulate the situation with high temperature and high humidity. The variational formulation for the fractional model is first proposed, which eliminates the singularity of homogeneous problem by multiplying a simple function factor. To prove the existence of weak solution of the variational problem, Galerkin approximation is utilized. The corresponding stability and uniqueness are also derived. To verify the reliability of the proposed model, numerical experiment is carried out, which indicates that our fractional model is appropriate for the heat transfer in firefighter protective clothing.