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A new variable density / physical property wall function formalism has been developed. The new formalism is designed to extend the validity range of wall functions to cover both the low- and high-Reynolds-number domains so that the restrictions on the non-dimensional near-wall mesh resolution can be avoided. The new formalism also accounts for the temperature gradient induced variations of density, viscosity, heat conductivity and specific heat capacity. The new wall function formalism is constructed in conjunction with a modified low-Reynolds-number turbulence model in order to avoid the conflicting requirements of low- and high-Reynolds-number models on the near wall mesh resolution. The new formulation is validated with test simulations of strongly heated air flows in circular tube against measurements and Direct Numerical Simulation (DNS) results.