- Algebraic truncation models were derived for the turbulent energy flux for high-speed shear flows with and without thermal and mechanical non-equilibrium effects. The equilibrium model was developed for high-temperature gases with caloric imperfections. Fluctuating dilatation moments were modeled via conservation of mass truncations. The model provided significant improvements, up to 20 percent, in the temperature predictions over the gradient diffusion model for a Mach number range of 0.02 to 11.8. Analyses also showed that the near wall dependence of the algebraic model agreed with expected scaling, where the constant Prandtl number model did not. This led to a simple modification of the turbulent Prandtl number model. A thermal non-equilibrium energy flux model was derived, where our experiments show that relaxation of an internal energy mode alters the basic transport of turbulence. Compressibility led to an explicit pressure gradient dependency with the present model. Analyses of a governing parameter indicated that these terms are negligibly small for low speeds. However, they may be important for high-speed flow. Comments towards extending the models to include pressure gradient flows are provided. Copyright 2009 by Rodney D. W. Bowersox.