Development and validation of a first principles fluid-thermal multi-physics solver for hypersonic boundary layer heat transfer problems

= density u = velocity, = (u; v; w) p = thermodynamic pressure T = thermodynamic temperature E = total energy, = e+ 1 2 uiui e = internal energy, = p=( 1) = stress tensor, ij = (@ui=@xj + @uj=@xi) + @uk=@xk ij S = source c = speci c heat capacity = gas ratio of speci c heats, = Cp=Cv k = thermal conductivity ; = rst and second coe cients of uid viscosity qj = uid heat ux vector, = k@T=@xj x = spatial coordinates, = (x; y; z) = computational coordinates, = ( ; ; ) t = time = convergence value

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