In this talk, we focus the initial-boundary value problem of compressible Euler equations with friction and heating that model the combined Fanno-Rayleigh flows through symmetric variable area nozzles. A new version of a generalized Glimm scheme (GGS) is presented for establishing the global existence of transonic entropy solutions. Modified Riemann and boundary Riemann solutions applied to design this GGS from the contraction matrices of the homogeneous Riemann (or boundary-Riemann) solutions. Moreover, extended Glimm-Goodman wave interaction estimates are investigated for ensuring the stability of the scheme and the positivity of gas velocity that leads to the existence of the weak solution. By showing the entropy inequality, we show that this weak solution is the entropy solution.