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In the present series of papers we propose a consistent description of the mass loss process. To study in a comprehensive way the effects of the intrinsic magnetic field of a close-orbit giant exoplanet (a so-called hot Jupiter) on atmospheric material escape and the formation of a planetary inner magnetosphere, we start with a hydrodynamic model of an upper atmosphere expansion in this paper. While considering a simple hydrogen atmosphere model, we focus on the self-consistent inclusion of the effects of radiative heating and ionization of the atmospheric gas with its consequent expansion in the outer space. Primary attention is paid to an investigation of the role of the specific conditions at the inner and outer boundaries of the simulation domain, under which different regimes of material escape (free and restricted flow) are formed. A comparative study is performed of different processes, such as X-ray and ultraviolet (XUV) heating, material ionization and recombination, cooling, adiabatic and Lyα cooling, and Lyα reabsorption. We confirm the basic consistency of the outcomes of our modeling with the results of other hydrodynamic models of expanding planetary atmospheres. In particular, we determine that, under the typical conditions of an orbital distance of 0.05 AU around a Sun-type star, a hot Jupiter plasma envelope may reach maximum temperatures up to ∼9000 K with a hydrodynamic escape speed of ∼9 km s–1, resulting in mass loss rates of ∼(4-7) · 1010 g s–1. In the range of the considered stellar-planetary parameters and XUV fluxes, that is close to the mass loss in the energy-limited case. The inclusion of planetary intrinsic magnetic fields in the model is a subject of the follow-up paper (Paper II). [ABSTRACT FROM AUTHOR]