The stability criterion is established for two-phase transpiration cooling with phase-transition equilibrium inside the porous wall.As an effective method of thermal protection, one now widely recommends the use of liquids which evaporate inside the cooled wall. Two-phase cooling offers some excellent features: a high absorption capacity of the coolant, which is due to evaporation of the liquid and the subsequent superheating of the generated vapor; there is no limitation here on the thermal flux density and on the shearing stresses at the outer surface; the discharging superheated vapor alters the temperature distribution in the outer boundary layer to such an extent that convective heat transfer to the surface abates appreciably; a temperature rise, within permissible limits, at the outer surface does further reduce the convection of heat and causes some of the heat to be dissipated into the ambient space by radiation. Despite these obvious advantages, such a cooling system has so far remained completely unexplored. The reason for this is not a lack of research activity, but that, as experiments have revealed, a process with phase transformation inside a cooled wall is unstable [1-6]. Among all thermoteehnical devices, those with phase transformation of the active medium are most prone to unstable operation whenever a small perturbation of the process parameters induces a transition of the system from one state to a very different other state [9][10][11][12][13]. Best known are such types of aperiodical instabilities in thermotechnical devices as critical boiling modes and sudden wide fluctuations in the flow rate of the active medium in the hot piping system of parallel-flow boilers.In an unstable two-phase cooling system it is impossible for the boiling zone inside the porous wall to stabilize. A result of a higher heat load is that the stream of liquid which evaporates at the surface becomes replaced by a stream of vapor. The flow rate of coolant under constant feed pressure decreases fast and, under heavy heat loads, this is accompanied by a burning of the wall.Instability under operating conditions typical of most experimental transpirators basically alters the system performance and gives rise to new dominant phenomena. We still have found no explanation for the essential characteristics of the stable process here and for the way in which various parameters affect them. According to the published evidence, two stable two-phase cooling systems have been so far developed successfully [6][7][8]. In both systems the stability is attained by the use of a multilayer porous structure, but ideas concerning the necessary properties of individual layers are vague. As to the effect of other parameters on the process stability, the authors of [7] have made some general assumptions which are valid for all two-phase systems.The lack of necessary data pertaining to the basic trends of the stable process here makes a thorough mathematical description and subsequent computer-aided analysis impossible.A logical way out of ...