A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.<\/p>\r\n","references":"[1]\tAskerov D.D., Pashaev A.M., Samedov A.S. The possibility of improving aviation gas turbine engines and the problem of thermal protection of their elements. Scientific works of NAA. Vol. 2, Baku, 2002.\r\n[2]\tBoyko A.V. Optimal design of axial turbomachines flow part. Kharkov, Vyscha Schkola, 1982.\r\n[3]\tGalitseyskiy B.M., Sovershennyi V.D., Formalev V.E., Chernyi Thermal protection of turbine blades. Moscow: MAI, 1996.\r\n[4]\t Golubeva O.I. Determination of temperature field of gas turbine blades. Works of CIAM, No. 129. - Moscow: Oborongiz, 1947.\r\n[5]\tKopelev S.Z., Slitenko A.F. Design and calculation of gas turbine cooling systems. Under. Ed. A.F. Slitenko. Kharkov; Publishing House Osnaova, 1994.\r\n[6]\tPashayev A.M., Askerov D.D., Sadykhov R.A. Modeling of temperature fields in aviation gas turbine engines. Works of Central Aerohydrodynamic Institute named after N.E. Zhukovsky, vol. 2661 - M: CAI, 2003.\r\n[7]\tPashayev A.M., Askerov D.D., Sadykhov R.A. Modeling of temperature fields in gas turbine engine elements. Works of X International. scientific and technical. conference \"Mechanical engineering and technosphere of XXI century\". Sevastopol, 2003.\r\n[8]\tPashayev A.M., Sadykhov R.A., Samedov A.S. Modeling of temperature fields of gas turbine blades. Bulletin of Bauman Moscow State Technical University, series: Mechanical engineering. Vol. 38, No. 1, 2000.\r\n[9]\t Pashayev A.M., Sadykhov R.A., Samedov A.S. Modern directions of creation high-temperature gas turbines. Works of VI International scientific and technical conference \"Mechanical engineering and technosphere at the turn of XXI century.\" - Donetsk, STU, Vol.2, 1999.\r\n[10]\tPashayev A.M., Sadykhov R.A., Efendiev O.Z., Samedov A.S. Effective methods for calculating gas turbine blades. Abstracts of XI All - Russian Interuniversity Scientific and Technical Conference \"Gas Turbine and Combined Installations and Engines\". Bauman Moscow State Technical University. - M .: SPRL, 2000.\r\n[11]\tSadykhov R.A. Mathematical modeling and control of multiply connected systems. In book. Actual problems of fundamental sciences. - Moscow: Bauman Moscow State Technical University, vol.1, 1991.\r\n[12]\tSadykhov R.A. Mathematical modeling and control of multiply connected systems in restricted environments with rejections. In book. Actual problems of fundamental sciences. - Moscow: Bauman Moscow State Technical University, vol.2, p.1, 1994.\r\n[13]\tSadykhov R.A., Samedov A.S. Modeling of temperature fields of elements of gas turbines. Scientific notes of Az.TU. Volume VI, \u21165. Baku, Az.TU, 1998.\r\n[14]\tHeat exchanging devices of combustion turbine and combined units \/ N.D. Gryaznov, V.M. Epifanov, V.L. Ivanov, E.A. Manushin. - M .: Mechanical Engineering, 1985.\r\n[15]\tHeat transfer in cooled parts of gas turbine engines of aircrafts \/ V.I. Lokay, M.N. Bodunov, V.V. Zhuikov, F.V. Shchukin. - M .: Mechanical Engineering, 1995.\r\n[16]\t Pashayev A., Askerov D., Sadykhov R., Ardil C. Development of Effective Cooling Schemes of Gas Turbine Blades based on computer simulating. IJCI Proceed. ISSN 1304-2386, vol.1, num:2. September 2003.\r\n[17]\tPashayev A.M., Sadykhov R.A., Samedov A.S. Highly effective methods of calculation temperature fields of blades of gas turbines. V International Symposium an Aeronautical Sciences \u201cNew Aviation Technologies of the XXI century\u201d, A collection of technical papers, section N3, Zhukovsky, Russia, august,1999.\r\n[18]\t Pashayev A.M., Sadykhov R.A., Hajiev C.M. The BEM Application in development of Effective Cooling Schemes of Gas Turbine Blades. 6th Bienial Conference on Engineering Systems Design and Analysis, Istanbul, Turkey, July, 8-11,2002.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 107, 2015"}