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A review of conjugate convective heat transfer problems solved during the early and current time of development of this modern approach is presented. The discussion is based on analytical solutions of selected typical relatively simple conjugate problems including steady-state and transient processes, thermal material treatment, and heat and mass transfer in drying. This brief survey is accompanied by the list of almost two hundred publications considering application of different more and less complex analytical and numerical conjugate models for simulating technology processes and industrial devices from aerospace systems to food production. The references are combined in the groups of works studying similar problems so that each of the groups corresponds to one of selected analytical solutions considered in detail. Such structure of review gives the reader the understanding of early and current situation in conjugate convective heat transfer modeling and makes possible to use the information presented as an introduction to this area on the one hand, and to find more complicated publications of interest on the other hand.

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Heat transfer between a hot, semi-infinite plate and thin liquid film flowing over its surface is considered. As the plate is semi-infinite, the finite cooled portion of the plate and the temperature at the moving film front are time variable. The heat transfer is transient, as opposed to the usual quasi-steady process that exists when the plate is infinite. To investigate the transient heat transfer, solutions describing the temperature fields of the wet and dry portions of the plate are conjugated at the moving film front. The basic characteristics of transient cooling process are found to be governed by a dimensionless parameter named the Leidenfrost number, which is the ratio of the Biot number and the square of the Peclet number. The plate temperatures at the moving front, the film velocity, and the time required to reach the wetting temperature are calculated.

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A saturated liquid-vapor mixture discharging from a pressurized thermal-insulated vessel through a nozzle or a valve is considered as an unsteady-flow problem. It is shown that in the case of relatively small energy losses a valve may be modeled as a converging nozzle. After losses exceed certain value a condition of constant enthalpy typical for throttling devices is applicable to a valve. On the basis of such consideration, the step by step calculation method for small time intervals or pressure drops is developed. The proposed approach allows obtaining all characteristics of the discharging process as functions of time. The expression defining the speed of sound in the case of discharging of wet vapor is derived. A special technique is proposed to calculate and correct the usually recommended value of critical pressure ratio. A numerical example of calculation is provided. To estimate the accuracy and limits of the applicability of the results presented in the paper a comparison with corresponding experimental data is needed.

A method of solution of the thermal boundary layer equation for a gas, together with the heat conduction equation for the turbine blade, using the boundary condition of the fourth kind (conjugate problem), is presented. The effect of the surface temperature distribution on the heat transfer coefficient (the effect of thermal history) is considered. This effect is important for gas turbine blades because the difference in temperatures between the blade’s surface and gas usually varies considerably along the blade’s surface; hence, the effect of thermal history can be significant. It is shown that the results, obtained accounting for thermal history, can differ substantially from results calculated with the assumption that the blade’s surface is isothermal. This might be one of the reasons why there is a marked difference between the actual temperature distribution of the turbine blade and the calculated one. It is important to consider the effect of thermal history since it is a fact that the major unknown in the design of turbine blade cooling systems is in the estimation of external heat transfer coefficient (Hannis and Smith, 1989).

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