Research of radiation-convective heat exchange on radiating surfaces at natural and forced convection is complex mathematical task and here we obtain approximate analytical formulations for this process. We consider two dimensional unsteady heat transfer between solid surface and fluid under the natural laminar convection within optically transparent grey media. Also we assume constant thermo-physical properties except density which is decreasing linearly with temperature. Complex radiative-convective unsteady heat transfer approximately can be considered as a multi-stage process. At the beginning heat transfer coefficient is time dependent but almost independent on longitudinal coordinate. Afterwards heat transfer coefficient becomes dependent on longitudinal coordinate but does not change over time. Analytic formulations obtained for those two stages could be merged along the "time-space" characteristic basing on the equality of heat flows and temperatures there. Solutions are constructed using asymptotic expansions. Theoretical analysis of the solutions revealed the following: effect of radiation leads to a change in the heat transfer coefficient from the values that are characteristic to the second order boundary conditions to the values that are characteristic for the first order boundary conditions. The rate of this transition depends on radiation coefficient. Experimental research confirmed correctness of the simplifications introduced.