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An approximate procedure of mathematical modeling of radiative and radiative-convective countercurrent heat exchange in metallurgical units has been given.Heat exchange of solid bodies and a gas in their countermotion is quite frequently realized in various branches of technology and primarily in metallurgy. Examples of such processes are heating of round billets in annular furnaces before piercing, heating of a burden in blast furnaces, cooling of pellets in stack-type coolers, etc. In exact solution, these problems are considered only in a linear formulation, whereas the processes themselves are nonlinear. This is because of the difficulties appearing in their nonlinear mathematical modeling. The arising complications can be successfully solved with the method of equivalent sources [1-3], which has been adequately tested in problems of concurrent and countercurrent heat exchange (CCHE).Radiative Countercurrent Heat Exchange. Let us consider the problem of countercurrent symmetric radiative heating of thermally massive bodies of a base shape in the following formulation [1-3]:∂θ ∂ρwhere we have θ s (τ) = θ (1, τ) ; θ (ρ, τ) = T m (ρ, τ) − T m ′ T g ′′ − T m ′ ; n m = (1 + m) n ; ρ = r R ;

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