Abstract
This paper focus on the heat recovery from the metallurgical and mining wastes. We propose and study a new and more realistic mathematical model for heat recovery from molten slag. Our model is based on time delay differential equations. In the theoretical part, we prove that a unique solution exists to the mathematical problem. In the numerical part, we establish an algorithm based on explicit fourth order Runge-Kutta method with delay; the new feature is that the delay must be larger enough than the step of integration. Compared to the classical model (without time delay), the numerical test proves that our model is more efficient and industrially more profitable.