A novel numerical model for billet reheating furnace

Abstract

A numerical model of billet reheating furnace is proposed, which includes heat fluxes calculation around four billet surfaces and two-dimensional conduction calculation inside billet. Radiation and convection heat fluxes on top and bottom surfaces are calculated simultaneously, based on quartic and linear difference between furnace gas and billet surface temperatures, while furnace gas temperature is determined according to thermocouple values along furnace length together with billet surface temperature. Lateral fluxes are also calculated considering angle factor on billets interval. Two-dimensional partial differential equation is acquired for billet conduction to determine temperature distribution, which is discretised and solved by Alternating Direction Implicit and TriDiagonal Matrix Algorithm. Two embedded thermocouple experiments were carried out to verify furnace gas temperature, the effect of billet interval on lateral heat flux calculation as well as billet temperature. It met agreement well with experiments on billet temperature, which could be a better prerequisite for further reheating furnace automatic control.

A combined adaptive entropy‐TOPSIS and model predictive control strategy for mixed loading and delay operations in the reheating furnace

“…And $$$ {\varepsilon}_w^{-}={\varepsilon}_w^{+}=0.7 $$$. However, in the paper, 28 they are obtained by the another different equation: $$$ \varepsilon =\frac{\varepsilon_g{\varepsilon}_s\left(1+{\varphi}_{ws}\left(1-{\varepsilon}_g\right)\right)}{\varepsilon_g+{\varphi}_{ws}\left(1-{\varepsilon}_g\right)\left[{\varepsilon}_s+{\varepsilon}_g\left(1-{\varepsilon}_g\right)\right]}. $$$ In contrast to the foregoing analysis, the results in our previous work 29 are given here as the identified total heat exchange factors along the length of reheating furnace.…”

“…And 𝜀 − w = 𝜀 + w = 0.7. However, in the paper, 28 they are obtained by the another different equation:…”

“…Secondly, the total heat exchange factors in the SHT model are always given as different constant in different papers (References 25, 27, and 28, etc.). For instance, in the paper, 25 the total heat exchange factors are given as follow: $$$ {\varepsilon}^{\pm }=\frac{1}{\left({\varepsilon}_s^{\pm }+{\varepsilon}_w^{\pm}\right)/\left({\varepsilon}^{\pm }{\varepsilon}_w^{\pm}\right)-1}.$…”

First-Optimize-Then-Discretize Strategy for the Parabolic PDE Constrained Optimization Problem With Application to the Reheating Furnace

“…Secondly, the total heat exchange factors in the PDE model are also given as different constant in different papers ( [16], [17],etc.). For instance, in the paper [16], the total heat exchange factors are given as follow:…”

“…And ε − w = ε + w = 0.7. Meanwhile, in the paper [17], they are obtained by the another different equation:…”