Constructal entransy dissipation rate minimization for variable cross-section insulation layer of the steel rolling reheating furnace wall

A variable cross-section (distributed thickness and width) insulation layer of the steel rolling reheating furnace wall is investigated subjected to the constraints of the total volume and cross-sectional area of the insulation material. According to the entransy dissipation extremum principle of the thermal insulation process, the thickness of the insulation layer is optimized by taking minimum entransy dissipation rate as optimization objective, and the optimal construct of the insulation layer is obtained. The results show that when the temperature distribution of the furnace is linear with the length, the optimal thickness of the insulation layer with minimum entransy dissipation rate is linear with the dimensionless longitudinal position, which is evidently different from that with minimum heat loss rate. When the dimensionless temperature at the low temperature side ε = 0, the minimum entransy dissipation rate of the insulation layer with distributed thickness is decreased by 33.33% than that with uniform thickness, and is decreased by 8.85% than that based on minimum heat loss rate. Essentially, the temperature gradient field obtained based on minimum entransy dissipation rate is more homogenous than that based on minimum heat loss rate, and the corresponding thermal stress performance is better. The decrement of the entransy dissipation rate tends to increase for the exponential temperature distribution case with a large exponent. Moreover, the insulation layer with triangular cross-section has a better global thermal insulation performance derived from entransy dissipation than those with rectangular and trapezoidal cross-sections. Therefore, the optimal construct obtained by adopting variable cross-section insulation layer (distributed thickness and width) and based on minimum entransy dissipation rate can improve the global thermal insulation performance of the insulation layer derived from entransy dissipation, and can reduce its average heat loss rate defined based on entransy dissipation simultaneously. The optimal construct obtained based on minimum entransy dissipation rate can provide a new scheme for the design of practical thermal insulation system different from that based on minimum heat loss rate, which can satisfy the different requirements in the design of practical thermal insulation systems.