Constructal optimization of variable cross-section insulation layer of steel rolling reheating furnace wall based on entransy theory

Based on the entransy dissipation extremum principle for thermal insulation process, the constructal optimizations of a variable cross-sectional insulation layer of the steel rolling reheating furnace wall with convective and compound heat transfer (mixed convective and radiative heat transfer) boundary conditions are carried out. An optimal construct of the insulation layer with minimum entransy dissipation rate can be obtained. Results show that the global thermal insulation performance of the variable cross-sectional insulation layer at minimum entransy dissipation rate is better than that of the constant cross-sectional one. The optimal constructs of the insulation layer obtained based respectively on the minimizations of the entransy dissipation rate and heat loss rate are different. The optimal construct of the insulation layer at minimum heat loss rate leads to a reduction of the energy loss, and that at minimum entransy dissipation rate leads to an improvement of the global thermal insulation performance. The difference between the optimal constructs of the variable cross-sectional insulation layer based on the minimizations of the entransy dissipation rate and the maximum temperature gradient is small. This makes the global thermal insulation performance and thermal safety of the insulation layer improved simultaneously. The constructal optimization of the insulation layer based on entransy theory can provide some new guidelines for the optimal designs of the insulation systems.