Constructal designs for insulation layers of steel rolling reheating furnace wall with convective and radiative boundary conditions

Constructal designs of multilayer insulation structures of a steel rolling reheating furnace wall are implemented by taking minimum heat loss rate (HLR) as optimization objective. Two boundary conditions of the insulation layers, convective heat transfer and combined convective and radiative heat transfer, are taken into account. The optimal constructs of the insulation layers with the two boundary conditions are obtained. The results show that for a multilayer insulation structure with convective heat transfer, the optimal thickness of each insulation layer is proportional to the square root of the temperature difference between the furnace wall and the ambient. For a multilayer insulation structure with combined heat transfer boundary condition, the optimal thicknesses of the multiple insulation layers increase with the dimensionless longitudinal coordinate. The HLR of the insulation layers with optimal thicknesses is reduced by 9.50% than that of the uniform ones, and this value decreases with the increase in dimensionless inlet wall temperature. Moreover, the nonuniformity of the convective heat transfer coefficient has an evident influence on the minimum HLR, but that of the surface emissivity is small.