An-Najah Staff

In this present paper we represent some important mathematical results on the physical model describing the heat transfer by conduction and radiation. The problem to be considered is the heat radiation exchange inside a non-convex body _ containing two conducting and opaque enclosures which are bounded by diffuse and grey surfaces and are surrounded by perfectly transparent and non-conductive medium. The combination of the radiation heat exchange with the normal heat conduction in yields a boundary value problem for the absolute temperature in stationary situation. Some properties of the heat radiative operator are represented and proved. The existence and the uniqueness of a weak solution of the non-local problem is also investigated

Steel structures in building are to be provided with external insulation to delay temperature rise and associated strength degradation when exposed to fire. However, due to delicateness and fragility of some insulation systems, damage might occur in these insulation systems during their service life, and such damage can lead to rapid rise in steel temperature and result in lower fire resistance of structural members. Currently, there are no simple calculation methods for quantifying the effect of insulation loss on steel temperature. In this paper, a simple approach is proposed for tracing the temperature profile in steel members with partial loss of fire protection. The method is developed based on modifying the existing one-dimensional finite difference solutions of the heat transfer equation. The validity of the proposed method is established by comparing the predictions from the proposed method against temperatures obtained from finite element heat transfer model that is created using ANSYS. The comparisons indicate that the proposed method is capable of predicting temperature in steel members with partially damaged insulation to a good degree of accuracy over a wide range of situations. Further, the simplicity of the proposed method makes it attractive for use in fire resistance assessment in steel structures.