| OCR Text |
Show 6 dT N p^-5f-=Ihi(Ti-T.)Ai <12> where V is the volume of the gas in the furnace and Aj is the surface area of the zone j. The convective heat transfer coefficient at the surface zone j, hj, is calculated from correlations taken from the published literature sources [7]. Heat Transfer Through Furnace Walls The transient temperature distributions in the furnace walls are calculated from an unsteady, one-dimensional heat conduction equation. It is recognized that heat conduction in the corners of the furnace cannot be accurately predicted using a one-dimensional model and a two-or three-dimensional model would be needed. But, a multi-dimensional heat conduction model for predicting the heat losses through the walls does not appear to be warranted, in view of the approximations made in treating radiation exchange in the furnace. For transient, one-dimensional heat conduction through the furnace wall, the energy equation is 3T a p c -^- = - w w 3t 3n ( 3T ^ k -^ V w d"J (13) where n is a coordinate normal to the wall. The boundary condition on the inner surface of the wall is given by aT w an where the total net heat flux is calculated from the radiation heat exchange and convective heat transfer models already described. The boundary condition on the outside of the walls exposed to the ambient temperature and surroundings is given by 3T -k w an = h(T -T .) (15) where h is the effective (convective plus radiative) heat transfer coefficient. Load Model Typically, loads of indirectly-fired reheating furnaces consist of crates filled with small metal parts, relatively small cylindrical and square metal billets, slabs of metal, etc. Loads consisting of a relatively large number of small stock parts placed on the bottom of the furnace are complex and difficult to model. Therefore, as a first approximation the load is assumed to be a uniform thickness slab placed on the hearth of the furnace. The total (radiative and convective) heat flux calculated by the enclosure model is used as a boundary condition to calculate the transient temperature distribution in the load. The transient one-dimensional heat conduction equation for the load is given by ^ a rk aiy P L C L at L ~ ay v L * J (16) where the coordinate is measured from the load surface. Transverse and longitudinal heat conduction in the load has been neglected (but, can readily be accounted for if warranted), because of the large width and length to thickness ratio. |
