OCR Text |
Show maximum at a definable optimum output, and returns to zero at a (theoretical) maximum output. Expressed alternatively in terms of the variation of firing rate with output, the Firing Curve thus defined has, qualitatively, a common form for all thermal devices -furnaces and engines -- being a concave-upwards curve, with defined lower and upper limits, respectively, at: zero load (Idle); and at the maximum load when the firing rate, theoretically, goes to infinity. It is also well established from numerous studies of experimental and industrial furnaces [3-5] that the Firing Curve written in thermal terms can be described by the Firing Equation that relates the thermal input, He, to the thermal output, H., thus: He = Ht + H. / a ° (1 - Hs / Hs rn) [1] where the three Firing Constants; Ht, H,rn, and aO; are, respectively, the Idle Heat at zero output, the maximum output, and the Intrinsic Efficiency. The Intrinsic Efficiency, aO, is at a first approximation the limiting value at Idle of a parameter, the Heat Utilization Factor [HUF], a, first defined by Thring and Reber [7] in 1945 as the ratio of the useful output to the net available energy supplied after subtraction of the energy required for the wall losses. Combined with Eq. 1 the definition becomes: [2] To a first approximation, the parameter, aO, the Intrinsic Efficiency is a constant; and when it is so, it can also be shown that it is equivalent to the ideal thermodynamic (limiting) thermal efficiency. In a more complete treatment, partially presented in this paper, the parameter, aO, has a second-order dependence on output, but with a limiting value at zero output that again corresponds to the ideal thermodynamic efficiency. The theoretical basis ofEq. 1 is the Integral Energy Equation applied to a control volume containing the thermal device (a furnace or engine). Since the Firing Equation is developed phenomenologically [3-5], the structure of the equation is independent of any particular device, thus providing generality; and, by extension, it is also independent of the 3 |