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Show diffusion equati0,5ls that arise from the radiation transfer modeling . Computation has been carried out using 20x20 uniform control volumes , and wall functions were employed to improve the resolution near the boundaries . For all the simulations , the computation was terminated when the maximum total energy imbalance was less than 0.05 percent of the heat input and the maximum mass imbalance of a control volume was less than 0.05 percent of the total mass flow rate in the furnace. BASELINE PROBLEM AND DISCUSSION OF RESULTS MODEL FURNACE To gain improved understanding of the complex physical and chem ical processes in a combustion furnace, a model simulating a typical furnace is considered as a baseline problem . The solution is obtained using the two-dimensional mathematical description of the system (see Fig. 1). The problem employs all of the mathematical mgdtls and boundary conditions that have been developed ' . Table 1 lists the system parameters of the baseline problem. The energy input to the combustion space is 2.5 MW when the total enthalpy of the incoming mixture is calculated with reference to the combustion product at 300 K. The combustion cham ber is maintained at atmospheric pressure. The composition of the fresh mixture is close to that generally used in natural gas-air-fired systems, i.e., a few percent excess air and natural gas containing about 95 percent of methane. The furnace size is typical of a medium size industrial furnace with an aspect ratio of five. The sink (load) temperature is close to the melting points of many metals and glass . The emissivities of the sink and the refractories are representative of real materials. The overall heat transfer coefficient of the refractory is an important model parameter affecting furnace performance and is in a range of many installations. The radiative boundary conditions for the burner port and exhaust depend on the configuration and materials of construction of the inlet and outlet. For maximum heat transfer efficiency , these openings are assumed to be perfectly reflecting. RESULTS FOR MODEL FURNACE - The flow field and turbulence quantities are depicted in Fig. 2. Fig. 2a shows the streamlines and indicates two dominant recirculation cells , while the incoming flow gradually expands as it proceeds along the furnace . Since the density decreases rapidly across the flame as the fuel burns, the bulk velocity also increases (Fig . 2b) . The effect of buoyancy is found to be negligible since the buoyancy force is much smaller than the inertia force . The ~xisten~e of recirculation is confirmed by many expenments , and the flow field is similar to the flow over a backward facing step . Turbulent kinetic energy is generated where the velocity gradient is sharp and/or the gradient of pressure is in the opposite direction of the density gradient . As a consequence, the production of turbulent kinetic energy is intense near the flame where 136 large velocity gradients exist (Fig. 2c). The turbulent kinetic energy is smaller along the centerline of the furnace than at the shear layer due to smaller production of the turbulence along the centerline . The turbulent kinetic energy along the centerline increases slowly . The turbulent viscosity near the center of the furnace (Fig. 2d) is about three orders of magnitude larger than the molecular viscosity. The total enthalpy continuously decreases as the fuel burns and as the waste gases lose their thermal energy both by radiation and convection (Fig. 3a). The combustion is seen to be very rapid due to the high inlet temperature of the fresh mixture. The mean gas temperature increases abruptly after passing through the flame and then slowly decreases (Fig. 3b) . The temperature rise rate of the fresh mixture due to radiant heating is found to be about 500 K/s . However, the rate is smaller downstream since the mixture also emits radiation as its temperature increases. The heat flux at the sink surface is depicted in Fig. 4 . More than 99 percent of the heat flux at the sink surface is attributed to radiation . This is due to the low gas velocity and the small temperature difference between the gas and the sink . The heat loss to the ambient is only 1.8 percent of the total heat input. The thermal efficiency , defined as the ratio of the heat transfer to the sink to the total heat input , is 36.9 percent. This corresponds to the thermal effectiveness of 69 .1 percent; the thermal effectiveness is unity when the exhaust gas temperature is equal to the sink temperature. RESULTS OF PARAMETRIC STUDY Furnace design parameters and operating conditions affect its performance; therefore, they are important from the viewpoint of energy efficiency , optimum design and operation of the furnace, as well as product quality control. Among the many parameters that affect the furnace performance , the following ones were considered to be of greatest interest: furnace size, firing angle, thermal insulation of the refractory, em issivity of sink, sink temperature and preheating of fresh mixture. To determine the effects of these parameters and conditions, a typical furnace is considered as the reference case , and one of these parameters is varied at a time from the base case for each simulation. The reference condition is the same as the one described in previous section . Variation of more than one parameter at a time is avoided , because this makes it difficult to interpret the individual effects . The effect of changing more than one parameter, however, can be found by linearly adding the effects of different parameters if the furnace condition does not differ too greatly from the reference case . For example , the thermal efficiency" can be found from |