460 CHAPTER XXIII 



temperature. The principles under which this obtains have been given in the 

 preceding sections, with special reference to bagasse. These hot gases come 

 into contact with the boiler, which is at a lower and constant temperature. 

 The rate at which the heat from the hot gases passes to the water in the boiler 

 is proportional in some way to the difference in temperature. Rankine 9 

 assumed that the rate was proportional to the square of the temperature 

 difference, and this assumption is developed very completely by Kent. 10 

 Accepting this assumption, the writer offers the following graphic analysis 

 with special reference to bagasse burning. 



Let the bagasse on combustion afford hot gases at a temperature of 

 2200 F. ; let the boiler be at a temperature of 350 F. (roughly 120 Ibs. 

 gauge) : the initial temperature difference is 1850 F. After the gases are 

 cooled down to 1200 F., the temperature difference is 850 F., and the rate 

 of transfer is proportional in the two cases to the squares of 1850 and 850. 

 The graph in Fig. 274 is obtained thus : On the horizontal axis are set out 

 the temperatures 2200, 2100 .... 450. From these points are drawn ordin- 

 ates proportional to the reciprocals of the squares of the temperature differ- 

 ences ; that is to say, to 1850, 1750 .... 100. The graph is then obtained 

 by drawing a curve through the ends of these ordinates. Then the area 

 enclosed between any two ordinates, the base line, and the curve, is propor- 

 tional to the heating surface required to reduce the temperature of the gases 

 from the temperature under the first ordinate to the temperature under the 

 second ordinate. In the graph above the curve have been inserted the areas 

 of each division of 100, and below the horizontal axis the total area at any 

 particular temperature. Thus to reduce the temperature from 800 to 700, 

 an area proportional to 709 units is required ; the total area required to 

 reduce the gases from 2200 to 700 being 2154 units. Again, on this basis 

 it follows that if a certain heating surface, say 3349 sq. ft., is sufficient to 

 reduce the hot gases to 600 F., then to reduce them to 500 F. an additional 

 1658 sq. ft. will be required ; that is to say, 5007 sq. ft. in all. Again, if 

 the external air be taken as 80 F., a reduction in temperature from 2200 

 to 80, or 2120 F., would represent 100 per cent, efficiency. A reduction 

 to 600 F. indicates a fall of 1600 F., so that at this temperature in the waste 



gases the efficiency is - - = 75.5 per cent. A reduction to 500 F. 



would similarly indicate an efficiency of 80 -I per cent., or an increase in 

 efficiency and steam production of 6-0 per cent., which would be obtained 

 by an increase in the heating surface from 3349 to 5007 or 49 per cent. 



Again, let a quantity of fuel be burnt such that the waste gases pass 

 away at 500 F., and let the heating surface be 5007 sq. ft. Let double the 

 quantity of fuel be burnt, or the original quantity per 2503 sq. ft. This 

 area is found from the graph to correspond to a temperature of 680 F., 

 and to an efficiency of 76 o : that is to say, doubling the fuel capacity of 

 a furnace only decreases the efficiency from 80 *i per cent, to 76-0 per cent. 

 In other words, a steam-producing plant is a very elastic system capable of 

 carrying great overloads with relatively very small decrease in efficiency. 



This discussion is very incomplete and treats^ of heat transfer by con- 

 ductance only, and also reflects the question of radiation losses. It has been 

 introduced rather to present the general principle involved, along with the 

 engineering problem, namely the determination of the economic heating 

 surface, questions of first cost of installation as well as fuel consumption 



