The cross-section of a steam boiler is shown in Figure P1.20. Water is boiled inside of tubes using combustion gases flowing over the tubes. The tubes are arranged in a square array that is eight rows high. The tubes may be bare on the outside or equipped with circular fins. The inside width of the boiler is 1.9m.

Table P1.20A shows the technical data for the tubes and fins (if any). The tubes are connected together by U-bends. The smallest U-bend available results in a centerline distance of 125 mm between adjacent tubes. Larger U-bends are available and can be used in this design.
Water is boiling inside the tubes at a pressure of 800 kPa, corresponding to a saturation temperature of 170.4°C. The combustion gases enter the furnace at Tgas = 580°C. The following design constraints are relative to the tubes and fins, 1. There must be a minimum of 3 mm of clearance between fins of adjacent tubes and between fins and the boiler walls.
2. For metallurgical purposes, the hottest part of the fin (i.e., the fin tip) must not exceed 400°C.
Another design constraint on the boiler is that it must have a minimum UA product of 23,500 W/K. The overall heat transfer coefficient, based on the steam side (i.e., the inside) of the tube, is given by,

The thermal resistances in this equation are,

The thermal resistance on the combustion gas side of the tube depends on the fin geometry. An expression for computing the gas side thermal resistance is,

In this equation,

Table P1.20B shows the fin data for available fin heights required to calculate the combustion gas resistance along with an expression to compute the fin tip temperature.
The base temperature of a fin can be calculated by equating two alternate expressions for the heat transfer rate from the combustion gases to the boiling steam,

Design the boiler by specifying the number of tubes in each horizontal row and the fin height such that the tube bank fits into the boiler while maintaining the specified clearances, maintaining a UA product of at least 23,500 W/K, and limiting the tip temperature of the fins to 400°C or less.

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TABLE P1.19 Design Specifications for the Pipe Network Design Flow Rate (L/s) Pipe Section Pipe Size (in) Working Hours Pump selected: Elevation of water surface in supply tank: Non-Working Hours Pressure Drop (kPa) Working Hours Non-Working Hours