A manufacturing facility requires saturated steam at \(120^{\circ} \mathrm{C}\) at a rate of \(1.2 \mathrm{~kg} / \mathrm{min}\). Design an electric steam boiler for this purpose under these constraints: \- The boiler will be in cylindrical shape with a heightto-diameter ratio of \(1.5\). The boiler can be horizontal or vertical. \- The boiler will operate in the nucleate boiling regime, and the design heat flux will not exceed 60 percent of the critical heat flux to provide an adequate safety margin. \- A commercially available plug-in type electrical heating element made of mechanically polished stainless steel will be used. The diameter of the heater cannot be between \(0.5 \mathrm{~cm}\) and \(3 \mathrm{~cm}\). \- Half of the volume of the boiler should be occupied by steam, and the boiler should be large enough to hold enough water for \(2 \mathrm{~h}\) supply of steam. Also, the boiler will be well insulated. You are to specify the following: (a) The height and inner diameter of the tank, \((b)\) the length, diameter, power rating, and surface temperature of the electric heating element, \((c)\) the maximum rate of steam production during short periods of overload conditions, and how it can be accomplished.

In this exercise, a design for an electric steam boiler was created for a manufacturing facility. The design constraints included the desired steam production rate, the heat flux, the electrical heating element, and the boiler's height-to-diameter ratio. The main steps in developing the design were: 1. Calculation of the boiler's volume required to hold enough water for a 2-hour supply of steam at the desired production rate. This was found to be 0.288 m³. 2. Derivation of the height and inner diameter of the boiler using the given height-to-diameter ratio. The boiler's height was found to be approximately 0.671 m, and the inner diameter was approximately 0.447 m. 3. Determination of the required heat flux and the corresponding power rating of the electric heating element. The required heat flux was calculated to be 5142.2 kJ/min, which corresponds to a power rating of 85.7 kW. 4. Calculation of the length, diameter, and surface temperature of the electric heating element. The heating element was found to have a length of approximately 9.09 m, a diameter of 0.035 m, and a surface temperature of about 156.8°C. 5. Determination of the maximum rate of steam production during short periods of overload and how it can be accomplished. The maximum rate of steam production was found to be 2 kg/min, achieved by increasing the power supplied to the electric heating element to operate at the critical heat flux. This design ensures that the electric steam boiler can produce steam at the required rate while adhering to the given constraints, making it suitable for use in the manufacturing facility.