The Design of an Electric Heater - Example

Title of Short Report Prepared by Name of Company Month, Year Student Name Student Number 1 Introduction This is a detailed report on the design of an electric heater that will be used in the reaction tank of a bio-diesel production system. The report will be forwarded to Bio-Neutral Pty Ltd. The company requested for design submissions from qualified companies that may meet a specified criteria. The criterion for the design is to be able to produce 12000L of bio-diesel within a span of 8 working hours, i.e. in each work shift. Bio-Neutral Pty Ltd will accept any design as long as it is functional and can be able to meet its objectives. The company subdivided the design project for the whole plant into 5 different subsections. The first 3 subsections are available for the contractors to chose. These are design of the tanks that holds the raw materials and mixtures, design of the electric heater model and rating and design of a pump and its rating to be used for the reaction chamber. Our company has chosen to design the electric heater model and power rating because it is our area of specialization. This report will outline all the calculations needed to give a desirable design that meet all the specifications of Bio-Neutral Pty Ltd in the client brief. 2 Technical Analysis a. Provided Information To help in the selection of the model and rating, a number of options have been laid out for the contractors by the company. We are to choose the one suitable for carrying out the outlined task. They are shown in the table below: Table 1.0 Electric Heater Specifications (all efficiencies η=1.0) Heater Model Input Power Rating Ph (kW) Cost Ch ($) H11 11kW 1000 H22 22kW 2000 H33 33kW 2700 H55 55kW 4000 H80 80kW 6500 Some constants/values that will help in the design process have also been provided. These are shown in the table below. Table 2.0 Items given and their corresponding values Material Variable (letter) Value or equaltion Canola oil- density ρc 920Kg/m3 Methanol- density ρm 791 Kg/m3 Sodium hydroxide- density ρs 2130 Kg/m3 Glycerin- density ρg 1260 Kg/m3 Oil/Methanol/Sodium Hydroxidemix-density(average) -Specific heat value ρc c 911Kg/m3 1.80kJ/kg/C A number of assumptions to be made that will affect this design include: i. All the energy that is generated by the heater is transferred to the liquid mixture ii. Any energy losses taking place in the pipes are ignored iii. The time to transfer materials between tanks is ignored. iv. All the supply tanks may be refilled as necessary b. Duration of bio-diesel production According to the client brief, methoxide mixing takes 15 minutes or 0.25 hrs, reaction tank process tales 1.75 hrs, reaction liquid cooling takes 1 hr and dry washing takes 1 hr. The total duration for bio-diesel production will be as shown below = 0.25+1.75+1+1 = 4hrs The aim is to produce 12000L in 8 hrs. That will imply that 6000L is produced every 4 hrs. The design should be able to meet this criterion. c. Energy and Power Our interest is the power rating of the electric heater. In order to determine the appropriate value, we have to know the energy needed to produce 6000L of bio-diesel. The equation for energy is given below. (KJ) (Equation 1) Where = Energy = Mass of the mixture in the reaction tank = Specific heat capacity of the liquid = Temperature Change We are given the specific heat capacity of the mixture to be 1.80kJ/kg/C and the temperature change is (50-25) =. The mass is not given and has to be calculated. d. Mass of the mixture Provided are the densities and volumes of the raw materials and mixture. The density (ρ), mass () and volume () relationship is used to calculate the mass. Kg/m3 (Equation 2) From equation 2, we come up with equation 3; (Kg) (Equation 3) Volume of the reaction tank is given by adding volumes of the methoxide with the volume of the oil. First we have to find the value of V Volume of the oil is V, Volume of methanol is 0.2V Volume of sodium hydroxide is: 7g/L of methanol 1L of methanol => 7g of sodium hydroxide Therefore, 0.2V L of methanol => 1.4Vg =0.0014V Kg Vol. = Mass/Density = 0.0014V/2130 = 6.572*10-7V m3 =6.572*10-4V L Total volume in the reaction tank = V + 0.2V + 6.572*10-4V = 1.2V Volume of glycerol = 0.08*1.2V = 0.096V Total Volume of the raw materials = Total volume out of the products 1.2V = 0.096V+6000 => V = 5434.783 L Volume in the reaction tank = 1.2* 5434.783 = 6521.740 L =6.522 m3 Using equation 3 to calculate the mass; Mass of reaction tank = 6.522*911 = 5941.542Kg e. Energy needed in the reaction tank We use equation 1; (KJ) = 5941.542*1.8*25 = 267369.39 kJ =267369390J From the assumption, Heat absorbed by the mixture = Heat supplied by the heater => Heat supplied by the heater = 267369390J f. Rating of the heater 3.6*106J = 1kWh Therefore 267369390J = 267369390/3.6*106 =74.269 kWh This is the energy that must be supplied by the heater in 1.75hrs. The rating per hour is therefore given by 74.269/1.75 = 42.440kW From the table of electric heater specifications, heater model H55 best fit the description with a rating of 55kW per hour. This implies that if the heater supplies 55kW per hour and only 42.44 kW are used, then the difference, i.e. 12.45kW is lost from the reaction tank to the air. 3 Conclusion The electric heater rating for the reaction tank is precisely identified by the calculations in the analysis. The production plant will operate 2 times within an 8 hr shift with each operation lasting 4 hrs. 6000L of bio-diesel will be produced every 4 hrs, making the total to be 12000L in each shift. The heater needed must be able to deliver 42.44kW per hour. The heater model and rating needed to achieve this is as in the table below. The heat lost by the reaction tank to air is given by the difference of the two energies, and is 12.45kW every hour. Table 3.0 Heater model and rating Heater Model Input Power Rating Ph (kW) Cost Ch ($) H55 55kW 4000 By assigning the design job to our company, Bio-Neutral Pty will successfully achieve its set out objective of producing 12000L within a period of 8hrs. 4 References ‘Client Brief.’ University Publication. University Publishers. Moaveni, S & Sharma, I 2011, Engineering Fundamentals: An Introduction to Engineering, New York, Cengage Learning. Wright, P 2002, Introduction to Engineering, New York: John Wiley & Son Read More