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Question 3 (140 marks) Introduction A heater is mounted on a wall and is designed to turn on at 1...

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Question 3 (140 marks) Introduction A heater is mounted on a wall and is designed to turn on at 1 kW when the temperature is below or equal to a lower threshold temperature (TL) and off when the temperature is above or equal to an upper threshold temperature (TU). The transport equation for this behaviour is;2;2;2;2, 0.2m, 0.2m;p;p;T T P c k x t x V TT c k x tx??????????????? (2);where T is the temperature of the air (which is initially 10?C),? is the density (which can be taken to be 1.225 kg/m3 at room temperature), cp is the specific heat at constant pressure (which is 1.005 kJ/kg.K at room temperature), k is the conductivity of air (which is 0.025 W/m.K at room temperature), P is the power of the heater and V = 2 m3 is the volume that the heating element acts on. The heater is modelled to apply heat uniformly within 20 cm of the wall, as noted in Eq. (2). The room is L = 5 m across and to solve for the temperature at the ends, assume that there is a ?ghost node? outside the domain which has the same temperature as the first interior node. For each case, determine: i. How long it takes for the heater to reach TU for the first time ii. How much energy is consumed by the heater in 8 hours (in units of kWh);Solve for each of the following situations: a) TL = 19?C and TU = 21?C. b) Repeat part (a) with a person in the middle of the room, who provides a constant source of heat of 30 W acting over the range 2 2 2 2 L w x L w???? applied over a volume of Vp = 10 m3 with w = 0.4 m. c) Repeat part (a) but find the minimum TU (as a whole number) so that the temperature 0.5 m from the heater reaches 15?C within one hour. Maintain TU ? TL = 2?C and produce the plots only for the first hour. d) Repeat part (a) using variable coefficients (which are functions of temperature). e) Repeat part (b) using variable coefficients (which are functions of temperature).;To calculate variable coefficients, use Eq. (3) and Table 1. The ideal gas law is;p RT?? (3);where the atmospheric pressure can be taken to be p = 101.3 kPa and the ideal gas constant for air is R = 287.0 J/kg.K. SI units must be used in Eq. (3).;Table 1: Properties of air at atmospheric pressure (National Bureau of Standards 1955);Temp (K) 150 200 250 300 350 400 450 500 cp (kJ/kg.K) 1.0099 1.0061 1.0053 1.0057 1.0090 1.0140 1.0207 1.0295 k (W/m.K) 0.013735 0.01809 0.02227 0.02624 0.03003 0.03365 0.03707 0.04038;ENG3104 Engineering Simulations and Computations Semester 2, 2014;Page 5 of 5;Requirements For this assessment item, you must produce MATLAB code which: 1. Simulates the heater operating in the room for 8 hours. 2. Produces an x-t contour plot, where the variable plotted on the x-axis is t, the variable plotted on the y-axis is x and the colour (the dependent variable) is the temperature. Depending on the memory of your computer, it may be difficult to plot for all timesteps, it is sufficient to plot no more than 5 values per second (the minimum interval between storing temperatures should be 0.2 seconds). 3. Produces a plot of the temperature as a function of time at five equally-spaced locations in the room, including the walls. For part (c), include the location where the temperature must meet a minimum value. 4. Determines how long it takes for the heater to first reach TU and reports the value to the Command Window. 5. For part (c), reports the minimum value of TU to the Command Window. 6. Calculates the total energy consumed by the heater. 7. Repeats the simulation for 4 other cases. 8. Has appropriate comments throughout.;Assessment Criteria Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks. Quality of the code 10 marks Quality of header(s) and comments 10 marks Quality of solution of Eq. (2) 50 marks Quality of plots (e.g., axis labels, titles) 10 marks Quality of reporting (including calculation of quantities) 10 marks Quality of solving part (b) 10 marks Quality of solving part (c) 20 marks Quality of solving part (d) 15 marks Quality of solving part (e) 5 marks;Reference National Bureau of Standards 1955, National Bureau of Standard (US) Circular 564.;Question 4 (10 marks) After submissions have closed for Assignment 2, you will be provided with a dummy submission for Assignment 2 containing a number of errors. Fill in the table in the file ?Corrections to Assignment 2 dummy submission.doc? with how the code should be amended. Do not submit corrections to your own Assignment 2 submission. Submission Submit your assignment by the due date to the StudyDesk. Note that:? MATLAB code must appear in a *.m file otherwise it will not be marked.? you should upload all of your files individually (not zipped together).? you will NOT receive any confirmation of receipt. If you can see that the files have uploaded, then you have successfully submitted your assignment. There is no need to click a ?send for marking? button, but you will have to click a button confirming that the submission is your own work.

 

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