ENGR-25_Prob_9_15_Solution.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Problem 9.15 Solution

ENGR-25_Prob_9_15_Solution.ppt 2 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Simulate ThermoStatic Control  By Engineering Analysis the ODE with Highest Order Term ISOLATED  Integrate to Isolate T(t) on LHS

ENGR-25_Prob_9_15_Solution.ppt 3 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Simulate ThermoStatic Control  Note for T(t) appears on BOTH Side of the Eqn → Use FEEDBACk The Integrand is in the form of a SUM  Also the thermostat in this case has a 2F DEADBAND Implement using SimuLink’s RELAY function

ENGR-25_Prob_9_15_Solution.ppt 4 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods The Part-a SimuLink Model  RELAY → Discontinuities Library  MUX → Commonly Used Blocks Library  SINE WAVE FUNCTION → Math Operations Library  TO WORKSPACE (simout) → Sinks Library

ENGR-25_Prob_9_15_Solution.ppt 5 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Test Large & Small Furnaces  The SimuLink Model

ENGR-25_Prob_9_15_Solution.ppt 6 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods The Output for Small Fnce  Note Small Fnce canNOT keep up with heating load when Ta drops below about 55F 2 Hour Time-Lag as predicted by plot(tout, simout(:,1), tout,simout(:,2)), xlabel('time (hrs)'),... ylabel('Temperature (F)'), title('Prob 9.15, part-a')

ENGR-25_Prob_9_15_Solution.ppt 7 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Low Power Fnce

ENGR-25_Prob_9_15_Solution.ppt 8 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Result for Large Fnce  The Large Furnace CAN Keep Up with Heat load at coldest Outside Temps  The R H *q max Product indicates the MAXIMUM Temp Difference that the Furnace+Insulation combination can accommodate  In This case (T-T a ) min = 70F – (50-10)F = 30F The Small Fnce is Overwhelmed

ENGR-25_Prob_9_15_Solution.ppt 9 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods High Power Fnce

ENGR-25_Prob_9_15_Solution.ppt 10 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Part b – Daily Energy Use  To Determine Daily Energy Use, E, Need to time-integrate the fnce Power Output over 24hrs  For an Arbitrary time  Refine the Part-a model to Gain Access to q max alone Use the integrator Block to find E

ENGR-25_Prob_9_15_Solution.ppt 11 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods The Part-b SimuLink Model  Note the Output scaling to “PG&E” Units 1 “Therm” = 100 kBTU

ENGR-25_Prob_9_15_Solution.ppt 12 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Energy Use  Small Fnce  Large Fnce St-Line → Fnce On 100% of time  Fewer Therms, but Cold Inside  Note Differing Slopes Before & After ~11hr

ENGR-25_Prob_9_15_Solution.ppt 13 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Appendix Model Construction

ENGR-25_Prob_9_15_Solution.ppt 14 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15a.mdl (1)

ENGR-25_Prob_9_15_Solution.ppt 15 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15a.mdl (2)

ENGR-25_Prob_9_15_Solution.ppt 16 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15a.mdl (3)

ENGR-25_Prob_9_15_Solution.ppt 17 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15a.mdl (4)

ENGR-25_Prob_9_15_Solution.ppt 18 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15a.mdl (5)

ENGR-25_Prob_9_15_Solution.ppt 19 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Part-a Configuration Parameters

ENGR-25_Prob_9_15_Solution.ppt 20 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15b.mdl (1)  Non GREEN Blocks are the same as in part-a

ENGR-25_Prob_9_15_Solution.ppt 21 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15b.mdl (2)

ENGR-25_Prob_9_15_Solution.ppt 22 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob_9_15b.mdl (3)

ENGR-25_Prob_9_15_Solution.ppt 23 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Part-b Configuration Parameters