Mathematical Thermal Model of a House

International Research Journal of Engineering and Technology (IRJET)

Volume: 09 Issue: 04 | Apr 2022 www.irjet.net

Mathematical Thermal Model of a House

e ISSN: 2395 0056

p ISSN: 2395 0072

Shridhar Koppal1, Prasanna Wagh2, Akshay Patil3, Shubham Bhaingade4

1B.E, Department of Mechanical Engineering, L.T.J.S.S. Lokmanya Tilak College of Engineering, Navi Mumbai, Maharashtra (India)

***

Abstract This paper presents an analysis of heat & temperature & how it affects the thermodynamics of a complex body such as a house & predict the temperature variation. For this, the model takes into consideration the different physical properties of a house & the weather around it. The analysis is done on the outside vs inside house temperature & the cost of electricity.

Key Words: Thermal model, House, Thermostat, Scilab, Thermodynamics

1. Introduction:

SpeakingabouthumancomfortASHRAE(AmericanSocietyofHeating,RefrigeratingandAir ConditioningEngineers)states “Humancomfortisthatconditionofmindwhichexpressessatisfactionwiththethermalenvironment”.Ahouseisacomplex permanentstructurecomprisingofdifferentcomponentssuchasRCCconstruction,bricks,woods,glass,steel&othermetals etc.Each&everycomponentaffectsthetemperaturedistributioninthehouse.Thenumberofpeople&variousappliancesalso affecthowthetemperatureisdistributedacrossthehouse.Thebestwaytoanalyses&improvethistemperaturecontrolisto prepareamodelcalculatingthetemperaturevariationbytakingalltheaffectingfactorsintoaccount.Improperthermaldesign ofthehousenotonlyleadtohumandiscomfortbutalsoincreasedcost&wastageofenergy.

2. Problem statement:

Whenconstructingahouse,itisparamountthattheheatflow&temperaturegradientiskeptinmindasitisutmostimportant for the inhabitants’ comfort. An ideal thermally designed house also resources energy intake & thus prevents wastage of precious natural resources. The interaction between the heating system & thermal demand of a house is complex due to variousfactorssuchasweather,outsidetemperature,inhabitants’comfort&eveneconomicstatus.Thephysicalproperties& characteristicsofthehousealsoplayanimportantrole.

3. Methodology:

Forthefollowingexperiment&study,asimpleremotehouseisselected.Thehouseisrectangularinshape&has1room.The househasgableroof,angledat40°attheapex.Thehousecontains6windowsofplainglass.Thehouseissituatedinacold regionwithnohumidityforeaseofcalculation.Duetothethermalconditions,thermostat&heaterareusedfortemperature control.

9001:2008

Journal of Engineering and Technology (IRJET)

Volume: 09 Issue: 04 | Apr 2022 www.irjet.net

8. WallConductivity 0.038*3600 J/Hr/m/C

9. WallThickness 0.2 m

10. WindowConductivity 0.78*3600 J/Hr/m/C

11. WindowThickness 0.01 m

Table 1: ProjectParameters

4.2 Components:

e ISSN: 2395 0056

p ISSN: 2395 0072

1. Thermostat: Thermostatisaregulatingdevicecomponentwhichsensesthetemperatureofaphysicalsystem&takes actionsothatthesystem’stemperatureisnearthepre determinedsetpoint.Thethermostatisaclosedloopcontroldevice whichmeansithasafeedbackelement&controlstheambienttemperatureofthehousebyadjustingtheheateroutput. The thermostat compares the current temperature of house with the required room temperature. According to the feedbackreceived,thethermostatturnsONorOFF&givesinformationtoheater.

Fig 1:SuperblockofThermostat

2. Heater: Anelectricheaterconvertselectricenergyintoheatenergy&outputsittothesystemtoraisetheambientroom temperature.Airisintroducedintotheheater&thetemperatureofthisairisincreased&releasedintothesystem.The recirculatedairismixedwithoutsideair&passedthroughapre heatcoiltopreventfreezingofwater&tocontrolthe evaporationofwater.Furthertheairispassedthroughare heatcoiltoraisethetemperatureofairtorequireddrybulb temperature.Thisconditionedairisdistributedintheconditionedspaceviafansofadedicatedventilationsystem.The electricheaterusesforcedconvectionmethodtoheattheair.

Whensignaledbythermostathotairblowsataconstantflowrate.

RateofheatgainbyHeater:

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International Research Journal of Engineering and Technology (IRJET)

Volume: 09 Issue: 04 | Apr 2022 www.irjet.net

e ISSN: 2395 0056

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Fig -2:SuperblockofHeater

3. House: Thehouseisthesystemcontainingthermostat&heater.Theboundaryofthesystemi.e.,thewallsofthehousedo convectiveheattransferwiththesurroundingair.

Rate of heat loss equation: Thermalenergylossfromtheroomisbyconvectionthroughthewalls&windows

Qloss= whereRisthermalresistance.

ChangingroomTemperatureequation.

Fig 3:SuperblockofHouse

Factor value: 7.529 | ISO 9001:2008

Research Journal of Engineering and Technology (IRJET)

Volume: 09 Issue: 04 | Apr 2022 www.irjet.net

e ISSN: 2395 0056

p ISSN: 2395 0072

5. EXPLANATION: Superblocksofthethermostat&heaterareconnectedtothehouse.Thehousereceivesinputfromthe temperaturesensor&sharesthatdatatothethermostat.Thethermostatuponreceivingthedataanalysesitandsends signaltotheheater.Theheaterinterpretsthereceivedcommand&,ifnecessary,increases/decreasesormaintainsthe heatingofthehouse.Themeterconnectedtotheheatercalculatesthecostofoperationoftheheater.Asignalrouting systemcalculatesthetemperaturevariationforanalysis.

6. Results: ThefollowingprojectisdonewiththehelpofScilabsoftware.Acontrolstrategyisdevelopedattachedtoobtain the temperature variation & cost of electricity of the house. The results show that as the outside temperature varies accordingtotheclimate&timesodoestheindoortemperaturevariesinaccordancewiththeheatsuppliedbytheheater. Thecontinuoustimesystemmeterattachedtotheheatermonitors&calculatesthecostofoperation&conveniently displaysitinagraphicalformat.Itisobservedthatthecostofoperationkeepsonincreasingwhilsttheheaterison& functioningbutitshowsvariousslopessuggestingdecreasingorincreasingoutputwhichshowsthecontrolbythermostat. Thisconcludesthemodelling&analysisofthehouse.

Chart 1:CostofHeater

Chart 1:Temperaturevariationofthehouse.

Factor value:

| ISO 9001:2008

International Research Journal of Engineering and Technology (IRJET)

Volume: 09 Issue: 04 | Apr 2022 www.irjet.net

e ISSN: 2395 0056

p ISSN: 2395 0072

7. Future scope: Tovalidatethesoftwareresultwehaveplottedthegraphsusingtheoreticalcalculations.Individualscan validatetheseresultsbydoingexperimentalverificationthatisbybuildingtheactualmodelorbydoingindustrialprojects relatedtoThermalmodelling.

8. Conclusion: Thefollowingprojectshedslightuponthefundamentalworkingsystemofhowheatingworksinahouse. Baseduponthedatacalculateditcanbeconcludedthattheheatingofthehouseisinfactdependentonthetemperature variationofthesurroundingclimate.ThethermostatsuccessfullycontrolstheHeater&providesutmostprecision&in turnprovidesthecomfortnecessary.Withthehelpofsystemmeter&signalroutingsystem,theheateroutput&cost deemedcanbedetermined.Allofthishelpsinunderstanding&improvingtheHVACsystemofahouse&canbefurther usedindeterminingofsimilarsystemsinlargerscale.Thepurposeoffindingvariousthermalaspectsofthehousesuchas costofheater,temperaturevariationhasbensuccessfullyattained.

Acknowledgement:

1. DecibelsLab,Bangalore.

2. Dr.S.D.Dalvi(ProjectGuide,LTCE)

References:

1. Thermal modelling of the building and its HVAC system using MATLAB/Simulink “S.Karmacharya,G.Putrus,C. Underwood,K.Markamov,SchoolofComputing,EngineeringandInformationScience2SchooloftheBuiltandNatural EnvironmentNorthumbriaUniversityNewcastleuponTyne,UK”

2. Modelling of thermal processes in apartment houses “Sven Peets, Tõnis Peets and Eugen Kokin Institute of Engineering,EstonianUniversityofLifeSciences,Fr.R.Kreutzwaldi56,51014Tartu.”Proc.EstonianAcad.Sci.Eng., 2006,12,1,59 71

3. MATHEMATICAL MODEL OF SELECTED OBJECT THERMAL PROPERTIES “K.Peszynski,W.Szmyt,S.Wawrzyniak, D.Perczynski”22nd InternationalConferenceEngineeringMechanics2016Svartika,CzechRepublic,9 12May2016

4. Thermal performance modelling of residential house wall systems “Fayez Aldawi, Firoz Alam, Abhijit Date, MohammadRasul;SchoolofAerospace,MechanicalandManufacturingEngineering,RMITUniversity,Melbourne, 3083,Australia,SchoolofEngineeringandtheBuiltEnvironment,CentralQueenslandUniversity,RockhamptonQLD 4702,Australia”ScienceDirectProcediaEngineering49(2012)161 168

Factor value: 7.529 | ISO 9001:2008