Question

The room shown in Figure 1 has a heater with heat flow rate input of q0. The thermal capacitances of the heater and the room air are C1 and C2, respectively. The thermal resistances of the heater–air interface and the room wall–ambient air interface are R1 and R2, respectively. The temperatures of the heater and the room air are T1 and T2, respectively. The temperature outside the room is T0, which is assumed to be constant.
a. Draw the circuit diagrams for the thermal system. (3)
b. Derive the governing equations for the system necessary to determine the transfer function T2/Qo (7)
c. Consider suitable analogous terms to obtain the analogy between the thermal system and equivalent
electrical system (You can use either direct or indirect Analogy). (7)
d. Draw the equivalent electrical circuit based on the governing equations obtained for the equivalent
electrical system in ‘c’ above. (3)

Room air T, с To Heater Figure 1

Answer 1

Given datu: Roomair To TC Vo Heat input to heatas is o thermal Capactana 4 heater = C1 themal Capactance 4Room ar = Cr Tempesatua 4 fl haaterT, Temperature ta Room kmesatasT Temperataa tth anbient Coutmale Room) To (Constunt) the thermal RemstanCa d. tu Heatee and Room interta He themal Rexstanca d he yoom oall and ambiant air intofoa the mal apactana is dofind as' Amount 4 haat reauied to chage dempesataa dagaer SinCa at1 aubbtanCa One (maxEpecfic aat a susstana

Heat Capactna heades-C heat stored by heater - Capacty & Room air C heat shored Heat Room air Tレ mbient To Heak Reomair Beat in a Heades frem heater be heatous t heat Shored. let heat ousfut toroom eat inニ 11 TIT 4CET RI oheee R, isthermal Re人tane heada and intafae Roomaix ees in Heat ous t heat Shord. 1/2-/4-1 Lるナ To-T R. R i thermad Remstanca Room oall and ambiet ai. wheee

themal airct ih: heat Shoraga&Capeonte To Th www TC TrCI Roomai'r F& overall Systen: Heat out t ttap Stored teaup i'n Rebga Ro To-T 49T+cT ro R Vo Te +GT +C- . en)() To t RZ CIT) TRE To R2 T2 Ve ThC-T +To +GTR Ti TRZ T2RC+CTR-TL +T

Trafir fun Chon: temparata change Change in hant ake eat dT+ (T-) ohers R- hosmal Remntanc Cheat Capaay d, mateu'al n Grerealrgahy q a Laplaa tranform cdTt L L[ Vin C LETJ= TEAT Lt ATA) Via (a)=CTA) +T) Vig Ca) RCs t) TCA) RC+ -1 Ro RICIHI 3 Elachi Cal Analopy f te asave +hasmal Ngghem ingven as: votage aNrrent flous Copetonte N ElactrCal Renshne Tempesnbuaa CT) heat flow heat Capacty thermal Rasintrana

T RI To (akint tenpesatus R1 the abane arat in ven Govesnig eapuahin V when Curred flow Votege drop zimpedence dtRe Circait twhere z R+ whee Xe 2T1F C where fin &euan a. GpaGtn