Question

Τ Liquid properties are constant (not functions of temperature). 2.2 A completely enclosed stirred-tank heating process is used to heat an incoming stream whose flow rate varies. w Ta Heating coil T Figure E2.2 The heating rate from this coil and the volume are both constant. (a) Develop a mathematical model (differential and algebraic equations) that describes the exit temperature if heat losses to the ambient occur and if the ambient temperature (T.) and the incoming stream's temperature (T) both can vary. (b) Discuss qualitatively what you expect to happen as T, and w increase (or decrease). Justify by reference to your model.

Answer 1

TiW المهم T Ti= feed temperature inlet - To autht feed temperature Q = heat input from coil. w a feed sale (mass flowrate) Na volume of the tank pa Density of the fluid. balignid might af tank let A = Areas of the talks W = authf, fed rate, Ce a specific heat of liquid. Assumption : mixing is uniform temperature inside the tank is uniform o volume as liquid and dinsity of the lignid is constant. & Heating rate from the Coil is const The general mass balance egnation rate of rate af] rate ay] accumutation as = mass 1-mass o mass imput Lautput ] Y rate Stion Lemay mays - Trateas ? depletion La mass

no generation frate as 7 accumutations = and no accumulation sate 7 Iratias as input output as mass X muss mass w-Wi a (pr) at - W-wi accumulation input output constant Cassume) e and w are SA ralpro It The general energy balance equation Trate - Iratias Isate , energy -lay energy accumu rate as lo frate ener and energy Aeneration expenditure no energy generation and expenditure] insout I I M senergy I output az P.

ratio de content and test Tev eplt-Tref) = prep a rate of energy input = wep (Ti-Tref) (from feed) ta (from coil) rate of energy aut - = heat tranger W.Lp (T-Tred) - Wiper-Tref) Co-efficient + UA, (T-Taj A- Area ay hinder Combining all parep d = Wep (Ti-Tref)+Q - Wi Cp (T-Try) - Uai (T-ta) IT - W (T-Tref) to bee - Wie (T- Tray) - VAI (T-Ta) This is the mathematical model (Ans (a) ever To increases then (b) I will increase W reases Them T increases if Ti) ir-creases then I decreses if Ti)T ww increases then I decreses if Tic

at of teed teed t. (Ti) temperature is increase then aut let temperature (T) will merese losses is not too much! it heat gf seed rate is increase meany Total energy import increage and will increase If surrend heat loss is much more then case increase then that or decrease T will to and heat losses. that will dempen on surround