A tank containing mw = 45 kg of liquid water initially at T1 = 318 K has one inl

Question

A tank containing mw = 45 kg of liquid water initially at T1 = 318 K has one inlet and one exit with equal mass flow rates. Liquid water enters at T1 = 318 K and a mass flow rate of 270 kg/hr. A cooling oil immersed in the water removes engery via heat transfer at a rate of 7.6 kW. The water is well mxed by a paddle wheel so that the water temperature, T(t) is uniform throughout the tank. The power output to the water from the paddle wheel is 0.6 kW. The pressure at the inlet and exit are equal; therefore, the difference in specify enthalpy between the inlet (T1) and exit [T(t)] is given by:

hi-hc = c [T1-T(t)]

with c the specific heat of water, c = 4,2 kJ/kg.K

All kinetic and potential energy effects can be ignored. Plot the variation of temperature with time. To do so, you will need to solve a first-order, ordinary differential equation, with the boundary condition : T(t=0)=T1=318 K

Explanation / Answer

%Brendan S. Andrew %3/19/2010 - HW 8 %Thermodynamics %This program will plot the variation of water temperature with time %of a tank containing 45 kg of liquid water initially at 45 *C with one %inlet and one exit having equal mass rates. The liquid enters at 45 *C %and a flow rate of 270 kg/hr. A cooling coil immersed in the liquid %removes energy at a rate of 7.6 kW. The water is well mixed by a paddle %wheel so that the water temperature is uniform throughout. The power %input to the water from the paddle wheel is 0.6 kW. The pressures at the %inlet and exit are equal and all kinetic and potential energy effects can %be neglected. clear all mw=45; %[kg] mdot=270/3600; %[kg/s] T1=45+273.15; %[K] Qdot=7.6; %[kJ/s] Wdot=0.6; %[kJ/s] Cp=4.186; %[kJ/kg-K] t=0; for i=1:1500; t(i)=(i-1); T2(i)=T1+((Wdot-Qdot)/(mdot*Cp))*exp((-mdot/mw)*t(i))+((Qdot-Wdot)/(mdot*Cp))-273.15; %[*C] end plot(t,T2,'-b'); xlabel('Time [s]'); ylabel('Temperature [circC]'); title('Water Temperature Variation of a Steady State System Over Time'); axis([0 1500 0 80]);

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.