Modeling Solar Heat Transfer in Storage Tank: Tips & Equations

[gdogg123]

We have a model where we are to predict the temperature of the water outlet stream of a storage tank. Basically we have a solar heating collector that heats up a fluid which is present in a storage tank. The flow process is that the fluid flows through the pipes to the solar collector and back to the tank after it is heated. The other side of the tank is connected to an inlet stream that allows cold water in a pipe to enter, that water extracts heat from the fluid and exits as heated water.

Assumptions:
1. zero heat loss occurs in the system
2. no heat accumulation occurs in the collector or the water pipe inside the storage tank.
3. storage tank is well mixed; no spatial temperature variation exists
4. the rate at which solar heat is collected(W/m^2) follows the following function: 200*(sin(t/24*3.14))^8, t is the time of the system in hours.

Data:
1. Collector Area= 20 m^2
2.Fluid volume within the storage tank= 1.5m^3
3. Fluid in the loop between collector and storage tank= 46% glycol + 54% water
4. Fluid flowrate in the above loop= 0.3 m^3/hour
5.Flowrate of water supply circuit = 1m^3/day
6. cold water temperature= 20 C
7. Heat transfer between the fluid in the tank and the water supply = 1000 W/C
8. When the system is started up, temperature of the collector-storaget tank is 40C

I am supposed to develop a mathematical model of the system based on the assumption that the log mean temperature difference can be applied between the fluid in the storage tank and the water being heated up in the pipe.

This is what I`ve done so far. The LMTD is dTA-dTB/ ln(TA/TB)

TA= T(after collector heat)-40C(initial temperaure)
TB= T(after heat extraction from fluid)-20C(initial temperature)

We also know that solar heat is collected at 20*200*(sin(t/24*3.14))^8 and that the heat is transferred to the fluid (TA after heat collection)

We also know that heat is transferred from the fluid at 1000 W/C which is TB(after heat extraction)

How do I develop the model? Should I take into consideration volume balance or energy balance? What equation should be applied here? I know its the heat conduction equation but
in which form? Please help.

 

[WhoWee]

We have a model where we are to predict the temperature of the water outlet stream of a storage tank. Basically we have a solar heating collector that heats up a fluid which is present in a storage tank. The flow process is that the fluid flows through the pipes to the solar collector and back to the tank after it is heated. The other side of the tank is connected to an inlet stream that allows cold water in a pipe to enter, that water extracts heat from the fluid and exits as heated water.

Assumptions:
1. zero heat loss occurs in the system
2. no heat accumulation occurs in the collector or the water pipe inside the storage tank.
3. storage tank is well mixed; no spatial temperature variation exists
4. the rate at which solar heat is collected(W/m^2) follows the following function: 200*(sin(t/24*3.14))^8, t is the time of the system in hours.

Data:
1. Collector Area= 20 m^2
2.Fluid volume within the storage tank= 1.5m^3
3. Fluid in the loop between collector and storage tank= 46% glycol + 54% water
4. Fluid flowrate in the above loop= 0.3 m^3/hour
5.Flowrate of water supply circuit = 1m^3/day
6. cold water temperature= 20 C
7. Heat transfer between the fluid in the tank and the water supply = 1000 W/C
8. When the system is started up, temperature of the collector-storaget tank is 40C

I am supposed to develop a mathematical model of the system based on the assumption that the log mean temperature difference can be applied between the fluid in the storage tank and the water being heated up in the pipe.

This is what I`ve done so far. The LMTD is dTA-dTB/ ln(TA/TB)

TA= T(after collector heat)-40C(initial temperaure)
TB= T(after heat extraction from fluid)-20C(initial temperature)

We also know that solar heat is collected at 20*200*(sin(t/24*3.14))^8 and that the heat is transferred to the fluid (TA after heat collection)

We also know that heat is transferred from the fluid at 1000 W/C which is TB(after heat extraction)

How do I develop the model? Should I take into consideration volume balance or energy balance? What equation should be applied here? I know its the heat conduction equation but
in which form? Please help.

It appears this is a closed system, but cold water can be added at 20 C - if so, at what flow rate? Is it "Flowrate of water supply circuit = 1m^3/day"?

 

[gdogg123]

Yes, the water flows at 1m^3 per day. I know that we have three balance volumes(the tank, the collector, and the water in the pipes). The collector and the water in the pipes are in steady state so an algebraic equation will be used for them.

But, we will have a differential equation for the tank. We also so that heat transferring to the water in the pipe is equal to = specific capacity water * flowrate per hour* (temperature of fluid-temperature of water)*1000. Q going to the fluid is equal to 20*200*(sin(t/24*3.14))^8= flowrate of fluid*specific capacity of fluid*(temperature of fluid in tank which is initially at 40).

However, how can we construct the differential equation to show the temperature change that occurs when heat is lost to the water and the temperature gain that occurs when heat is added by the heated fluid? Also, we are to use the LTMD, how can I incorporate that when I have several unknowns?