hydroponic system 8

[daviddor]

Hii everyone .
i am designing an hydroponic system , and there is one calculation that really gives me a hard time , i will be very happy if someone can help me with this. I simplified the equation that i need to develop down below. thank you very much for any help.

Question
An isolated tank contains M amount of water. A pipe connected to the tank with a pump, delivering the water in a close circle back to the tank through the atmosphere. Assuming the water temperature distribution is equal in the tank at the beginning . Create an equation of the temperature in the tank relative to the time .

Given :
water flow through the pipe 3M/h (three times the water tank per hour)
Initial temperature at the tank T1
Atmosphere temperature T0
Length of the pipe L
h0 - convective heat transfer coefficient of the air
hW -convective heat transfer coefficient of the water
k- pipe thermal conductivity (W/m·K)
d – pipe diameter

*Can use any other obvious data that is needed and can be reached easily online .
Please explain every step, equation and assumption that is used.

 

[IRstuff]

The value you picked and calculated is irrelevant for your purposes, since your limiting path is the free convection of the plumbing to the ambient AIR. Nevertheless, your obsession with the plumbing is ill-advised, since you've conveniently ignored a number of other thermal paths. This is bad engineering; you do not pick the solution and then try to find supporting data for it. You need to analyze the ENTIRE system and then determine what is critical and what is not.

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[pierreick]

Hi,
Global heat transfer coefficient, based on convection, conduction and radiation outside pipe is about 21 W/m2 K leading to an increase of temperature of 0.2 C due to hot air, based on partial information supplied, for 7.2 m3/h of water, wind 5m/s, rugosity PVC 0.0015 mm, Thermal conductivity PVC and water 0.17 w/m-K @ 0.598 w/m-K respectively, Cp water 4180 J/kg K.
Heat increase is not significant and should be reduced with water make up.
Pierre

 

[daviddor]

@pierreick thank you very much for reminding me about the radiation i will add it to the coefficient of heat . How do i know by the way the temperature of the surface/pipe roughly? i need it for the formula of the resistance of radiation

*** does it make sense , when i am adding the radiation , the temperature increases less?

 

[pierreick]

Hi,

hr= ε*τ*(Tskin^4-Tamb^4)/(Tskin-Tamb)
τ stefan bolzman constant
5.67037E-08 W/(m2*K4)

Iterative calculation, Suppose Tskin, perform all the calculation of U, Q Heat lost or gained, Get Tskin and compare with initial value.

note: hr take account a difference of temperature not a sum like you wrote.

Pierre

 

[daviddor]

Thank you very much Pierre, IT HELPS A LOT, im still getting this way U equals to 1 comparing to 10 before means less temperature increase, only 0.1 , make sense? i feel like should be more increase since the radiation ...

we talking about direct solar radiation sometimes...

 

[pierreick]

Hi,
A document you and others should consider for the calculation of heat transfer of above and underground insulated piping systems.

Good luck
Pierre

 

[daviddor]

Ok, i don't know why but everywhere i see they calculate the radiation and convection outside thermal coefficients as series not as parallel like here:

also here:

anyway now with this calculation i am getting a U of 15 W/m^2*k instead of 12. i think its good

 

[daviddor]

Any thoughts why it is like this? , thank you

 

[pierreick]

Hi,
2 processes competing outside, Convection and radiation .
Pierre