# Hot water tank modelling

1. Jun 28, 2012

### wolverin

Hello friends,

I am into modelling of electric hot water tank which is vertical and has the capacity of 120 litres. I just assumed certain charactersitics of an existing heater so as to be more realistic in my approach. Now I am facing certain troubles in my calculations, if you know please help me out with this.

I have done the stratification of my hot water tank with the elementary equations of joules law, heat equation and convection equation so as to know how my temperature vary with stratification. I considered for my heater, a two node stratification with the heating element at the top of the tank. I frammed the equation for the two nodes and got the output for a particular power of 3kW (which is assumed from an existing 120 l heater). Now I would like to know how my output temperature will affected when there are losses.

The output temperature considered for domestic use is 60°C for cleaning purpose and 40°C for drinking and bathing purpose. So I want to frame the losses based on the fact to get this temperature at the taps after the losses has been considered.
My heating range of heater is till 65°C after that I have coded the thermostat to cut the supply.

So now let me explqin the losses:

To my knowledge there are 3 losses in a electric vertical hot water tank:
1. Storage Losses
2. Distribution Losses
3. Generation Losses

So for storage losses: for an existing hot water tank of capacity 120 liters the cooling constant is 0.38 W/litre K day. So I have assumed this constant to my heater as I did not get any equation to support my inference. If you have got any idea about to calculation of storage loss that would be really helpful

Now for distribution losses:

I dont have to get through all the losses like mechanical, I am more concentrated into thermal losses affected my pipe material. I would like to know the pipe specifications used
in a 120 liters heater. SO that I can converge at an idea of framing heat loss per metre of pipe.

I have done calculations based on two formulas which I came thorough the sites that I have reffered.

The first formula I got is for a cylindrical tube of made of copper.
Input details are
Temperature of hot water at the tank : 65°C
Temperaure of Cold water: 20°C ( I have doubt in this whether I should give the outlet of the pipe, I think it is yes... It must be the outlet temperature at the pipe if so it is 60°C/40°C)

Length of the pipe assumed is 5 metres
Outer radius of pipe = 1.8 cm
Inner radius of pipe is 1.6 cm ( I would like to take more realistic values of radius for 120l I dont know whether these values will maximum accuracy in temperature at the outlet(60/40°C)

I would like to know flow through the pipe. In the brouchere of various companies it written specific discharge is for example for which I considered for 120 l it is 22litres/min. So I dont know whether it is flow rate of cold and hot water mixed or only the hot water.

and material used for the pipe is copper (pure) so the thermal conductivity of copper is found to be 400W/mK. I dont know which alloying element is used to make copper pipes. I would like to know more exact values and procedure to frame the losses for distribution.

I have also considered the fact of adopting convection and conduction by consdering thermal resistance in series so as to calculate energy lost per unit length.

So I want to know the details of the specification of pipes used in the given tank of 120 liter capacity so as to calculate the losses and flow rate .

I have missed some points I am always at your availablity