# Heater - how to define power needed taking into account air thermal dissipation

My objective is to heat a liquid inside a bottle. I have a air gap of 2 cm between the bottle and the heating element (resistive layers). The heater and the bottle is surrounded by a bottle insulator, so the volume of air to heat is fixed.

I did the calculation to know how many power I need in order to heat my liquid from 18°C to 37.5°C in 5 minutes with these formulas, taking into consideration weigh of the bottle, delta temperature and specific heat of glass material.

Q = cp * m * dt

• Q is heat required (kJ)
• Cp = specific heat (kJ/kg K, kJ/kg°C)
• Weight of bottle and liquid inside (kg) = 750 g

Then I deduced power needed: P = q / t

• P = power (kJ/s, kW)
• T = time (s)

P = 9.75W

My questions now are:

• How can I calculate the thermal dissipation between my heater physical element and my bottle of liquid as I have a air gap of 2 cm between both elements
• How can I deduce the real power I need with my heater element to be able to heat my liquid ?
• What is for you the best solution to heat my liquid in term of heater technology ?

I looked on google and I was able to determine my R factor for the whole assembly = 0.5 (due to air which is playing as insulator). But it's really hard to understand how to do this calculation and the steps of the calculation...

Can you help me ?

• This will be quite a complicated thermodynamic problem... I'll be interested to see if you get an answer. But you're probably better off on physics.se or engineering.se; it's well off topic here. – user_1818839 Nov 11 '20 at 16:51
• I’m voting to close this question because it is not a problem of electrical engineering. In theory if your insulation is good, the air gap inside the insulated volume may be tolerable but it will mean running your heater at an elevated temperature; you may want to consider improving thermal transfer by placing the heater in contact, using a band heater, etc. – Chris Stratton Nov 11 '20 at 18:59