Is there a simple model of temperature rise with time available for an internally heated tank losing heat to an ambient environment?

I would like to model the temperature rise (or specifically the time it takes to reach a given temperature) within a steel tank containing water, taking into account the increased conduction of heat to the ambient surroundings as the tank temperature increases. The Simulink model of a house is very useful but over-complicated for this simple analysis. The tank is 2.5m cubed, the walls are 0.02m thick and is heated by a 4000 watt submersible heated located at its centre. The ambient temperature is 10C and I would like to model how long it takes to reach 44.4C within the tank and then 80C. I'm sure it's a simple problem but I'm struggling to find a quick solution.

Many thanks.

Answer 1

[Yifeng Tang]

Something like this, with right parameters (which is usually the hard and time consuming part).