Known Parameters for the Boiler Test Object

Before starting the simple modelling I think it is worth looking at the known parameters for the boiler test object. From these there will be some simple assumptions and estimations.

Assumptions

  • Lumped point mass.
  • Single temperature measurement represents the temperature of the object.
  • Heat capacity does not change with temperature.
  • Local air temperature represents ambient conditions.
  • Local ambient conditions are uniform throughout testing.
  • Heat is only considered to be lost through ends of the object and copper surface.
  • Heat lost through the end is just a function of object temperature and not test insulation.
  • Mass and heat capacity of the object is just the mild steel core and copper shell.

Mass

The object was weighed at 683g. The copper shell is well defined and so I can calculate the volume and then with the density (8960kg/m3) the mass. This was then subtracted from the total to give the mass of the mild steel core.

Copper shell mass = 95g

Steel core mass = 588g

As a check I calculated the more complicated volume of the mild steel core and using a density for mild steel (7840kg/m3) got a mass of 587g. This gives me confidence and for these calculations I will use the 588g for the mild steel.

Heat Capacity

The specific heat capacity of copper = 385J/kg.K and for mild steel = 511J/kg.K

Using the calculated mass for the two parts this gives a combined object heat capacity = 337J/K

Simplified Model

This simplified model means there is a heat input to the object and two heat outputs. The change in temperature of the object and the heat capacity of the object will give the total energy change of the object.

The maximum insulation versus the unclad test cases will be used to estimate the heat lost through the ends of the object versus the shell.


model of a model boiler

A Model of the Model Boiler

So, I’m building a Model of the Model Boiler. The model is a mathematical model and to be honest it is in the simplest terms. The boiler is the small vertical one made as a test case for the miniature traction engine. However, I think this will help to explain the calculations that I can then make. 

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