Brewing Vessel Calibration Constants
A brewing vessel is calibrated by adding heated strike water to it and measuring the temperature decay of the water over time. This provides two calibration constants; the vessel's heat capacity, cv [J/K], and its heat loss coefficient, hlc [W/K].
The assumptions here are:
- The heat loss during the initial 5 minutes can be included into the vessel's heat capacity calculations
- The heat loss from 5 minutes on can be attributed to exponential heat loss through the vessel walls
- The specific heat of ingredients and the vessel's heat capacity are constant
Note that Mathcad uses implicit unit conversions, you may need to do this explicitly in your code.
Water temperature at specific times (minutes)
Convert water volume to mass
Find Heat Capacity of Vessel
Initial Temperature of vessel
Heat capacity of strike water
Conservation of energy gives...
Solving for vessel's heat capacity
Sanity check for equilibrium temperature
Characterize Temperature Decay
Time constant of temperature decay
Temperature vs. time function
Plot exponential temperature decay
(prevent solver from substituting values)
Find time derivative of temperature decay at the following time:
Find Heat Loss Coefficient of Vessel
Example on how to use the calibration constants
The calibration constants are used to select a strike water temperature to hit a target mash temperature. The example will also show what the temperature is at the end of the mash.