BJ 5/28/09

edit 3/21/2017

Unit definitions

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.

Ambient

Water temperature at specific times (minutes)

Water volume

Convert water volume to mass

Specific heat of water

Find Heat Capacity of Vessel

Initial Temperature of vessel

Strike water temperature

Equilibrium temperature

Heat capacity of strike water

Conservation of energy gives...

Solving for vessel's heat capacity

Sanity check for equilibrium temperature

Check

Characterize Temperature Decay

Time constant of temperature decay

Temperature vs. time function

... in deg F

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

Power loss at T = T5

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.

Mass of grist

Mash thickness

Mash water volume

Mass of mash water

Heat capacity of water

Specific heat of grist

Heat capacity of grist

Grist temperature

Target mash temperature

Strike water temperature

Mash temp time constant

Mash time

Temperature at mash end