I'm puzzled that one of the guys posting above said he needs to go 16 F above to get to the mash temp. Is this because you are adding water slowly into your mash tun?
No, it's because we are raising the temperature of the grain and the tun to mash temperature with the hot liquor infusion, and the hot liquor infusion has to carry this additional heat energy into the tun. This problem is an exercise in applied thermodynamics. Let's examine the equation that I posted.
strike_liquor_temperature = (0.2 / hot_liquor_to_grist_ratio_in_quarts_per_pound) x (desired_strike_temperature - grist_temperature) + desired_strike_temperature
There's a concept in thermodynamics known as specific heat capacity. Specific heat capacity is the ratio of the amount of heat energy added to an object to the rise in temperature resulting from the addition of the heat energy. Twenty pounds of grain has the same amount of heat capacity as 1 gallon of water, that is, the amount of heat energy necessary to raise the temperature of a gallon of water 1 degree is equal to the amount of heat energy required to raise the temperature of 20 pounds of grain 1 degree.
The value 0.2 in the equation shown above represents the specific heat weighting factor for a pound of grain with respect to a quart of water. If 20 pounds of grain has the same specific heat capacity as a gallon of water, then 1 pound of grain has the specific heat capacity of 1/20th of a gallon of water, which equals 0.05 in decimal. As there are four quarts in a gallon, we have to multiply this value by 4 to convert it to specific heat capacity with respect to a quart of water, which equals 0.05 * 4 = 0.2.
Now, because we generally mash with a grist ratio of one than one quart per pound of grain, we need to further scale the grain-weighting factor. We perform this step by dividing 0.2 by the number of quarts per pound that we use during mash-in (i.e., hot_liquor_to_grist_ratio_in_quarts_per_pound in the equation shown above).
In the next part of the equation, we calculate the difference between the strike temperature (our rest temperature) and the grist temperature. The subexpression "(desired_strike_temperature - grist_temperature)" accomplishes that goal.
Now, we need to convert the temperature difference that we just calculated to specific heat in quarts because one pound of grain only has as much specific heat capacity as 1/5th of a quart of water. That's where the weighting factor that we previously calculated comes into play. In the example that I gave earlier in the thread, the temperature difference between the grist before mash-in was 77F. The desired strike temperature was 151F, resulting in a temperature differential of 74 degrees Fahrenheit. We are using 1.5 quarts per pound; therefore, the weighting factor 0.2 gets reduced to 0.13.
strike_liquor_temperature = (0.2 / 1.5) * (151 - 77) + 151 = 0.13 * 74 + 151 = 161F (72C)
Hopefully, I have not lost the members of the forum at this point. The subexpression "0.13 * 74" shown in the equation above represents the amount of heat energy as water necessary to raise the temperature of the grist to 151F. Every quart of water that we infuse must carry the heat energy necessary to raise a quart of water 10 degrees above the strike temperature because that heat energy will be absorbed by the grist, resulting in the grist temperature rising to 151F.
The next part of the problem is the most difficult to approximate, which is why it is best arrived at empirically. The tun itself has a specific heat capacity, and it is not sitting at strike temperature when we mash-in; hence, we have to add additional heat energy to cover this thermal loss. Whereas the amount of heat energy necessary to raise a pound of grain X number of degrees given V volume of strike liquor to a given strike temperature remains linear as long as the ratio of quarts to pounds remains the same, the amount of heat energy required to raise the tun to strike temperature remains static because the tun's mass does not change with respect to mash size. In effect, the amount of additional heat energy per quart necessary to raise the tun to strike temperature decreases as the volume of the mash increases.