[Theory] Sous vide initial bath temperatures and modeling sousvide

I've had this idea for a while but got some time to put it on paper recently and wanted to see if anyone else had considering this and could comment. The main problem with sous vide for quality and safety is the time it takes for food to reach the bath temperature (the rise time). A sous vide cook involves a rise and a hold. During the rise, food is warming to the hold temperature and along the way will transition through the 'danger zone' of ~4-60 C (or whatever your upper limit is here, maybe as low as 45 C). During that time, bacteria are multiplying and they increase the load that needs to be inactivated during the hold time. Any shortening of the rise time would improve the product safety, process efficiency, and marginally improve product quality.

For every sous vide cook I've seen, the initial bath temperature is set to the hold temperature. This is simple but it doesn't really make sense since the food is likely starting at ~4 C (refrigerator temperature) so the bath will cool when the food is placed inside and the controller will have to supply extra heat to compensate. Meanwhile, the rise time will increase as a result. But, if the bath temperature was set a few degrees hotter than the hold temp at the beginning of the process, we could shorten the rise time without really risking overcooking any part of the food since even the surface takes some time to heat up.

So, with that in mind, here is a very, very simple total internal energy based model for a sous vide cook. This only looks at the first instant of cooking and actually pretends that there is no heating element supplying energy to the bath. If anyone is really handy with COMSOL and wants to build a real model PM me, I'm super in.

System energy balance:

U_bath(t=0) + U_food(t=0) = U_bath(t=inf) + U_food(t=inf) U_bath(t=0) = U_bath(t=inf) + [U_food(T=inf) - U_food(t=0)]

For internal energy, U = mcT (m = mass; c = specific heat capacity, T = temperature)

mcT_bath(t=0) = mcT_bath(t=inf) + mc_food x [T_food(t=inf) - T_food(t=0)]

mc_bath x [T_bath(t=0) - T_bath(t=inf)] = mc_food x [T_food(t=inf) - T_food(t=0)]

Let: x = c_food/c_bath Let: y = m_food/m_bath Assume: T_food(T=0) = 4 C Assume: T_food(t=inf) = T_bath(t=inf) = T_f Let T_bath(t=0) = T_i

Then:

T_i - T_f = xy[T_f - 4 C] T_i = T_f[xy+1] - xy(4 C)

For water, c = 4.18 kJ/kgC For meat: c = ~3 kJ/kgC (varies but may estimate between 2.6 and 3.2)

x = 0.72

Suppose: y = m_food/m_bath = 1/8 (i.e. the bath mass is 8 times the food mass). Since xy will be much less than 1 for most systems, we can neglect the second term and reduce the equation to:

T_i ~= T_f[xy+1] = 1.09T_f

This result surprised me. This suggests that if you don't want the heating element to do any work and the bath is well insulated, increasing initial temperature by about 9% would compensate entirely for the cold food.

Now, suppose we wanted to consider how the outside shell of the food will warm to ensure it doesn't overcook under these conditions. Let's suppose there is an outer shell of the food which corresponds to 20% of its weight. After this shell warms, the element will kick in and maintain the bath at its hold temperature. Then we can just play around with this model and change the value of y to 20% of its value, so y' = 0.2y = 0.025.

Under these conditions: T_i = 1.018T_f, which amounts to only a 2% temperature increase to cover the rise.

This model doesn't account for any energy losses to the environment and those could be significant. It depends a lot on the water to food ratio which can get pretty low for some cooks. 1:8 is quite generous, for a situation that's closer to 1:3 and using the 20% shell idea this comes to: T_i = 1.048T_f which is about a 5% increase in the bath temp, something pretty significant.

Any thoughts on this? Has anyone tried increasing the initial bath temp or monitoring it through the first few hours of a cook? I think this kind of modeling could be useful, particularly since many controllers take a while to stabilize and might stabilize faster if they were set high and dropped low instead of having to heat to reach the hold temp. Feedback welcome and appreciated.

Submitted September 19, 2016 at 10:39PM by galacticsuperkelp http://ift.tt/2deb0sy sousvide