I would like to sous vide a chuck roast for 24 - 48 hours at 135° F…

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https://www.nerdchefs.com/sous-vide-chuck-roast-recipe/
I would like to sous vide a chuck roast for 24 - 48 hours at 135° F (per the recipe linked below). However, I don't have a sous vide machine, and I don't want to buy one. I already have a large dehydrator which can hold a large dutch oven and has temperature control. Therefore, it seems like the following should work instead:

1. Fill dutch oven with water, leaving enough room for the roast.
2. Heat water on the stove to 145° F.
3. Put roast in zip lock bag, and place in water.
4. Put dutch oven and roast into dehydrator at 135° F.
5. Add water heated to 135° F as needed to account for any losses due to evaporation.

The initial higher temp is to account for the heat lost to the roast as it rises to the 135° F target. The water in the dutch oven should dampen temperature fluctuations around the target temp.

Anyone see any problems with doing it this way?