I'm a microbiologist and my physics is not up to par for figuring this out. I've requested our engineering department to perform a temperature mapping of the vessel, but they can't do it for me. I have a cylinder shaped stainless steel tank. I don't know it's thickness, but estimate it to be 1/2 cm to 1 cm if that is important. It will be filled with $1600$ L of fermentation fluid (I'd guess water or beer would be similar fluid to use). I estimate the tank to have a holding volume of $2000$ L ($2\times 10^6$ cm$^3$). The "water" will be at ~$22°$C and will sit in an incubator (air heating) set to $35°$C. I need an estimate on how long it will take these fluids to reach at least $34°$C in the air bath incubator.
I tried to figure this out on my own and ran across the formula $A/t=KA(t_h-t_c)/d$. But solving it is a different ball game. I don't know how to figure out what each letter means to solve this puzzle.
Are there other variables or equations I need to figure this out?