1. Placing/Returning food on a Tanur/Kupach oven; or a Kirah oven fueled with wood whose fire was not covered:[1]

Note: Regarding the logistics behind the Tanur, Kupach, and Kirah oven-See “The Laws of Shehiyah” Chapter 1 Halacha 3.

A Tanur oven: A Tanur which was fueled even with straw or twigs, and even if its coals were swept or covered, which one left food on it in one of the permitted ways explained in the laws of Shehiyah [either the food was half cooked or meat was completely raw before Shabbos] then [nevertheless, in a case that one removed it], it is forbidden to return the pot on Shabbos even if the pot is still in ones hands and he had intention to return it, and even if any further cooking of the food will make it condense in a way that is damaging to the food.

The Kupach  oven; and Kirah oven whose fire is not covered: Similar [to the laws of a Tanur] is also the law for a Kupach which was fueled with olive waste or wood [even if its coals were swept or covered] being that [a Kupach fueled with olive waste or wood] has the same laws as a Kirah which was fueled with olive waste or wood which was not swept or covered, in which case it is forbidden to return a pot onto it on Shabbos in any situation[2].

The reason for why one may not return a pot onto the above ovens in any situation is due: to a Rabbinical decree as, [if one were allowed to do so] he may come to stoke the coals. Now, even though with regards to leaving a pot from before Shabbos [even on a Tanur and Kupach] we are not worried that one will come to stoke the coals in a case that further cooking of the food will make it condense in a way damaging to it, nevertheless here with regards to returning the pot onto these ovens on Shabbos we are more stringent.[3]

Returning pots onto stoves:[4] Those ovens which do not have a hollow inside, but are flat, and their inside and outside are one piece[5], it is permitted to return to them [if their fire is covered, just like by a Kirah oven, which will be explained next].

Placing food next to a Tanur and Kupach oven: See below.

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[1] Admur 253:15

^[2] Meaning even if the to be mentioned conditions of returning a pot to a Kirah are fulfilled.

[3] As perhaps in order to keep the food warm he may come to stoke the coals.

[4] Admur 253:17

^[5] Meaning that it is not an oven in today’s sense which is a hollow box of which one bakes food inside of, but rather is a flat piece of material, of which one cooks food on top of, similar to what we call stoves today.

[6] As this is similar to a Kirah oven which has good fuel which has not been covered, of which the law is that one may never place or return food to it on Shabbos.