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## Main Question or Discussion Point

Hi,

I´m looking for a model or formula to calculate the time that

is needed to cool under natural conditions (not forced air flow, water, etc.) a pile of steel billets produced at a melt shop. The process is as follows: steel billets with square

cross section of 140 mm x 140 mm and 12.7 m. long are produced via the casting of liquid steel. These billets are placed separated one from the other on a cooling bed, until they reach aprox. 450 °C. Then they are stored in a yard, where they are

placed side by side. Here they sit tightly close one to another; each billet touches the next one along the face that has a horizontal measure of 12.7 m. When the yard has 20 contiguous billets (we can call this a bed of 20 billets), then the next

billets are piled on top of this bed, until another bed of 20 billets is formed. The process continues in such way, until 25 beds are completed. So, we have a pile 2.8 m wide, 3.5 m. high

& 12.7 m. depth.

I´m faced with this problem: these steel billets will be shipped later to another industrial plant, that is far away. So flat bed trailers will be used to transport the billets. The platforms of the trailers are made from steel and wood; so the billets will

sit on top of wood, and we have to be careful in allowing the billets to cool down to a temperature of 150 °C or less, in order to rest assured that the wood won´t catch fire.

I have observed that it´s not the same to ship billets from the top beds; these ones have cooled to a lower temperature. Suppose that we want to ship the hole pile, truck after truck, with no loading delays. We will see that after finishing with the uppermost beds, the next ones will be hotter, due to the temperature gradient that exists from the center of the pile to each of the sides.

In short, about the adding and removing of billets: we can assume at this point that once they are piled, they will remain were they are, until the time for shipment comes. Then, let´s assume that once we begin removing billets from top, and continuing toward the bottom of the pile, the time for this operations is equal to zero, so that there is no additional complication for the theoretical model. In other words, what I would like is this:

Input data: initial temperature (eg. 450 °C)

Size of solid body: as described above

Based on this, there is an amount of energy stored in the form of heat, and a temperature gradient begins to develop. I would like the model to predict which is the innermost temperature of the body (eg. center) after 24, 36, ...etc. hours.

So, I´m looking for a model or formula to predict the temperature of the center of a billet depending on the bed (lowest one, second lowest, etc.), the time that has

passed since the pile was formed and the initial temperature.

Thank you.

I´m looking for a model or formula to calculate the time that

is needed to cool under natural conditions (not forced air flow, water, etc.) a pile of steel billets produced at a melt shop. The process is as follows: steel billets with square

cross section of 140 mm x 140 mm and 12.7 m. long are produced via the casting of liquid steel. These billets are placed separated one from the other on a cooling bed, until they reach aprox. 450 °C. Then they are stored in a yard, where they are

placed side by side. Here they sit tightly close one to another; each billet touches the next one along the face that has a horizontal measure of 12.7 m. When the yard has 20 contiguous billets (we can call this a bed of 20 billets), then the next

billets are piled on top of this bed, until another bed of 20 billets is formed. The process continues in such way, until 25 beds are completed. So, we have a pile 2.8 m wide, 3.5 m. high

& 12.7 m. depth.

I´m faced with this problem: these steel billets will be shipped later to another industrial plant, that is far away. So flat bed trailers will be used to transport the billets. The platforms of the trailers are made from steel and wood; so the billets will

sit on top of wood, and we have to be careful in allowing the billets to cool down to a temperature of 150 °C or less, in order to rest assured that the wood won´t catch fire.

I have observed that it´s not the same to ship billets from the top beds; these ones have cooled to a lower temperature. Suppose that we want to ship the hole pile, truck after truck, with no loading delays. We will see that after finishing with the uppermost beds, the next ones will be hotter, due to the temperature gradient that exists from the center of the pile to each of the sides.

In short, about the adding and removing of billets: we can assume at this point that once they are piled, they will remain were they are, until the time for shipment comes. Then, let´s assume that once we begin removing billets from top, and continuing toward the bottom of the pile, the time for this operations is equal to zero, so that there is no additional complication for the theoretical model. In other words, what I would like is this:

Input data: initial temperature (eg. 450 °C)

Size of solid body: as described above

Based on this, there is an amount of energy stored in the form of heat, and a temperature gradient begins to develop. I would like the model to predict which is the innermost temperature of the body (eg. center) after 24, 36, ...etc. hours.

So, I´m looking for a model or formula to predict the temperature of the center of a billet depending on the bed (lowest one, second lowest, etc.), the time that has

passed since the pile was formed and the initial temperature.

Thank you.