Is it reasonable to have a hair belly?This solid heat conducting problem is worth exploring

The following article comes from WeChat public account: China Science and Technology Press, author CSPBOOKS

Picture source: Qian Tuwang.com

Hardcore analysis, is the saying of Mao's belly?

The process of cooking under the woolen belly can be understood as a solid heating problem. The hair belly in the hot pot restaurant is usually cut into thin slices. If the hairy belly is put into a boiling pot, the heating on both sides is even, so we can make some simple assumptions:

Set the temperature of the hot pot to 100 ° C; the cross -section of the hair belly is a tablet shape with thickness 2:

The process of heating hair can be divided into two parts. The first part is the heating of the surface of the wool belly and the boiling soup in the pot, and the second part is the heat conduction inside the hair belly. Since the whole piece of hair belly is put into the pot, the process of thermal conductivity is symmetrical. We only need to take half to analyze it.

To make the result more intuitive, you can make a simple image. The horizontal coordinate represents the distance from the surface of the hair belly, and the vertical coordinate represents the temperature.

When heating, the temperature near the surface of the hair belly will rise rapidly, and the rest still maintains the original temperature T0, as shown in the blue curve HB in the figure. Over time, the range of temperature rising will continue to expand. After a period of time, the temperature of the inner layer of the hair belly will gradually be affected, and the range of the temperature rising will continue to expand. ) The curve shown.

From the perspective of food safety, when the ingredients are heated to above 90 ° C, consumption is safe. The HG curve is the curve of the temperature distribution of the entire hair belly when the hair belly is finally removed.

In summary: The farther the surface is, the slower the temperature. So just look at when the center of the hairy belly is cooked.

As we all know, temperature differences can cause heat transfer. It can be seen intuitively in the image that at the beginning, the temperature difference between the center of the hairy belly and the surface is very large, so the heat transfer will be obvious. Over time, the temperature difference between the center of the hair belly and the nearby will become smaller and smaller, so the heat transfer effect will gradually weaken, and the temperature rising speed will be attenuated.

So what exactly does the temperature of the center of the hair belly, the speed of the temperature rising, and the attenuation of the attenuation? We can simply calculate the process of heating of hair belly:

Introduce the remaining temperature

The above fourth forms are turned into

Using separation variable method, you can get an analysis of the infinite outline temperature:

The root of the transcendent equation below:

The parameters substituted into the hairy belly use the approximate fit formula method and combine the temperature of the temperature in the center of the unlimited large tablet, the curve of the infinite large tablet, and the Q/Q0 curve of the infinite large tablet.

Instead of temperature analysis and explanation expression:

Finally, the image is:

According to the calculation results, it can be found that the time required for the cooked wool to cook is about 15 seconds. From seven and eight, it is 15, so from a physical point of view. This approach is really right!

This article is authorized to reprint from WeChat public account: China Science and Technology Press Author: CSPBOOKS

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Reprinted content only represents the author's point of view

It does not represent the high energy office of the Chinese Academy of Sciences

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Edit: __ chuang__

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