Hypothetical Scenario (Steel Rod + Heat + Vacuum)

[LKMW]

One end of 1m steel rod of 3cm diameter is welded to the interior wall of a steel container (steel: 310s or 2520). The other end of the steel rod is not in contact with anything. The pressure in the container is below 0.01mpa (vacuum). A heat source of 1100 Degree Celcius is applied externally to the attached point. After two 30 minute intervals (first at 30 minutes, then at 60 minutes), what is the temperature of the hanging end of the steel rod?

---OR (perhaps simplified)---

Steel Rod: 1m length, 3cm diameter

It is placed in a vacuumed environment (no air to conduct away the heat). If one end is heated externally (outside of the vacuum) at 1100 Degree Celcius, what is the temperature of the other end of the rod after a) 30 minutes and b) 1 hour.

 

[Mapes]

Hi LKMW, welcome to PF. Perhaps the simplest way of tackling the problem is to estimate the thermal diffusion time from the equation $t\approx L^2/D$. This will give the approximate time for a temperature change to propagate (i.e., the approximate time until the temperature at the end of the bar is a large fraction of 1100°C). From looking online, it looks like the thermal diffusivity of steel is about 10^-5 m² s^-1, which implies a time of about 1700 minutes. Since we'd expect a continuous increase, approximately linear, over this time, our first estimate is a temperature increase on the order of 10°C at the end of the rod after 30-60 minutes .

A crude approximation, but at least it tells us whether the answer is closer to room temperature or 1100°C (I'd go with the first). A better analysis might use finite element analysis to look at the conductive heat transfer through the rod, and a still better analysis would incorporate radiative transfer from the rod to and from the surroundings.

 

[Mene]

I would first analyze the materials involved in this scenario. Steel, specifically 310s or 2520, is known for its high strength and resistance to heat and corrosion. The 1m steel rod with a 3cm diameter is a relatively large and sturdy object that can withstand high temperatures. The vacuum environment also plays a crucial role as it eliminates the transfer of heat through convection, making it an ideal condition for testing the heat conductivity of the steel rod.

In this scenario, the heat source of 1100 Degree Celcius is applied externally to the attached point of the steel rod. This means that the heat is only being applied to one specific area of the rod, and the rest of the rod is not in direct contact with the heat source. This will result in a temperature gradient along the length of the rod, with the attached end being significantly hotter than the hanging end.

After 30 minutes, the hanging end of the steel rod will have absorbed some heat from the attached end through conduction. However, since there is no air to conduct away the heat, the temperature at the hanging end will still be significantly lower than the attached end. The exact temperature will depend on the rate of heat transfer and the thermal conductivity of the steel rod.

After 60 minutes, the temperature at the hanging end will continue to increase, but it will not reach the same temperature as the attached end. This is because the heat source is still only applied to one end of the rod, and there is still no air to dissipate the heat. The temperature at the hanging end will eventually reach a steady state, where the rate of heat transfer from the attached end is equal to the rate of heat dissipation through convection to the surrounding vacuum environment.

In conclusion, the temperature of the hanging end of the steel rod after 30 minutes and 60 minutes will depend on various factors such as the thermal conductivity of the steel rod, the rate of heat transfer, and the size and temperature of the heat source. However, it is safe to say that the hanging end will not reach the same temperature as the attached end due to the unique conditions of this scenario. Further experimentation and analysis would be needed to determine the exact temperature of the hanging end at specific time intervals.