Boundary Equation for Water Cooled Cylinder

  • Thread starter sangy
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In summary, the problem being discussed is a concentric cylinder with water flowing through the inner cylinder and gas with a high temperature in the outer cylinder. The boundary equation for the outermost boundary of the cylinder would be heat convection at r=r_o. There is no r=0 boundary condition for a cylinder. The solution involves a Bessel function, where one of the functions goes to infinity at zero and can be cancelled out. It is important to specify the type of problem being solved in order to provide a more detailed answer.
  • #1
sangy
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There is a cylinder which is water cooled from outside.I want to know what would be the boundary equation for water cooled boundary.
 
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  • #2
How about r = const?

You really need to say what sort of problem you are trying to solve here if you want anything more than this.
 
  • #3


Sir,
Ya its a concentric cylinder.
Last cylinder has water following through it.
the inner cylinder has gas in it, which has high temperature. The water is flowed through this cylinder boundary as it should not melt the cylinder (Quartz tube).
Please let me know the boundary condition for outermost boundary of the cylinder.
 
  • #4
If the outer wall is being cooled, then that's the boundary condition, heat convection at r=r_o. If its a cylinder, then there is no r=0 boundary condition. The solution is a Bessel function which at zero you can simply cancel one of them out...man I worded that poorly.

At zero, you have (IIRC) something like T(r) = I(r) + J(r). I believe one of those functions goes to infinity at zero, so you can cancel it out.
 

1. What is the Boundary Equation for Water Cooled Cylinder?

The Boundary Equation for Water Cooled Cylinder is a mathematical formula that describes the thermal boundary conditions of a cylinder being cooled by water. It takes into account factors such as the cylinder's dimensions, material properties, and the temperature and flow rate of the water to determine the rate of heat transfer and temperature distribution within the cylinder.

2. How is the Boundary Equation for Water Cooled Cylinder derived?

The Boundary Equation for Water Cooled Cylinder is derived from the general heat transfer equation, which relates the rate of heat transfer to the temperature gradient and thermal properties of the materials involved. By applying this equation to the specific case of a cylinder being cooled by water, and considering the boundary conditions at the surface of the cylinder, the Boundary Equation for Water Cooled Cylinder is obtained.

3. What are the assumptions made in the Boundary Equation for Water Cooled Cylinder?

Some common assumptions made in the Boundary Equation for Water Cooled Cylinder include: steady-state conditions, uniform temperature distribution within the cylinder, constant material properties, and laminar flow of water. However, these assumptions may vary depending on the specific case being studied and can be adjusted to account for different conditions.

4. How is the Boundary Equation for Water Cooled Cylinder used in practical applications?

The Boundary Equation for Water Cooled Cylinder is used in various engineering and scientific applications, such as the design and analysis of cooling systems for engines, turbines, and other heat-generating components. It allows engineers to predict and optimize the cooling performance of a cylinder, and make informed decisions about factors such as material selection, cooling system design, and operating conditions.

5. What are the limitations of the Boundary Equation for Water Cooled Cylinder?

The Boundary Equation for Water Cooled Cylinder is a simplified model that may not accurately represent all real-world scenarios. It assumes ideal conditions and neglects some factors that may affect the heat transfer process, such as radiation, convection from the surrounding air, and non-uniform temperature distribution within the cylinder. Therefore, it should be used with caution and its results should be verified through experiments or more complex simulations.

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