Time to achieve specific heat transfer for fluid flowing in a pipe

In summary: P.H. "A Practical Solution of the Navier-Stokes Equation for the Flow of Fluids in Pipes." Journal of Engineering Mathematics 44, no. 1 (2000): 38-53.Assuming that the wall temperature is fixed, the heat equation can be used to find the temperature at any point within the pipe. In order to solve for the temperature at the entrance of the pipe, the equation must be solved in two dimensions using the convective heat resistance term in the radial coordinate system. Once the temperature at the entrance of the pipe is known, the temperature of the fluid can be calculated by integrating the heat equation along the length of the pipe.
  • #1
MoeHij
1
0
I am currently in the process of designing a section of pipe in which a fluid will flow within, and would like to determine the specific heat transfer which may occur once the fluid enters the pipe, until it exits. The fluid will be flowing at a constant velocity "V" at a Temperature "T1" at the entrance of a pipe with length "L".

In other terms, I want to find the length of pipe it would take for a fluid to be heated to a certain temperature when it is being passed through a pipe which is placed in specified external conditions.
I think this must be done by deriving a differential equation which includes convective and conductive heat resistance terms both in radial and axial coordinate systems. The differential equation must then be solved in order to calulate the time the fluid must spend in the pipe, and from there calculate the length of pipe required using the selecting fluid flow velocity in the pipe.
 
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  • #3
  • #4
Hi MoeHij. Welcome to physics forums.

See Bird, Stewart, and Lightfoot, Transport Phenomena. They show how to set up and solve such problems for laminar flow, with and without viscous heating being significant. They also show how to handle the problem of heat transfer in a pipe when the flow is turbulent (high Reynolds number).

Chet
 
  • #5


I would approach this problem by first gathering all relevant information about the fluid and the pipe, such as the fluid properties, pipe dimensions, and external conditions. Then, I would use the principles of heat transfer to develop a mathematical model of the system, taking into account convective and conductive heat resistance terms in both the radial and axial directions.

Next, I would use this model to derive a differential equation that describes the rate of change of temperature of the fluid as it flows through the pipe. This equation would take into account the fluid velocity, initial temperature, and the properties of the fluid and the pipe.

Once the differential equation is derived, I would solve it using appropriate mathematical techniques, such as separation of variables or numerical methods, to determine the time required for the fluid to reach a desired temperature. From there, I could calculate the length of pipe required by using the fluid flow velocity and the time calculated.

It is important to note that this calculation would provide an estimate and may not account for all factors that could affect the heat transfer, such as turbulence or boundary conditions. Therefore, it would be necessary to conduct experiments or use more sophisticated models to validate the results.

In conclusion, determining the time required for a fluid to reach a specific temperature in a pipe would involve developing a mathematical model, deriving a differential equation, and solving it to obtain the necessary parameters. I would also consider conducting further research and experiments to validate the results and account for any potential uncertainties.
 

1. What is specific heat transfer for fluid flowing in a pipe?

Specific heat transfer is the amount of heat energy that is transferred per unit mass of fluid as it flows through a pipe. It is a measure of how efficiently the fluid can absorb or release heat.

2. How is specific heat transfer calculated for a fluid in a pipe?

The specific heat transfer for a fluid in a pipe can be calculated by dividing the heat transfer rate by the mass flow rate of the fluid. This will give the specific heat transfer per unit mass of fluid.

3. How does the flow rate affect the time to achieve specific heat transfer?

The flow rate of the fluid in the pipe is directly related to the time it takes to achieve specific heat transfer. Higher flow rates will result in faster heat transfer, while lower flow rates will require more time to achieve the desired heat transfer.

4. What factors can affect the time to achieve specific heat transfer for a fluid in a pipe?

Some factors that can affect the time to achieve specific heat transfer for a fluid in a pipe include the flow rate, pipe diameter, fluid properties (such as viscosity and density), and the type of heat transfer (convection, conduction, or radiation).

5. How can specific heat transfer be increased for a fluid in a pipe?

Specific heat transfer can be increased by increasing the flow rate, using a larger diameter pipe, and choosing a fluid with a higher specific heat capacity. Additionally, using heat transfer-enhancing techniques such as fins or turbulators can also increase the specific heat transfer in a pipe.

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