Heat Transfer in Fluid Flow

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This Demonstration illustrates the basics of heat transfer in the internal flow of a fluid. The radial temperature profile, mean temperature, surface temperature, and Nusselt number behavior are displayed for a thin-walled pipe with a selection of two different surface conditions: constant temperature or constant heat flux. You can vary the area ratio (surface area over cross sectional area), the Reynolds number, and the Prandtl number in order to observe the effects on the system. In addition, the dimensionless axial position slider lets you see the development of the thermal boundary layer profile along the length of the pipe.

Contributed by: Adam Cho and Brian Vick (June 2014)
Open content licensed under CC BY-NC-SA



The first plot displays a cross section of the pipe and illustrates the dimensionless thermal boundary layer and the temperature profile of the fluid at a given point. The axis represents the diameter of the pipe, written in the dimensionless form and ranging from to . As you vary the axial position, the temperature profile develops along the thermal boundary layer until the flow is fully developed.

The second plot shows the dimensionless mean and surface temperatures.

Lastly, the third plot shows the local and average Nusselt numbers divided by the fully developed Nusselt number. For the constant heat flux condition, only the local Nusselt number is plotted.

Explore the effects of varying the three dimensionless parameters. As the snapshots illustrate, different combinations of the surface conditions and parameters can result in a wide array of results.

A list of the variable definitions is given below.


- axial position,

- radial position,

Inlet Conditions

- inlet temperature, (°C)

- mean velocity, (m/s)

Surface Conditions

- surface temperature, (°C)

- surface heat flux,

Pipe Geometry

- pipe length, (m)

- pipe diameter, (m)

Fluid Properties

- density,

- specific heat,

- kinematic viscosity,

- thermal conductivity,

- thermal diffusivity,

Dimensionless Numbers

- area ratio,

- Reynolds number,

- Prandtl number,

- axial position,

- entry length,

Snapshot 1: Behavior for constant surface temperature and low Reynolds number flow. The thermal entry length is very short and the mean temperature reaches the surface temperature within the length of the pipe. This is an example of a long pipe with slow fluid flow.

Snapshot 2: Behavior for constant surface temperature and smaller area ratio, with a medium value for the Reynolds number. Here, thermal entry length extends beyond the length of the pipe and the mean temperature increases only slightly. This is an example of poor heat transfer into fast fluid flow in a short pipe.

Snapshot 3: Behavior for constant heat flux, with average conditions. Here, after going through an initial development period, the difference between surface temperature and the mean temperature is constant.

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