Thermal entry length
The thermal input length is used to define the boundary between the developed(fully) heat flow and the heat flow i.e undeveloped in a /cooling/heating pipe flow.
Overview:
Fully developed heat flow in a pipe can be considered in the following situation. If the wall of the pipe is constantly heated or cooled so that the heat transfer from the wall to the stream through contact has a fixed value, then the extreme temperature of the stream rises steadily at a set rate. flow-driven.
For example, a pipe can be completely covered with an electric heating pad with the introduction of the flux after discharging uniform heat flux from the pad. At a distance from the inlet of the stream, a fully developed heat flow is reached when the heat transfer coefficient of the stream becomes stable and the temperature profile has the same shape next to the flow. [1] This distance is defined as the thermal induction length, which is important for engineers to design efficient heat transfer processes.
Quantitative measurement:
Metaphorically, if xa is chosen as the axis parallel to the pipe and x = 0 is chosen as the starting point of the pipe flow, the thermal entry length is defined as the distance (x> 0) a is required for the associated Nusselt Nu number. with the flow of the pipe decreasing within 5% of its value for a fully developed heat flow [1].
Depending on different flow conditions (laminar, turbulent, entry shapes, etc.), the Nusselt number has different dependencies on the Reynolds number, Prandtl number, and flow resistance feature.
Simple setting:
A simple example is a laminar flow that is already hydrodynamically developed at x = 0, and a stable and constant pipe wall temperature is maintained. In this case, the thermal induction length can be measured by a simple equation written as:
(Leh (5%)) / D = 0.033 ReDPr [1]
where D is the pipe diameter, ReD is the Reynolds number and Pr is the Prandtl number.
Since the Reynolds number is constant for a fully hydrodynamically developed current (where the velocity of the current does not change), the above equation shows that the length of the thermal inlet is proportional to the Prandtl number [1], which is defined as the ratio of movement. dispersion rate to the thermal dissipation rate of a liquid. That is, a low Pr material, with its thermal dissipation rate closer to its momentum dissipation rate, can achieve a fully developed heat flow at a shorter speed compared to a high Pr material in this situation.
Complex situation:
In a more complex situation (turbulent flow, rectangular entrance, open-ended entrance, etc.), there is rarely an easy way to work out the entire thermal entry. If the laminar flow, i.e. Reynolds number is less than or equal to 2100 to 2300, the thermal induction length can be within 5 diameters for high Pr and low Pr materials with no major disturbances or eddies [1]. For gases and water at higher temperatures, the Prandtl number is close to 1 and the length of the thermal inlet can be between 15 and 40 diameters [1]. Overall, determining the length of the thermal inlet can be difficult and requires an understanding of the heat transfer fluids and fluidity. A list of various calculations and tables can be found in several reading sources.
Length of entry (dynamic dynamics):
In mobile dynamics, the inlet length is the speed at which a current travels after it enters a pipe before the current reaches full development. [1] Length of inlet refers to the length of the inlet section, the area that follows the entrance of the pipe where impacts from the inner wall of the pipe spread into the inlet. -streaming as an expanding boundary level. Where flow characteristics do not change with greater speed across the pipe. There are many different entry lengths to account for a number of streaming situations. Length of thermal input describes the formation of a temperature image. [2] It may be necessary to sense the length of an entry for the effective positioning of an instrument, such as water flow meters.
Hydrodynamic entry length:
The hydrodynamic entry area refers to the area of a pipe where liquid enters a pipe improving the image of distance as a result of slow forces moving from the inner wall of a pipe. [1] This area is characterized by the non-uniform flow. [1] The liquid enters a pipe at an equal speed, then liquid particles in the layer in contact with the pipe surface come to a complete stop due to non-slip positioning. As a result of slow forces within the stream, the layer in contact with the pipe surface resists the movement of adjacent layers and gradually pulls adjacent layers of liquid down. , creating a distance image. [4] To maintain cosmetic conservation, the velocity of the layers in the center of the pipe increases the speed to compensate for the reduced distance of the streams near the surface of the pipe. This improves the gradient of the distance across the cross-section of the pipe. [5]
Boundary cover:
The layer in which the shear forces are slow is called the boundary layer. [6] This level of limitation is a hypothetical concept. It divides the flow in a pipe into two sections: [6]
1. Boundary cover section: The region with slow impacts and large speed changes. [6]
2. The irrotational flow area (heart): The region in which there are slow effects and very small speed changes, also called inviscid heart. [2]
Moving in the direction of flow and eventually reaches the center of the pipe and fills its whole pipe. This area from the inlet of the pipe to the point where the end-stage covers the entire pipe is called the hydrodynamic inlet area and the length of the pipe in this area is called the hydrodynamic inlet length. In this region, the image of distance is developing and so the hydrodynamically evolving current is called the flow. After this division, the image of the distance is fully developed and remains unchanged. This region is called the fully developed hydrodynamic. However, this is not the fully developed flow current until the normal temperature profile becomes stable. [6]
In the case of laminar flow, the speed profile is in the fully developed parabolic region but in the case of turbulent flow, it gets a little flatter due to a dynamic combination in a radial direction and eddy movement.
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