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Chapter 6: Problem 37

What is turbulent thermal conductivity? What is it caused by?

Short Answer

Expert verified
Answer: Turbulent thermal conductivity is the enhancement in heat conduction due to the presence of turbulence in the fluid flow. It is not an intrinsic property of the material, but rather depends on the characteristics of the turbulent flow, such as flow velocity and turbulence intensity. It is caused by the random and chaotic motion of fluid particles in a turbulent flow, which leads to mixing of fluid layers, increased contact area between the heated surface and fluid particles, and promotes further mixing, ultimately resulting in increased heat transfer rates.

Step by step solution

01

Define thermal conductivity

Thermal conductivity is a property of a material that describes its ability to conduct heat. It is denoted by the symbol \(k\) and depends on the temperature and composition of the material. In general, the rate at which heat is conducted through a material depends on the temperature gradient (the difference in temperature between the two ends of the material) and the thermal conductivity of the material.
02

Define turbulent flow

Turbulent flow is a type of fluid flow in which the fluid particles move in a random and chaotic manner, resulting in a highly disordered motion. Turbulent flow differs from laminar flow, which is characterized by a smooth, orderly motion of fluid particles. Turbulence can be developed in a fluid due to various factors, such as high flow velocities, rough surfaces, and abrupt changes in flow direction.
03

Turbulence and heat transfer

When a fluid flows over a heated surface, heat is transferred from the surface to the fluid through conduction. The rate of heat transfer can be greatly influenced by the nature of the flow. In laminar flow, heat transfer occurs mainly through conduction, as the fluid particles move in layers along the heated surface. On the other hand, in turbulent flow, the chaotic and random motion of fluid particles enhances heat transfer by mixing the fluid and increasing the contact between the heated surface and the fluid particles. As a result, turbulence can significantly increase the rate of heat transfer in a fluid.
04

Define turbulent thermal conductivity

Turbulent thermal conductivity is the enhancement in heat conduction due to the presence of turbulence in the fluid flow. It is denoted by the symbol \(k_t\) and is used to account for the increased rate of heat transfer in turbulent flows. Turbulent thermal conductivity is not an intrinsic property of the material, but rather depends on the characteristics of the turbulent flow, such as the flow velocity and turbulence intensity.
05

Causes of turbulent thermal conductivity

Turbulent thermal conductivity is caused by the random and chaotic motion of fluid particles in a turbulent flow. This disordered motion leads to the mixing of fluid layers and increases the effective contact area between the heated surface and the fluid particles. In addition, turbulence can also cause fluid particles to break away from the heated surface, thus promoting further mixing and increasing the rate of heat transfer. Overall, turbulent thermal conductivity is driven by the enhanced heat transfer mechanisms associated with the chaotic motion of fluid particles in a turbulent flow.

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Most popular questions from this chapter

What is the physical significance of the Reynolds number? How is it defined for external flow over a plate of length \(L\) ?

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Will a thermal boundary layer develop in flow over a surface even if both the fluid and the surface are at the same temperature?

In an effort to prevent the formation of ice on the surface of a wing, electrical heaters are embedded inside the wing. With a characteristic length of \(2.5 \mathrm{~m}\), the wing has a friction coefficient of \(0.001\). If the wing is moving at a speed of \(200 \mathrm{~m} / \mathrm{s}\) through air at 1 atm and \(-20^{\circ} \mathrm{C}\), determine the heat flux necessary to keep the wing surface above \(0^{\circ} \mathrm{C}\). Evaluate fluid properties at \(-10^{\circ} \mathrm{C}\).

For laminar flow over a flat plate the local heat transfer coefficient varies as \(h_{x}=C x^{-0.5}\), where \(x\) is measured from the leading edge of the plate and \(C\) is a constant. Determine the ratio of the average convection heat transfer coefficient over the entire plate of length \(L\) to the local convection heat transfer coefficient at the end of the plate \((x=L)\).
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