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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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermal Conductivity
Thermal conductivity is a key property that helps us understand how heat flows through different materials. Imagine you have a metal spoon in a hot pot of soup. The handle of the spoon gets hot because heat travels through the metal. This ability to transfer heat is called thermal conductivity.
  • Denoted by the symbol \( k \)
  • Depends on factors like temperature and the material鈥檚 composition
  • Higher thermal conductivity means better heat transfer through the material
When you touch one end of an iron rod with a flame, heat travels to the other end, even without the ends touching. That鈥檚 thermal conductivity at play.
Turbulent Flow
Turbulent flow is quite different from smooth, orderly fluid motion. Imagine the chaos of a river rapid compared to the calm flow of a small stream. In turbulent flow, the fluid motion is random and chaotic.
  • Characterized by random movement of fluid particles
  • Contrast with laminar flow, where fluid moves in orderly layers
  • Caused by high velocities, rough surfaces, or sudden changes in flow direction
Turbulent flow is like when you're stirring your soup aggressively. Everything mixed up smoothly and quickly. This chaos enhances certain processes like mixing and heat transfer.
Heat Transfer
Heat transfer happens when heat moves from one body to another, and it occurs mainly in three ways: conduction, convection, and radiation. If you put your hand near a fire, you feel the heat through radiation. Holding the hot spoon is conduction, and stirring soup distributes heat through convection.
  • Conduction occurs with direct contact
  • Convection involves the movement of fluids
  • Radiation happens through electromagnetic waves
In fluid dynamics, when a fluid flows over a heated surface, the mode of heat transfer can change the rate at which heat is carried away or absorbed. For turbulent flow, heat transfer by conduction is enhanced, making the process faster and more efficient.
Fluid Dynamics
Fluid dynamics is the science of how fluids (liquids and gases) move and behave. Understanding these movements helps in designing things like airplanes, cars, or even understanding weather patterns.
  • Focuses on forces and the resulting motion in fluids
  • Divided into two main types: laminar and turbulent flow
  • Important in engineering applications and natural phenomena
In fluid dynamics, several principles like Newton's laws, pressure, and viscosity play a role in explaining how and why fluids move in certain ways. Turbulent flows are particularly significant because they enhance processes like mixing and heat transfer, which are crucial in many engineering systems.

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Most popular questions from this chapter

For steady two-dimensional flow over an isothermal flat plate in the \(x\)-direction, express the boundary conditions for the velocity components \(u\) and \(v\), and the temperature \(T\) at the plate surface and at the edge of the boundary layer.

In turbulent flow, one can estimate the Nusselt number using the analogy between heat and momentum transfer (Colburn analogy). This analogy relates the Nusselt number to the coefficient of friction, \(C_{f}\), as (a) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (b) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\) (c) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\)

Metal plates are being cooled with air blowing in parallel over each plate. The average friction coefficient over each plate is given as \(C_{f}=1.33\left(\operatorname{Re}_{L}{ }^{-0.5}\right.\) for \(\operatorname{Re}_{L}<5 \times 10^{5}\). Each metal plate length parallel to the air flow is \(1 \mathrm{~m}\). Determine the average convection heat transfer coefficient for the plate, if the air velocity is \(5 \mathrm{~m} / \mathrm{s}\). Evaluate the air properties at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Consider a flow over a surface with the velocity and temperature profiles given as $$ \begin{aligned} &u(y)=C_{1}\left(y+y^{2}-y^{3}\right) \\ &T(y)=C_{2}-e^{-2 C_{2} y} \end{aligned} $$ where the coefficients \(C_{1}\) and \(C_{2}\) are constants. Determine the expressions for the friction coefficient \(\left(C_{f}\right)\) and the convection heat transfer coefficient \((h)\).

How does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher?
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