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Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering PDF Download

Convective Heat Transfer Examples

1. Melt Spinning of Polymer fibers

2. Heat transfer in a Condenser

3. Temperature control of a Re-entry vehicle

Fiber spinning

The fiber spinning process presents a unique engineering problem, primarily due to the effects of shape variations, heat and possibly the viscoelastic behavior of the materials (polymers for example) typically used. This becomes evident when the design of the spinneret geometry is needed to produce a specified fiber size and shape. Determining the proper die geometry given the desired final fiber shape is further complicated by the heat and viscoelastic effects. In addition, since the fiber is pulled from the spinneret, the final dimensions of the fiber are difficult to determine. The effects of viscous heating and air cooling must be monitored to ensure that the material does not degrade because of extreme local temperatures, often difficult to measure because of the small size. The stresses and deformation of the material must also be predicted to avoid the fiber from breaking. All these effects complicate the design of the fiber spinning process.

Definition of a Heat Transfer Coefficient

For heat transfer in conducting systems, we have seen that we can express the heat flux across a surface S as

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

We have used a similar representation to develop detailed descriptions of mass and transfer in a number of situations where the physics or chemistry is well-understood, e.g., permeation through a membrane, heat transfer to a sphere. We showed that we could get a description of the macroscopic transfer across an interface by the use of a Heat Transfer Coefficient.

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

We do nor always have such a good model or understanding. The are other equivalent physical situations, e.g., turbulent flow in a pipe. There we use a measure of the frictional loss in the pipe as a “momentum transfer coefficient”. The dimensionless form was the Friction Factor. The dimensionless mass transfer coefficient is the Nusselt Number.

Nu = hL/k

Methods of Analysis

1. Detailed Solution of the Conservation Laws

2. Approximate Analysis

3. Dimensional Analysis

4. Empirical Correlation of Data

We have seen several examples of Detailed Solution and we have done some Approximate Analysis, e.g., mass transfer to or from a flowing film, heat transfer from a solid sphere. What we did was to transform the exact problem into a simpler more solvable one using mathematical analysis. What we do in the next few lectures is examine in greater detail the last three methods as tools to analyze heat transfer and to design processes.

Approximate Analysis and Film Theory

Film Theory is the simplest and oldest approach in the use of mass transfer coefficients and in their prediction. The Theory is attributed to Nernst.

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Examine the neighborhood of the phase boundary. We assume that the flow field consists of two regions, a uniform region in the bulk of the fluid far from the surface and a region in the vicinity of the boundary where viscosity dominates (since there is no slip at the boundary).

Film Model

The film model presumes that the velocity field is linearized in some sense near the boundary so that

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

This means that the film has a thickness

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

But recall the definition of the friction factor

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

If we introduce that notion into our analysis

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Not surprisingly we can relate the fractional layer thickness to the Reynolds number

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Dimensionless Heat Transfer Coefficient

We defined the Heat Transfer Coefficient, h , by

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

so that the Nusselt number is given as

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering 

Observe that

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

so that

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Then we observe a relation rather like the ones we calculated in our more detailed models.

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

The Chilton-Colburn Analogy

In the 1930s, based on the Nernst Film Theory, two duPont researchers proposed an analogy between heat transfer (and we have seen, mass transfer) and momentum transfer. They defined a dimensionless number termed a j-factor, jH.

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

For mass transfer, the relation was

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

Simple film theory, then, predicts that

Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

or simplified  Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering

The document Concepts of Convective Heat Transfer | Heat Transfer - Mechanical Engineering is a part of the Mechanical Engineering Course Heat Transfer.
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FAQs on Concepts of Convective Heat Transfer - Heat Transfer - Mechanical Engineering

1. What is convective heat transfer in chemical engineering?
Ans. Convective heat transfer in chemical engineering refers to the process of transferring heat through the movement of fluids, such as liquids or gases. It involves the transfer of thermal energy from a hotter surface to a cooler surface, facilitated by the fluid flow. This process is crucial in various industrial applications, such as heat exchangers, cooling towers, and chemical reactors.
2. How is convective heat transfer different from conductive heat transfer?
Ans. Convective heat transfer and conductive heat transfer are two different mechanisms of heat transfer. While conductive heat transfer occurs within a solid or stationary medium, convective heat transfer involves the transfer of heat through the motion of fluids. In conductive heat transfer, heat is transferred through direct contact and molecular interactions, whereas in convective heat transfer, heat is transferred through the bulk movement of fluid particles.
3. What are the different types of convective heat transfer?
Ans. There are two main types of convective heat transfer: natural convection and forced convection. Natural convection occurs when the fluid motion is induced solely by density differences caused by temperature variations. Forced convection, on the other hand, involves the use of external devices, such as fans or pumps, to create fluid motion and enhance heat transfer.
4. How is convective heat transfer coefficient determined?
Ans. The convective heat transfer coefficient is a measure of the effectiveness of convective heat transfer. It represents the rate of heat transfer per unit area per unit temperature difference between the fluid and the surface. The convective heat transfer coefficient can be determined experimentally by conducting heat transfer tests or through theoretical calculations using empirical correlations based on the properties of the fluid and the geometry of the system.
5. What factors affect convective heat transfer?
Ans. Several factors influence convective heat transfer, including the velocity of the fluid, the temperature difference between the fluid and the surface, the physical properties of the fluid (such as viscosity and thermal conductivity), and the geometry of the system. Additionally, the presence of fouling or scaling on the heat transfer surface, turbulence in the fluid flow, and the type of fluid (liquid or gas) also impact convective heat transfer.
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