Question

The fins attached to a surface are determined to have an effectiveness of \(0.9\). Do you think the rate of heat transfer from the surface has increased or decreased as a result of the addition of these fins?

Short answer

Answer: The rate of heat transfer from the surface has decreased due to the addition of fins with an effectiveness of 0.9.

Step-by-step solution

Define effectiveness

Effectiveness (\(\epsilon\)) is a dimensionless quantity that compares the heat transfer rate between a finned surface and an unfinned surface. An effectiveness value of 1 means the heat transfer rate is the same with or without the fins, while a value greater than 1 indicates improved heat transfer. If the effectiveness is less than 1, the fins reduce heat transfer.

Compare the given effectiveness value with 1

In this exercise, the effectiveness of the fins attached to the surface is given as \(\epsilon = 0.9\). Our task is to determine whether this value indicates an increase or decrease in the rate of heat transfer.

Determine the effect of fins on heat transfer rate

Since the effectiveness value is \(\epsilon = 0.9\), which is less than 1, we can conclude that the rate of heat transfer from the surface has decreased due to the addition of these fins.

Key concepts

Heat Transfer Enhancement

Understanding heat transfer enhancement is crucial for developing more efficient thermal systems. In thermal engineering, fins are widely used to increase the surface area available for heat transfer, thus potentially improving the overall heat dissipation from a surface.

Consider a finned surface, for which the term 'effectiveness' quantifies the improvement in heat transfer when compared to an unfinned surface. The higher the effectiveness, the more pronounced the heat transfer enhancement. However, in our exercise, the effectiveness is given as 0.9, meaning that instead of enhancing, it implies a decrease in heat transfer, which might seem counterintuitive. This situation could arise due to various practical factors such as additional thermal resistance introduced by the fins or poor fin design.

To really enhance heat transfer, fins must be designed to provide a net positive effect. This requires careful consideration of material, geometry, and placement so that the added conduction and convection processes facilitated by the fins outweigh any potential disadvantages.

Thermal Engineering Education

In thermal engineering education, it's essential to convey the real-world complexities of heat transfer processes to students. Through solving textbook exercises, such as the one concerning fin effectiveness, students gain insight into the subtleties of thermal systems and learn how to apply theoretical concepts in practical scenarios.

Educators should emphasize that not all thermal solutions, such as the addition of fins, will automatically enhance heat transfer. The analysis of fin effectiveness, involving a comparison of actual performance against the ideal scenario, is a key learning outcome. Students should also be made aware of the importance of conducting experiments and simulations in conjunction with theoretical studies to fully grasp the performance of thermal systems.

Dimensionless Quantities in Heat Transfer

Dimensionless quantities play a vital role in the analysis of heat transfer problems. They allow engineers and students to draw comparisons between different thermal systems without the need for specific unit measurements. Effectiveness, as highlighted in the exercise, is one such quantity.

Effectiveness highlights the ratio of the actual heat transfer to the maximum possible heat transfer. It is deeply tied to other dimensionless numbers, such as the Nusselt number, which relates the convective to the conductive heat transfer at a surface, or the Biot number, which compares the internal resistance within a body to the external resistance to heat transfer.

By understanding these quantities, students can better grasp the principles of scale similarity and nondimensional analysis, which are indispensable in thermal engineering for designing experiments, comparing thermal systems, and developing new heat transfer solutions.