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Chapter 9: Problem 116

Square panels \((250 \mathrm{~mm} \times 250 \mathrm{~mm}\) ) with a decorative, highly reflective plastic finish are cured in an oven at \(125^{\circ} \mathrm{C}\) and cooled in quiescent air at \(29^{\circ} \mathrm{C}\). Quality considerations dictate that the panels remain horizontal and that the cooling rate be controlled. To increase productivity in the plant, it is proposed to replace the batch cooling method with a conveyor system having a velocity of \(0.5 \mathrm{~m} / \mathrm{s}\).

Short Answer

Expert verified
In short, to decide whether to replace the batch cooling method with a conveyor system for square panels cured at \(125^{\circ} \mathrm{C}\), we analyzed the given data, understood the cooling process, assessed the impact of the conveyor system, considered factors that need to be addressed, and analyzed the benefits and drawbacks of the conveyor system. After a thorough analysis, a decision can be made, taking into account quality control and improved productivity.

Step by step solution

01

Understand the given information

In this step, let's take a closer look at the provided data. We have: 1. Square panels with dimensions \(250\mathrm{~mm} \times 250\mathrm{~mm}\). 2. The panels are cured in an oven at \(125^{\circ} \mathrm{C}\). 3. The panels are cooled in quiescent air at \(29^{\circ} \mathrm{C}\). 4. Quality requirements mandate that the panels remain horizontal during the cooling process, and the cooling rate must be controlled. 5. Proposed replacement of the batch cooling method with a conveyor system having a velocity of \(0.5 \mathrm{~m} / \mathrm{s}\).
02

Understanding the cooling process

Now that we understand the given information, let's discuss the cooling process. When the panels come out of the oven, they are hot, and they have to cool down to room temperature. In the current situation, the panels are cooled in a batch process in still air (referred to as quiescent air). They are kept in a horizontal position so that the cooling rate can be maintained at a constant and controlled level.
03

Assess the impact of the conveyor system

The proposed change involves replacing the batch method with a conveyor system with a velocity of \(0.5\mathrm{~m/s}\). This would involve moving the panels horizontally at a constant speed of \(0.5\mathrm{~m/s}\) while they cool down. The idea behind this change is to increase productivity and efficiency in the plant by reducing the time spent cooling the panels by having them move continuously.
04

Considerations for the new cooling method

In assessing whether the conveyor system's cooling method will work or not, a few factors must be considered: 1. Does the conveyor system maintain the specified horizontal position of the panels throughout the cooling process? 2. Can the conveyor system maintain the controlled cooling rate that is required? 3. Can the conveyor system deliver an improvement in productivity, considering the potential impact on quality control due to the change in the cooling method?
05

Analyzing the benefits and drawbacks of the conveyor system

Assuming the conveyor system follows the requirements laid out in step 4, we can analyze the potential benefits and drawbacks of using the conveyor system: - Advantages: Increased productivity, potential for reduced cooling time, continuous flow instead of cooling in batches - Disadvantages: High initial investment in setting up the conveyor system, potential decrease in quality due to change in cooling method After analyzing these points and determining the risks and benefits, one could decide whether to replace the batch cooling method with a conveyor system or not. It's essential to weigh quality control versus improved productivity to make sure the change doesn't negatively affect the final product quality. In conclusion, by breaking down the exercise into steps, the student can better understand the problem and easier analyze the cooling method to be chosen. Details about the cooling rate, productivity, and quality should be considered before making a decision on the proposed change.

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Key Concepts

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

Cooling Process
The cooling process is crucial for materials and products that have been exposed to high temperatures during manufacturing, such as the decorative plastic panels mentioned in our exercise. After being cured in an oven at a high temperature, the panels must be brought back to a lower, stable temperature before they can be safely handled or used in further applications. To maintain quality, the rate at which the panels cool is important; cooling too quickly can cause warping or internal stresses, while cooling too slowly may be inefficient.

During this process, heat is transferred from the panels to the surrounding air. This transfer occurs through convection, conduction, and radiation, but in the case of quiescent air cooling, natural convection is the primary mode since the air is still and there are no external forces aiding in the heat flow. To optimize cooling, it is vital to ensure even temperature distribution across the panel's surface and minimize any interruptions to the process that could lead to differential cooling rates.
Quiescent Air Cooling
Quiescent air cooling is a method where objects are allowed to cool naturally in a motionless air environment. It's a passive cooling system, meaning it doesn't require additional energy input to facilitate the heat transfer process, as opposed to forced-air cooling where fans or blowers are used. The temperature difference between the hot object and the cooler ambient air drives the cooling process.

When the plastic panels from our exercise are placed in quiescent air at 29掳C, heat transfer occurs naturally through convection. As the hot surface of the panel comes into contact with cooler air, the air absorbs the heat and rises due to density differences, allowing cooler air to take its place and further absorb heat. This results in a gradual decrease of the panel鈥檚 temperature. However, since the air is not moving, this mode of heat transfer can be relatively slow and can be uneven, especially for large surfaces that require consistent quality control.
Conveyor Cooling System
A conveyor cooling system, as proposed to increase productivity, involves moving the panels along on a conveyor belt as they cool. The motion of the conveyor allows for continuous processing of the panels, leading to a potentially faster cooling process when compared to stationary batch cooling in quiescent air. This system can enable a consistent exposure to ambient air and improve heat transfer efficiency.

However, there are challenges that must be considered, such as the need to maintain a controlled and even cooling rate across all panels as they are transported. Panels must be kept horizontal to avoid warping, and there should be sufficient space between them to ensure consistent air flow. Moreover, if the conveyor system speeds up the cooling too much, it could negatively impact the material properties of the panels鈥攕omething that's crucial to maintain as part of quality control. Ultimately, implementing a conveyor cooling system must balance the benefits of increased throughput with maintaining the required quality of the final product.

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Most popular questions from this chapter

Consider a large vertical plate with a uniform surface temperature of \(130^{\circ} \mathrm{C}\) suspended in quiescent air at \(25^{\circ} \mathrm{C}\) and atmospheric pressure. (a) Estimate the boundary layer thickness at a location \(0.25 \mathrm{~m}\) measured from the lower edge. (b) What is the maximum velocity in the boundary layer at this location and at what position in the boundary layer does the maximum occur? (c) Using the similarity solution result, Equation \(9.19\), determine the heat transfer coefficient \(0.25 \mathrm{~m}\) from the lower edge. (d) At what location on the plate measured from the lower edge will the boundary layer become turbulent?

The maximum surface temperature of the \(20-\mathrm{mm}-\) diameter shaft of a motor operating in ambient air at \(27^{\circ} \mathrm{C}\) should not exceed \(87^{\circ} \mathrm{C}\). Because of power dissipation within the motor housing, it is desirable to reject as much heat as possible through the shaft to the ambient air. In this problem, we will investigate several methods for heat removal. (a) For rotating cylinders, a suitable correlation for estimating the convection coefficient is of the form $$ \begin{gathered} \overline{N u}_{D}=0.133 \operatorname{Re}_{D}^{2 / 3} \operatorname{Pr}^{1 / 3} \\ \left(\operatorname{Re}_{D}<4.3 \times 10^{5}, \quad 0.7<\operatorname{Pr}<670\right) \end{gathered} $$ where \(R e_{D} \equiv \Omega D^{2} / \nu\) and \(\Omega\) is the rotational velocity (rad/s). Determine the convection coefficient and the maximum heat rate per unit length as a function of rotational speed in the range from 5000 to \(15,000 \mathrm{rpm}\). (b) Estimate the free convection coefficient and the maximum heat rate per unit length for the stationary shaft. Mixed free and forced convection effects may become significant for \(R e_{D}<4.7\left(G r_{D}^{3} / P r\right)^{0.137}\). Are free convection effects important for the range of rotational speeds designated in part (a)? (c) Assuming the emissivity of the shaft is \(0.8\) and the surroundings are at the ambient air temperature, is radiation exchange important? (d) If ambient air is in cross flow over the shaft, what air velocities are required to remove the heat rates determined in part (a)?

Liquid nitrogen is stored in a thin-walled spherical vessel of diameter \(D_{i}=1 \mathrm{~m}\). The vessel is positioned concentrically within a larger, thin-walled spherical container of diameter \(D_{o}=1.10 \mathrm{~m}\), and the intervening cavity is filled with atmospheric helium. Under normal operating conditions, the inner and outer surface temperatures are \(T_{i}=77 \mathrm{~K}\) and \(T_{o}=283 \mathrm{~K}\). If the latent heat of vaporization of nitrogen is \(2 \times 10^{5} \mathrm{~J} / \mathrm{kg}\), what is the mass rate \(m(\mathrm{~kg} / \mathrm{s})\) at which gaseous nitrogen is vented from the system?

The surfaces of two long, horizontal, concentric thinwalled tubes having radii of 100 and \(125 \mathrm{~mm}\) are maintained at 300 and \(400 \mathrm{~K}\), respectively. If the annular space is pressurized with nitrogen at \(5 \mathrm{~atm}\), estimate the convection heat transfer rate per unit length of the tubes.

Consider laminar flow about a vertical isothermal plate of length \(L\), providing an average heat transfer coefficient of \(\bar{h}_{L}\). If the plate is divided into \(N\) smaller plates, each of length, \(L_{N}=L / N\), determine an expression for the ratio of the heat transfer coefficient averaged over the \(N\) plates to the heat transfer coefficient averaged over the single plate, \(\bar{h}_{L, N} / \bar{h}_{L, 1}\).
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