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Chapter 3: Problem 7

Why are the convection and the radiation resistances at a surface in parallel instead of being in series?

Short Answer

Expert verified
Answer: Convection and radiation resistances at a surface are in parallel instead of being in series because both mechanisms occur simultaneously and independently from each other, allowing for separate pathways for heat flow. The total rate of heat transfer at the surface is the summation of the heat transferred through convection and radiation.

Step by step solution

01

Define Convection Resistance

Convection resistance represents the resistance to heat transfer by convection between a solid surface and the surrounding fluid. In other words, it describes the difficulty for heat to transfer from the surface to the fluid (or vice versa) due to the movement of fluid particles.
02

Define Radiation Resistance

Radiation resistance represents the resistance to heat transfer by radiation between a hot surface and its cooler surroundings. It accounts for the heat transfer through thermal radiation, which is the emission of electromagnetic waves (usually infrared) from a heated object.
03

Analyze Heat Transfer Mechanisms

In a real-world scenario, both convection and radiation heat transfer mechanisms occur at the same time at a surface. The heat transfer by convection is usually conducted from a solid surface to the surrounding fluid (or vice versa) and depends on the temperature difference between the surface and the fluid. On the other hand, the heat transfer by radiation is between the surface and the surroundings (typically air) and relies on the temperature difference between the surface and the surroundings.
04

Explain Parallel Resistances

When two resistances are in parallel, they allow for the heat to transfer across them simultaneously. In the case of convection and radiation resistances, both mechanisms occur at the same time and have separate pathways for heat flow. The total rate of heat transfer at the surface (Q) is the summation of the heat transferred through convection (Q_conv) and radiation (Q_rad): \[Q = Q_{conv} + Q_{rad}\]
05

Explain Why Resistances are Not in Series

For resistances to be in series, the heat transfer must pass through both resistances in sequence, one after the other. However, in the case of convection and radiation, the heat transfer does not go through a specific order. Both mechanisms transfer heat simultaneously and independently from each other. In conclusion, the convection and radiation resistances at a surface are in parallel instead of being in series because both mechanisms occur simultaneously and independently from each other, allowing for separate pathways for heat flow.

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Key Concepts

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

Understanding Convection Resistance
Convection resistance refers to the difficulty that heat experiences as it tries to move between a solid surface and the fluid around it. Whether it's air, water, or any other fluid, this process involves heat being transferred as the fluid particles move. The formula for convection resistance is usually expressed as \[ R_{conv} = \frac{1}{h A} \]where \(h\) is the convection heat transfer coefficient, and \(A\) is the area of the surface. This equation reflects how the efficiency of heat transfer increases with a higher convection coefficient and a larger area. Convection can occur naturally, due to buoyancy effects, or be forced, by fans or winds. Understanding this resistance helps in designing systems that efficiently use airflow, like heating or cooling systems, to manage temperature.
  • Higher convection coefficient = less resistance.
  • Larger surface area = less resistance.
Exploring Radiation Resistance
Radiation resistance is quite different from convection resistance as it involves heat transfer via electromagnetic waves. This kind of transfer doesn't require a medium (like air or water) and can even occur in a vacuum. When dealing with radiation resistance, we usually focus on thermal radiation, which is mostly in the infrared spectrum. The resistance to radiation is defined by the equation: \[ R_{rad} = \frac{1}{\epsilon \sigma A (T_s^4 - T_{sur}^4)} \]where \(\epsilon\) is the emissivity of the surface, \(\sigma\) is the Stefan-Boltzmann constant, \(A\) is the area, \(T_s\) is the surface temperature and \(T_{sur}\) is the surrounding temperature. The emissivity value serves as an indicator of how effectively a surface can emit energy as radiation. Radiation resistance demonstrates how much a surface's ability to radiate heat is impacted by its emissivity and the temperature differences. This is crucial in applications where high temperatures and significant energy emissions are involved.
  • Lower emissivity = higher resistance.
  • Greater temperature difference = less resistance.
The Concept of Parallel Resistances
When convection and radiation resistances are described as parallel, it means they allow for heat to be transferred at the same time through separate avenues. In this arrangement, both heat transfer mechanisms function independently and do not affect each other directly, allowing concurrent heat flow. The total heat transfer rate \(Q\) is therefore the sum of the heat transferred by convection \(Q_{conv}\) and by radiation \(Q_{rad}\):\[ Q = Q_{conv} + Q_{rad} \]This formula underscores the benefit of having these mechanisms in parallel; they can each contribute to the heat transfer without one being a bottleneck to the other. It's similar to having two open gates allowing cars to flow through simultaneously, instead of in a single line.
  • Parallel means simultaneous transfer.
  • Independent paths lead to efficient flow.
Understanding Heat Transfer Mechanisms
Heat transfer mechanisms can be fascinating because they describe how energy moves from one place to another, like from the sun to the Earth's surface or from a radiator to the air in a room. In practical applications, convection and radiation often occur together, making it necessary to grasp how both work and interact. Convection involves heat moving via fluid motion, often visible in heating systems or weather patterns, creating a "conveyor belt" of energy. Radiation allows heat transfer through electromagnetic waves, crucial for instances like warmth from a campfire or sunlight. Both mechanisms have their unique characteristics and operate simultaneously when heat is transferred from a surface to its surroundings. By understanding these basic principles, engineers and scientists can design more efficient systems that use energy wisely, ensure comfort, or protect equipment from overheating. This concept also shows why knowing each mechanism individually is important as it enables better control in practical scenarios.
  • Convection: heat flow through moving fluids.
  • Radiation: heat flow through electromagnetic waves.

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Most popular questions from this chapter

A 3-m-diameter spherical tank containing some radioactive material is buried in the ground \((k=1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). The distance between the top surface of the tank and the ground surface is \(4 \mathrm{~m}\). If the surface temperatures of the tank and the ground are \(140^{\circ} \mathrm{C}\) and \(15^{\circ} \mathrm{C}\), respectively, determine the rate of heat transfer from the tank.

Consider a wall that consists of two layers, \(A\) and \(B\), with the following values: \(k_{A}=0.8 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, L_{A}=8 \mathrm{~cm}, k_{B}=\) \(0.2 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, L_{B}=5 \mathrm{~cm}\). If the temperature drop across the wall is \(18^{\circ} \mathrm{C}\), the rate of heat transfer through the wall per unit area of the wall is (a) \(180 \mathrm{~W} / \mathrm{m}^{2}\) (b) \(153 \mathrm{~W} / \mathrm{m}^{2}\) (c) \(89.6 \mathrm{~W} / \mathrm{m}^{2}\) (d) \(72 \mathrm{~W} / \mathrm{m}^{2}\) (e) \(51.4 \mathrm{~W} / \mathrm{m}^{2}\)

The plumbing system of a house involves a \(0.5-\mathrm{m}\) section of a plastic pipe \((k=0.16 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) of inner diameter \(2 \mathrm{~cm}\) and outer diameter \(2.4 \mathrm{~cm}\) exposed to the ambient air. During a cold and windy night, the ambient air temperature remains at about \(-5^{\circ} \mathrm{C}\) for a period of \(14 \mathrm{~h}\). The combined convection and radiation heat transfer coefficient on the outer surface of the pipe is estimated to be \(40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and the heat of fusion of water is \(333.7 \mathrm{~kJ} / \mathrm{kg}\). Assuming the pipe to contain stationary water initially at \(0^{\circ} \mathrm{C}\), determine if the water in that section of the pipe will completely freeze that night.

Superheated steam at an average temperature \(200^{\circ} \mathrm{C}\) is transported through a steel pipe \(\left(k=50 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, D_{o}=8.0 \mathrm{~cm}\right.\), \(D_{i}=6.0 \mathrm{~cm}\), and \(L=20.0 \mathrm{~m}\) ). The pipe is insulated with a 4-cm thick layer of gypsum plaster \((k=0.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). The insulated pipe is placed horizontally inside a warehouse where the average air temperature is \(10^{\circ} \mathrm{C}\). The steam and the air heat transfer coefficients are estimated to be 800 and \(200 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. Calculate \((a)\) the daily rate of heat transfer from the superheated steam, and \((b)\) the temperature on the outside surface of the gypsum plaster insulation.

A plane wall surface at \(200^{\circ} \mathrm{C}\) is to be cooled with aluminum pin fins of parabolic profile with blunt tips. Each fin has a length of \(25 \mathrm{~mm}\) and a base diameter of \(4 \mathrm{~mm}\). The fins are exposed to an ambient air condition of \(25^{\circ} \mathrm{C}\) and the heat transfer coefficient is \(45 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the thermal conductivity of the fins is \(230 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), determine the heat transfer rate from a single fin and the increase in the rate of heat transfer per \(\mathrm{m}^{2}\) surface area as a result of attaching fins. Assume there are 100 fins per \(\mathrm{m}^{2}\) surface area.
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