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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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Most popular questions from this chapter

Consider a stainless steel spoon \(\left(k=8.7 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{F}\right)\) partially immersed in boiling water at \(200^{\circ} \mathrm{F}\) in a kitchen at \(75^{\circ} \mathrm{F}\). The handle of the spoon has a cross section of \(0.08\) in \(\times\) \(0.5\) in, and extends 7 in in the air from the free surface of the water. If the heat transfer coefficient at the exposed surfaces of the spoon handle is \(3 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot{ }^{\circ} \mathrm{F}\), determine the temperature difference across the exposed surface of the spoon handle. State your assumptions. Answer: \(124.6^{\circ} \mathrm{F}\)

Consider two finned surfaces that are identical except that the fins on the first surface are formed by casting or extrusion, whereas they are attached to the second surface afterwards by welding or tight fitting. For which case do you think the fins will provide greater enhancement in heat transfer? Explain.

A 1-m-inner-diameter liquid-oxygen storage tank at a hospital keeps the liquid oxygen at \(90 \mathrm{~K}\). The tank consists of a \(0.5-\mathrm{cm}\)-thick aluminum \((k=170 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) shell whose exterior is covered with a \(10-\mathrm{cm}\)-thick layer of insulation \((k=0.02 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). The insulation is exposed to the ambient air at \(20^{\circ} \mathrm{C}\) and the heat transfer coefficient on the exterior side of the insulation is \(5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The rate at which the liquid oxygen gains heat is (a) \(141 \mathrm{~W}\) (b) \(176 \mathrm{~W}\) (c) \(181 \mathrm{~W}\) (d) \(201 \mathrm{~W}\) (e) \(221 \mathrm{~W}\)

Exposure to high concentration of gaseous ammonia can cause lung damage. To prevent gaseous ammonia from leaking out, ammonia is transported in its liquid state through a pipe \(\left(k=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, D_{i}=2.5 \mathrm{~cm}\right.\), \(D_{o}=4 \mathrm{~cm}\), and \(L=10 \mathrm{~m}\) ). Since liquid ammonia has a normal boiling point of \(-33.3^{\circ} \mathrm{C}\), the pipe needs to be properly insulated to prevent the surrounding heat from causing the ammonia to boil. The pipe is situated in a laboratory, where the average ambient air temperature is \(20^{\circ} \mathrm{C}\). The convection heat transfer coefficients of the liquid hydrogen and the ambient air are \(100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), respectively. Determine the insulation thickness for the pipe using a material with \(k=\) \(0.75 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) to keep the liquid ammonia flowing at an average temperature of \(-35^{\circ} \mathrm{C}\), while maintaining the insulated pipe outer surface temperature at \(10^{\circ} \mathrm{C}\).

Consider an insulated pipe exposed to the atmosphere. Will the critical radius of insulation be greater on calm days or on windy days? Why?
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