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Chapter 3: Problem 4

Can we define the convection resistance for a unit surface area as the inverse of the convection heat transfer coefficient?

Short Answer

Expert verified
Answer: Yes, the convection resistance for a unit surface area can be defined as the inverse of the convection heat transfer coefficient. This relationship is derived from the equations of convection heat transfer coefficient (h) and convection resistance (R_conv), where h = 1 / R_conv.

Step by step solution

01

Understand the concepts involved

In order to answer this question, we need to comprehend two main topics: 1. Convection Resistance: In heat transfer, resistance represents the opposition to heat transfer. For convection, this opposition occurs due to the fluid flow over a surface. 2. Convection Heat Transfer Coefficient (h): This is a measure of the efficiency at which energy is transferred due to convection per unit area. It depends on the nature of the fluid and its flow properties.
02

Define the equations related to convection resistance and heat transfer coefficient

The convection heat transfer coefficient is typically represented as: h = Q / (A * ∆T) Where: - Q is the convective heat transfer (in Watts or W) - A is the surface area over which convection is occurring (in square meters or m^2) - ∆T is the temperature difference between the solid surface and the fluid (in Kelvin or K) Now, the convection resistance (R_conv) can be defined as the opposition to heat transfer per unit area. Mathematically, R_conv = ∆T / (Q/A)
03

Manipulate the heat transfer coefficient equation to establish the inverse relationship

Now, we will manipulate the equation we obtained for the convection heat transfer coefficient (h): h = Q / (A * ∆T) And, we will also rewrite the convection resistance equation: R_conv = ∆T / (Q/A) Notice that: Q / (A * ∆T) = 1 / (R_conv) Comparing these equations, we can see that: h = 1 / R_conv
04

Conclude the relationship between convection resistance and heat transfer coefficient

Based on the derived relationship h = 1 / R_conv, we can conclude that the convection resistance for a unit surface area can indeed be defined as the inverse of the convection heat transfer coefficient.

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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: \(124.6^{\circ} \mathrm{F}\)

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 -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 temperature of the exterior surface of the insulation is (a) \(13^{\circ} \mathrm{C}\) (b) \(9^{\circ} \mathrm{C}\) (c) \(2^{\circ} \mathrm{C}\) (d) \(-3^{\circ} \mathrm{C}\) (e) \(-12^{\circ} \mathrm{C}\)

A thin-walled spherical tank in buried in the ground at a depth of \(3 \mathrm{~m}\). The tank has a diameter of \(1.5 \mathrm{~m}\), and it contains chemicals undergoing exothermic reaction that provides a uniform heat flux of \(1 \mathrm{~kW} / \mathrm{m}^{2}\) to the tank's inner surface. From soil analysis, the ground has a thermal conductivity of \(1.3 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and a temperature of \(10^{\circ} \mathrm{C}\). Determine the surface temperature of the tank. Discuss the effect of the ground depth on the surface temperature of the tank.

Hot water at an average temperature of \(70^{\circ} \mathrm{C}\) is flowing through a \(15-\mathrm{m}\) section of a cast iron pipe \((k=52 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) whose inner and outer diameters are \(4 \mathrm{~cm}\) and \(4.6 \mathrm{~cm}\), respectively. The outer surface of the pipe, whose emissivity is \(0.7\), is exposed to the cold air at \(10^{\circ} \mathrm{C}\) in the basement, with a heat transfer coefficient of \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The heat transfer coefficient at the inner surface of the pipe is \(120 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Taking the walls of the basement to be at \(10^{\circ} \mathrm{C}\) also, determine the rate of heat loss from the hot water. Also, determine the average velocity of the water in the pipe if the temperature of the water drops by \(3^{\circ} \mathrm{C}\) as it passes through the basement.

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.
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