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Chapter 2: Problem 1

How does transient heat transfer differ from steady heat transfer? How does one-dimensional heat transfer differ from two-dimensional heat transfer?

Short Answer

Expert verified
Answer: The main differences between transient and steady heat transfer are related to the constancy of the temperature distribution within the system: transient heat transfer involves temperature distribution changes over time, while steady heat transfer maintains constant temperature distribution. The primary differences between one-dimensional and two-dimensional heat transfers involve spatial considerations: one-dimensional heat transfer assumes heat transfer occurs in one direction, while two-dimensional heat transfer accounts for variations in temperature and heat flow in two spatial directions.

Step by step solution

01

Definition of Transient Heat Transfer

Transient heat transfer refers to the process where the temperature distribution within a system changes over time. This occurs when the heat transfer rate within the system is time dependent, which means that the rate at which heat is transferred is not constant.
02

Definition of Steady Heat Transfer

Steady heat transfer, on the other hand, is the process where the temperature distribution within a system remains constant over time. In this case, the heat transfer rate is time independent, meaning that the rate at which heat is being transferred remains constant.
03

Differences between Transient and Steady Heat Transfer

The main difference between transient and steady heat transfer is the constancy of the temperature distribution within the system. In transient heat transfer, the temperature distribution changes over time, whereas in steady heat transfer, the temperature distribution remains constant. In other words, a system experiencing transient heat transfer will eventually reach a steady state, where the temperature distribution stops changing, and steady heat transfer takes place.
04

Definition of One-dimensional Heat Transfer

One-dimensional heat transfer is a simplification of the heat transfer process in which heat transfer is assumed to take place only in one direction within the system. This type of heat transfer is usually applied to cases with large differences in conductivity or thickness in one direction compared to others, such as a long rod or a wall.
05

Definition of Two-dimensional Heat Transfer

Two-dimensional heat transfer accounts for heat transfer in two spatial directions within a system. This is a more realistic representation of the heat transfer process and is typically used when the temperature distribution varies in two directions. Examples of two-dimensional heat transfer include heat transfer in a rectangular plate or across the corner of a wall.
06

Differences between One-dimensional and Two-dimensional Heat Transfer

The primary difference between one-dimensional and two-dimensional heat transfer lies in the spatial considerations. One-dimensional heat transfer is a simplification that assumes heat transfer occurs only in one direction, while two-dimensional heat transfer accounts for variations in temperature and heat flow in two spatial directions. Understanding the correct dimensionality of a given problem is essential for accurate analysis and modeling of the heat transfer process.

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Most popular questions from this chapter

What kind of differential equations can be solved by direct integration?

The heat conduction equation in a medium is given in its simplest form as $$ \frac{1}{r} \frac{d}{d r}\left(r k \frac{d T}{d r}\right)+\dot{e}_{\text {gen }}=0 $$ Select the wrong statement below. (a) The medium is of cylindrical shape. (b) The thermal conductivity of the medium is constant. (c) Heat transfer through the medium is steady. (d) There is heat generation within the medium. (e) Heat conduction through the medium is one-dimensional.

Consider the uniform heating of a plate in an environment at a constant temperature. Is it possible for part of the heat generated in the left half of the plate to leave the plate through the right surface? Explain.

Consider a large plane wall of thickness \(L=0.3 \mathrm{~m}\), thermal conductivity \(k=2.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and surface area \(A=\) \(12 \mathrm{~m}^{2}\). The left side of the wall at \(x=0\) is subjected to a net heat flux of \(\dot{q}_{0}=700 \mathrm{~W} / \mathrm{m}^{2}\) while the temperature at that surface is measured to be \(T_{1}=80^{\circ} \mathrm{C}\). Assuming constant thermal conductivity and no heat generation in the wall, \((a)\) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, \((b)\) obtain a relation for the variation of temperature in the wall by solving the differential equation, and \((c)\) evaluate the temperature of the right surface of the wall at \(x=L\).

Consider a 20-cm-thick large concrete plane wall \((k=0.77 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) subjected to convection on both sides with \(T_{\infty 1}=27^{\circ} \mathrm{C}\) and \(h_{1}=5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) on the inside, and \(T_{\infty 2}=8^{\circ} \mathrm{C}\) and \(h_{2}=12 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and \((c)\) evaluate the temperatures at the inner and outer surfaces of the wall.
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