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# 物理代写|传热学代写Heat Transfer代考|MECH344 INTRODUCTION: CONDUCTION, CONVECTION, AND RADIATION

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## 物理代写|传热学代写Heat Transfer代考|INTRODUCTION: CONDUCTION, CONVECTION, AND RADIATION

Conduction is caused by the temperature gradient through a solid material. For example, Figure $1.1$ shows that heat is conducted through a wall of a building or a container from the high-temperature side to the low-temperature side. This is a onedimensional (1-D), steady-state, heat conduction problem if $T_1$ and $T_2$ are uniform. According to Fourier’s conduction law, the temperature profile is linear through the plane wall.

Fourier’s Conduction Law
$$q^{\prime \prime}=-k \frac{\mathrm{d} T}{\mathrm{~d} x}=k \frac{T_1-T_2}{L}$$
and
$$q^{\prime \prime} \equiv \frac{q}{A_{\mathrm{c}}} \text { or } q=q^{\prime \prime} A_{\mathrm{c}}$$
where $q^{\prime \prime}$ is the heat flux $\left(\mathrm{W} / \mathrm{m}^2\right), q$ is the heat rate $(\mathrm{W}$ or $\mathrm{J} / \mathrm{s}), k$ is the thermal conductivity of solid material $(\mathrm{W} / \mathrm{m} \mathrm{K}), A_{\mathrm{c}}$ is the cross-sectional area for conduction, perpendicular to heat flow $\left(\mathrm{m}^2\right)$, and $L$ is the conduction length $(\mathrm{m})$.

One can predict heat rate or heat loss through the plane wall by knowing $T_1, T_2, k$, $L$, and $A_c$. This is the simple 1-D steady-state problem. However, in actual applications, there are many two-dimensional (2-D) or three-dimensional (3-D) steady-state heat conduction problems; there are cases where heat generation occurs in the solid material during heat conduction. Also, transient heat conduction problems take place in many engineering applications. In addition, some special applications involve heat conduction with a moving boundary. These more complicated heat conduction problems will be discussed in the following chapters.

## 物理代写|传热学代写Heat Transfer代考|Convection

Convection is caused by fluid flow motion over a solid surface. For example, Figure $1.2$ shows that heat is removed from a heated solid surface to cooling fluid. This is a 2-D boundary-layer flow and heat transfer problem. According to Newton, the heat removal rate from the heated surface is proportional to the temperature difference between the heated wall and the cooling fluid. The proportionality constant is known as the heat transfer coefficient; the same heat rate from the heated surface can be determined by applying Fourier’s Conduction Law to the cooling fluid.
1.1.2.1 Newton’s Cooling Law
$$q^{\prime \prime}=-\left.k_f \frac{d T}{d y}\right|{\text {at wall }}=h\left(T_s-T{\infty}\right)$$
Also,
$$h=\frac{q^{\prime \prime}}{T_s-T_{\infty}}=\frac{-\left.k_f \frac{d T}{d y}\right|{y=0}}{T_s-T{\infty}}$$
and
$$q^{\prime \prime}=\frac{q}{A_s} \quad \text { or } \quad q=q^{\prime \prime} A_s$$

where $T_s$ is the surface temperature $\left({ }^{\circ} \mathrm{C}\right.$ or $\left.\mathrm{K}\right), T_{\infty}$ is the fluid temperature $\left({ }^{\circ} \mathrm{C}\right.$ or $\left.\mathrm{K}\right)$, $h$ is the heat transfer coefficient $\left(\mathrm{W} / \mathrm{m}^2 \mathrm{~K}\right), k_f$ is the thermal conductivity of fluid $(\mathrm{W} / \mathrm{mK}), A_s$ is the surface area for convection, exposed to the fluid $\left(\mathrm{m}^2\right)$.

It is noted that the heat transfer coefficient depends on fluid properties (such as air or water as the coolant), flow conditions (i.e., laminar or turbulent flows), surface configurations (such as flat surface or circular tube), and so on. The heat transfer coefficient can be determined experimentally or analytically. This textbook focuses on analytical solutions. From Equation (1.3), the heat transfer coefficient can be determined by knowing the temperature profile in the cooling fluid during convection. With this analytical profile, the temperature gradient near the wall, $d T / d y$, can be used to determine the heat transfer coefficient. However, this requires solving the 2-D boundary-layer equations and will be the subject of the following chapters. Before solving 2-D boundary-layer equations, one needs the heat transfer coefficient as the convection boundary condition $(\mathrm{BC})$ in order to solve the heat conduction problem. Therefore, Table $1.1$ provides some typical values of heat transfer coefficient in many convection problems. As can be seen, in general, forced convection provides more heat transfer than natural convection; water as a coolant removes much more heat than air; and boiling or condensation, involving a phase change, has a much higher heat transfer coefficient than single-phase convection.

## 物理代写|传热学代写热传导代考|简介:传导，对流，和辐射

$$q^{\prime \prime}=-k \frac{\mathrm{d} T}{\mathrm{~d} x}=k \frac{T_1-T_2}{L}$$

$$q^{\prime \prime} \equiv \frac{q}{A_{\mathrm{c}}} \text { or } q=q^{\prime \prime} A_{\mathrm{c}}$$
where $q^{\prime \prime}$ 是热流密度 $\left(\mathrm{W} / \mathrm{m}^2\right), q$ 是热率 $(\mathrm{W}$ 或 $\mathrm{J} / \mathrm{s}), k$ 固体材料的导热系数是多少 $(\mathrm{W} / \mathrm{m} \mathrm{K}), A_{\mathrm{c}}$ 传导的截面积是否垂直于热流 $\left(\mathrm{m}^2\right)$，以及 $L$ 为导通长度 $(\mathrm{m})$.

## 物理代写|传热学代写Heat Transfer代考|对流

1.1.2.1牛顿冷却定律
$$q^{\prime \prime}=-\left.k_f \frac{d T}{d y}\right|{\text {at wall }}=h\left(T_s-T{\infty}\right)$$

$$h=\frac{q^{\prime \prime}}{T_s-T_{\infty}}=\frac{-\left.k_f \frac{d T}{d y}\right|{y=0}}{T_s-T{\infty}}$$

$$q^{\prime \prime}=\frac{q}{A_s} \quad \text { or } \quad q=q^{\prime \prime} A_s$$

where $T_s$ 是表面温度 $\left({ }^{\circ} \mathrm{C}\right.$ 或 $\left.\mathrm{K}\right), T_{\infty}$ 是流体温度 $\left({ }^{\circ} \mathrm{C}\right.$ 或 $\left.\mathrm{K}\right)$， $h$ 换热系数是多少 $\left(\mathrm{W} / \mathrm{m}^2 \mathrm{~K}\right), k_f$ 流体的导热系数是多少 $(\mathrm{W} / \mathrm{mK}), A_s$ 对流的表面积是否暴露在流体中 $\left(\mathrm{m}^2\right)$.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。