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关于latex图片插入出现的问题
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本人用ctex编辑一篇文档，用的{cctart}模板编辑，编译用的pdftex。在文档中插入几张图片均能用pdf正常输出，但在我用同样的方法再插入一张图片后，编译没有问题，可以打开pdf却打不开，显示错误：文档打开时出错，文件已损坏并无法修复。但我试着将插入图片的位置调整一下后，又有可能正常输出并打开，我想问下大神，这算怎么回事啊？？（应该不是我插入图片的命令什么有问题，因为我之前插入的能正常输出，我用同样的方法在此基础上在插入时出的错！）非常感谢，希望大家能帮帮我！ 以下是我的源代码 \documentclass[11pt]{cctart} \usepackage{latexsym,amssymb,amsmath} \usepackage{graphicx} \usepackage{epstopdf} \usepackage{subfigure} \usepackage{float} \usepackage{psfig} \setlength{\parindent}{0cm} %段落中第一行缩进设为12pt \setlength{\parskip}{3pt plus1pt minus2pt} %plus伸展值minus收缩值 \setlength{\baselineskip}{20pt plus2pt minus1pt} \setlength{\textheight}{21true cm} \setlength{\textwidth}{14.5true cm} \title{\bfseries Two energy conservation principles in convcctive heat optiminization} \author{Fang Yuan, Qun Chen*\\汇报人：李贵} \begin{document} \maketitle \zihao{4}\ziti{B} \quad Abstract \\ \hspace*{2\ccwd}\zihao{-4} In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree.We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.\\ \zihao{4}\ziti{B} 2.\quad 对流换热的最优化原则\\ \zihao{-4}\ziti{B} 2.1\quad 传热性能和场协同程度的关系\\ 对于无内热源的不可压流对流换热过程，忽略粘性耗散，能量方程可以表示为： \[{\rho}c_pU\cdot{\nabla}T={\nabla}{\cdot}(\lambda{\nabla}T)~~(3)\] 对（3）式进行积分，忽略进口和出口的纵向热传导，并运用高斯定理有： \[\iiint_V{\rho}c_pU{\cdot}{\triangledown}TdV=\iiint_V{\rho}c_p\lvert{U}\rvert{\lvert{\nabla}T\rvert}cos{\beta}dV=\iint_S{\vec{n}}{\cdot}({\lambda{\nabla}T})dS~~(4)\] 引入以下无量纲参数： \[\bar{U}=\frac{U}{U_m},~~{\nabla}{\bar{T}}=\frac{{\nabla}T}{(T_m-T_b)/D}~~(5)\] 则（4）式可以化为： \[\iiint_{v_0}(\bar{U}{\cdot}{\nabla}{\bar{T}})d\vec{V}=\frac{Nu}{Repr}=Fc~~(6)\] $Fc$为场协同数，表示流体速度和温度梯度在整个流场中的协同程度。从（6）式可以看出，对于给定入口流速，由于$Re$和$Pr$为常数 ，所以$Nu$随$Fc$的增大而增大。即换热性能越好。 \zihao{-4}\ziti{B} 2.2\quad 火积耗散与传热性能的关系\\ 在（3）式左右两边乘以温度$T$，我们得到， \[U\cdot{\nabla}(\frac{1}{2}\rho{c_p}T^2)={\nabla}\cdot(\lambda{T}{\nabla}T)-\lambda\lvert{\nabla}T\rvert^2~~(8)\] 即， \[U\cdot{\nabla}G={\nabla}\cdot(\lambda{T}{\nabla}T)-\lambda\lvert{\nabla}T\rvert^2~~(9)\] 令$\phi_h=\iiint_v\lambda\lvert{\nabla}T\rvert^2dV$,可以作为不可逆的量度。 对（8）式在整个流场积分，并运用高斯定理，有： \[\phi_h=\iint_S{-q^{''}}T\cdot\vec{n}dS+\frac{\rho{c_p}U_{in}{T_{in}}^2}{2}-\frac{\rho{c_p}U_{out}{T_{out}}^2}{2}~~(10)\] 当边界热通量$q^{''}$给定时，（10）式可以表示为; \[\phi_h={-q^{''}}\cdot\vec{n}S\iint_S{\frac{T}{S}}dS+\frac{\rho{c_p}U_{in}{T_{in}}^2}{2}-\frac{\rho{c_p}U_{out}{T_{out}}^2}{2}~~(11)\] 因为流体吸收或释放的热量等于通过边界转移的热量，所以（11）式可以进一步简化为： \[\phi_h=Q（T_b-\frac{T_{in}+T_{out}}{2}）~~(12)\] 其中，$\frac{T_{in}+t_{out}}{2}$表示流体的平均温度，$T_b$表示平均边界温度。 \[Q\delta({\Delta}T)=\delta(\phi_h)~~(13)\] 其中，${\Delta}T=T_b-\frac{T_{in}+T_{out}}{2}$表示温差。 \\ 由（13）式可知，对于总边界热流量不变的情况，在热传递区域，最小火积耗散率可以导出流体和边界的最小 温差。（the minimum entransy dissipation rate in the heat transfer domain leads to the least temperature difference between the fluid and the wall） 对于给定边界温度$T_b(T_b>T_{in})$,由（10）式可得， \[(T_b-T_{in}-\frac{Q}{US\rho{c_p}})\delta{Q}=\delta(\phi_h)~~(15)\] 由于${\delta}^2Q<0$,(15)式是最大值原理。也就是说，当边界温度固定时，火积耗散最大导致热流量最大 （when the boundary temperature is fixed, the maximum entransydissipation rate in the heat transfer domain leads to the largest heat flow rate, i.e. the optimal heat transfer performance.） \\ 另外，如果对流传热发生在一个有内热源的封闭系统，则，能量守恒方程可以表示为： \[{\rho}c_pU\cdot{\nabla}T={\nabla}{\cdot}(\lambda{\nabla}T)+q_v~~(16)\] 其中$q_v$表示热源。假设只有一个边界温度是恒温，其它边界都是绝热的，（16）式两边乘以T,有， \[\nabla\cdot{(\rho{c_p}UT^2/D)}-\frac{c_pT^2}{2}\nabla\cdot(\rho{U})=-\nabla\cdot{({\lambda}T{\nabla}T)}-{\lambda}\lvert{\nabla}T\rvert^2+q_vT~~(17)\] 对（17）式积分，并利用高斯公式和变分方法的，有， \[\phi_h=Q(T_f-T_b)~~(18)\] 其中$Q=q_vV$式总热流量，$T_f$是平均温度。这种情况，当 \[Q\delta(T_f)=\delta(\phi_h)~~(19)\] 从（19）式可知，在这种条件下，在腔中，最小火积耗散可以导致最小平均温度。（it is clear that the minimum entransy dissipation in this condition leads to the minimum average temperature in the cavity.） 总的来说，在不同边界条件下，最小火积耗散原则和最大火积耗散可以简单的称为EDEP，即火积耗散极值原理可以优化传热性能。 （the extremumof entransy dissipation leads to the optimal heat transfer performance.） \zihao{-4}\ziti{B} 2.3\quad 基于欧拉方程的FSP\\ \[\Pi=\iiint_V\{{\rho}{c_p}U{\cdot}{\nabla}T+C_{\phi_m} +A[{\rho}{c_p}U\cdot{\nabla}T-{\nabla}T\cdot({\lambda}{\nabla}T)~~(21)] +B{\nabla}T\cdot(\rho{U})\}dV\] 由火积散极值原理得到的欧拉方程： \[\rho{U}\cdot{\nabla}U=-{\nabla}P+\mu{\nabla}^2U+(C_{\phi}A{\nabla}T+\rho{U}\cdot{\nabla}U)~~(29)\] \zihao{-4}\ziti{B} 2.4\quad 基于欧拉方程的EDEP（The EDEP-based Euler’s equation）\\ \[\Pi=\iiint_V\{{\lambda}{\nabla}T{\cdot}{\nabla}T+C^{'}_{\phi_m} +A^{'}[{\rho}{c_p}U\cdot{\nabla}T-{\nabla}T\cdot({\lambda}{\nabla}T)]+ B^{'}{\nabla}T\cdot(\rho{U})\}dV~~(30)\] \[C^{'}_{\phi}=\frac{\rho{c_p}}{2C^{'}}~~(33)\] \[F=C^{'}_{\phi}A^{'}{\nabla}T+\rho{U}\cdot{\nabla}U~~(34)\] 总的来说，场协同程度和火积耗散率两个物理量不仅都可以作为评价传热性能的指标，而且都能指导我们通过变分法获得 在约束条件下获得最佳流场。\\ \zihao{4}\ziti{B} 3.\quad a fin-and-flat tube换热器的优化\\ \zihao{-4}\ziti{B} 3.1\quad 数值模型\\ \hspace*{2\ccwd}\zihao{-4}Fig 1 is the sketch of the elementary pattern of air-side geometry of an actual condenser with the detailed parameters listed in Table 1, where a laminar heat transfer process takes place. In this paper, only half of the tube and two half of the fins are presented due to the symmetry, and the air is taken as the working fluid with constant physical properties, including:$\rho=1.128kg m^{-3}$,$\mu=1.91\times10^{-5}kg m^{-1}s^{-1}$,$\lambda=0.0276 Wm^{-1}K^{-1},c_p=1005Jkg^{-1}K^{-1}$ \begin{figure}[!htbp] \centering \includegraphics[height=6cm,width=8cm]{fig1.eps} \caption{The sketch of the computational domain and boundary conditions} \end{figure} \hspace*{2\ccwd}\zihao{-4}The meshes at the sections of $z=8.25mm$, $x=2mm$ and $y=0.65mm$ are showed in Fig. 2(a)-(c), respectively, which are more condensed in the near wall and entrance regions, where the steeper velocity gradients are expected. In order to set boundary condition of variable A at outlet conveniently, the computational domain is extended downstream ten times the fin length, and then the gradient of variable A at outlet is assumed to be zero. \begin{figure}[!htbp] \centering \includegraphics[height=8cm,width=5cm]{fig2.eps} \caption{Computation meshes of the calculating domain} \end{figure} \zihao{-4}\ziti{B} 3.3\quad Mesh independence of the solution\\ \hspace*{2\ccwd}\zihao{-4}For the sake of adopting an appropriate grid system, a grid refinement is conducted to investigate the influence of the grid density on the numerical results. The simulation results of five different grid systems at a constant boundary temperature are shown in Fig. 3. Compared to the finest grid 133$\times$42$\times$696, the grid 133$\times$42$\times$520 yields 0.2\% lower Nu. Thus, the grid 133$\times$42$\times$696 has the sufficient precision for numerical simulation.\\ To further validate the computational model, the predicted heat transfer characteristics (j-factor) under different Reynolds numbers is also compared with that calculated from the empirical relation proposed by Sieder and Tate [38], which are provided in Fig. 4. \zihao{-4}\ziti{B} 3.3\quad Optimization at a constant boundary temperature\\ When the airflow with the inlet velocity and temperature of 2m/s and 308K, respectively, and the wall temperature of the rectangular domain keeps at 327K, Fig. 5(a)-(c) show the optimal distributions of velocity vector, velocity magnitude and temperature at the cross section of z=8.25mm based on the EDEP with $C^{'}_{\phi}=-1\times10^(-2)$in Eq.(31). \begin{figure}[!htbp] \centering \includegraphics[height=5cm,width=6cm]{fig3.eps} \caption{The Nusselt number, Nu, versus the grid number} \end{figure} \hspace*{2\ccwd}\zihao{-4}There exist five vortexes in the computational domain, which play the role of strengthening the mixture of the flow near the wall with the mainstream so as to transfer more heat from the boundary into the mainstream. In addition, from Fig. 5(b), it is clear that the velocity magnitude of vortex which reflects the strength of vortex becomes larger from the near tube region to the center between every two tubes. \begin{figure}[!htbp] \centering \includegraphics[height=5cm,width=6cm]{fig4.eps} \caption{The heat transfer characteristics, j-factor, versus the Reynolds number, Re.} \end{figure} \hspace*{2\ccwd}\zihao{-4}Increasing $C^{'}_{\phi}=-3.5\times10^(-2)$, we may get the optimized results at the same cross section shown in Fig. 6(a)-(c).The comparison of Figs. 5 and 6 indicates that the vortexes formed at the cross section increase to nine with the average velocity magnitude and temperature becoming larger and higher, respectively. Therefore, it can be concluded that as the absolute value of$C^{'}_{\phi}$ which represents the viscous dissipation rate is increasing, the flow with much more turbulence will be obtained so as to increase the heat flux from the boundary, and consequently optimize heat transfer. \begin{figure}[!htbp] \centering \includegraphics[height=8cm,width=10cm]{fig5.eps} \caption{Optimal distributions of velocity vector, velocity magnitude and temperature based on the EDEP at z=8.25mm ($C^{'}_{\phi}=-1\times10^{-2}.$)} \end{figure} \hspace*{2\ccwd}\zihao{-4}Based on Eqs. (24) and (32), Fig. 7 gives the Nu variation with different viscous dissipation rates. The results show that the Nu increases along with the viscous dissipation rate and the optimized trend curves based on two optimization principles are nearly the same \begin{figure} \centering \includegraphics[height=5cm,width=6cm]{fig7.eps} \caption{The Nusselt number, Nu, versus viscous dissipation rate, $\Phi_m$} \end{figure} \hspace*{2\ccwd}\zihao{-4}Moreover, Fig. 8(a)-(c) show the optimal distributions of velocity vector, velocity magnitude and temperature at the cross section of z=8.25mm based on the FSP, respectively. In a word, the optimized results are in reasonable agreement with our theoretical analysis, i.e. the FSP and EDEP optimizations for a prescribed boundary temperature are the same, they both can effectively maximize the total heat flow rate. \zihao{4}\ziti{B} 3.4\quad Optimization at a constant heat flux\\ \hspace*{2\ccwd}\zihao{-4}For the prescribed heat flux $q^{''}$ in the simulation model, based on the EDEP where $C^{'}_{\phi}=1.25\times10^(-2).$, the optimal distributions of velocity vector, velocity magnitude and temperature are shown in Fig. 9(a)-(c), respectively. Eleven vortexes exist in the computational domain, which reduce the heat transfer temperature difference by 24.2\%, and increase the Nu by 31.9\%. \hspace*{2\ccwd}\zihao{-4}Fig. 10 gives the Nu at different viscous dissipation rates based on the EDEP. Increasing the overall viscous dissipation rate effectively enlarges the Nu based on the EDEP. It exactly corresponds with the theoretical analysis. \hspace*{2\ccwd}\zihao{-4}According to the physical meaning of variational method, the Euler’s equation derived based on the FSP will not make any contribution to decrease the temperature difference. Fig. 11 indicates that the optimized results are the same but with the viscous dissipation decreasing 5.24\% and the Nu reducing 3.94%. Therefore, the numerical results further prove that, for prescribed heat flow rate boundary conditions, only the EDEP does work. \zihao{4}\ziti{B}4\quad Optimization in a foursquare cavity \zihao{4}\ziti{B} Conclusion\quad\\ \hspace*{2\ccwd}\zihao{-4}By establishing the relationships of the field synergy degree and the entransy dissipation over the entire domain with the total heat flow rate (temperature difference) in convective heat transfer processes for both open and closed systems, we find that both the field synergy degree and the entransy dissipation rate are suitable for evaluating heat transfer performance. With the criterion of maximum field synergy degree, the FSPbased Euler’s equation is derived by the variational method, and thereafter compared to the one deduced from the EDEP. It indicates that both the FSP and the EDEP will obtain the best flow pattern for a given boundary temperature, regardless of the different forms of the governing equations of variables A and A’. However, for a prescribed heat flux boundary condition, since the field synergy degree over the entire domain keeps constant, the Euler’s equation based on the FSP, in this case, makes no contribution to heat transfer optimization. Next, we investigate the laminar heat transfer process in the air side of a fin-and-flat tube heat exchanger. For a prescribed temperature boundary, with the viscous dissipation rate increasing, both two optimization principles will make the Nu increase. Moreover, for the same dissipation rate, the optimization results based on the EDEP and the FSP are the same. However, for a prescribed heat flux boundary condition, only the optimized flow based on the EDEP enlarges the Nu, whereas the optimization based on the FSP makes no sense. Furthermore, a similar process in a foursquare cavity is also optimized and the same conclusion is obtained, which is well agreed with the theoretical analysis. In conclusion, the EDEP and the FSP are both suitable for the optimization of heat transfer to improve energy utilization performance, where the EDEP is superior due to its effectiveness in heat tranfer optimization with prescribed boundary heat fluxes. \end{document} |
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