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關于latex圖片插入出現(xiàn)的問題
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本人用ctex編輯一篇文檔，用的{cctart}模板編輯，編譯用的pdftex。在文檔中插入幾張圖片均能用pdf正常輸出，但在我用同樣的方法再插入一張圖片后，編譯沒有問題，可以打開pdf卻打不開，顯示錯誤：文檔打開時出錯，文件已損壞并無法修復。但我試著將插入圖片的位置調整一下后，又有可能正常輸出并打開，我想問下大神，這算怎么回事�。�？（應該不是我插入圖片的命令什么有問題，因為我之前插入的能正常輸出，我用同樣的方法在此基礎上在插入時出的錯！）非常感謝，希望大家能幫幫我！ 以下是我的源代碼 \documentclass[11pt]{cctart} \usepackage{latexsym,amssymb,amsmath} \usepackage{graphicx} \usepackage{epstopdf} \usepackage{subfigure} \usepackage{float} \usepackage{psfig} \setlength{\parindent}{0cm} %段落中第一行縮進設為12pt \setlength{\parskip}{3pt plus1pt minus2pt} %plus伸展值minus收縮值 \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*\\匯報人：李貴} \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 對流換熱的最優(yōu)化原則\\ \zihao{-4}\ziti{B} 2.1\quad 傳熱性能和場協(xié)同程度的關系\\ 對于無內熱源的不可壓流對流換熱過程，忽略粘性耗散，能量方程可以表示為： \[{\rho}c_pU\cdot{\nabla}T={\nabla}{\cdot}(\lambda{\nabla}T)~~(3)\] 對（3）式進行積分，忽略進口和出口的縱向熱傳導，并運用高斯定理有： \[\iiint_V{\rho}c_pU{\cdot}{\triangledown}TdV=\iiint_V{\rho}c_p\lvert{U}\rvert{\lvert{\nabla}T\rvert}cos{\beta}dV=\iint_S{\vec{n}}{\cdot}({\lambda{\nabla}T})dS~~(4)\] 引入以下無量綱參數： \[\bar{U}=\frac{U}{U_m},~~{\nabla}{\bar{T}}=\frac{{\nabla}T}{(T_m-T_b)/D}~~(5)\] 則（4）式可以化為： \[\iiint_{v_0}(\bar{U}{\cdot}{\nabla}{\bar{T}})d\vec{V}=\frac{Nu}{Repr}=Fc~~(6)\] $Fc$為場協(xié)同數，表示流體速度和溫度梯度在整個流場中的協(xié)同程度。從（6）式可以看出，對于給定入口流速，由于$Re$和$Pr$為常數 ，所以$Nu$隨$Fc$的增大而增大。即換熱性能越好。 \zihao{-4}\ziti{B} 2.2\quad 火積耗散與傳熱性能的關系\\ 在（3）式左右兩邊乘以溫度$T$，我們得到， \[U\cdot{\nabla}(\frac{1}{2}\rho{c_p}T^2)={\nabla}\cdot(\lambda{T}{\nabla}T)-\lambda\lvert{\nabla}T\rvert^2~~(8)\] 即， \[U\cdot{\nabla}G={\nabla}\cdot(\lambda{T}{\nabla}T)-\lambda\lvert{\nabla}T\rvert^2~~(9)\] 令$\phi_h=\iiint_v\lambda\lvert{\nabla}T\rvert^2dV$,可以作為不可逆的量度。 對（8）式在整個流場積分，并運用高斯定理，有： \[\phi_h=\iint_S{-q^{''}}T\cdot\vec{n}dS+\frac{\rho{c_p}U_{in}{T_{in}}^2}{2}-\frac{\rho{c_p}U_{out}{T_{out}}^2}{2}~~(10)\] 當邊界熱通量$q^{''}$給定時，（10）式可以表示為; \[\phi_h={-q^{''}}\cdot\vec{n}S\iint_S{\frac{T}{S}}dS+\frac{\rho{c_p}U_{in}{T_{in}}^2}{2}-\frac{\rho{c_p}U_{out}{T_{out}}^2}{2}~~(11)\] 因為流體吸收或釋放的熱量等于通過邊界轉移的熱量，所以（11）式可以進一步簡化為： \[\phi_h=Q（T_b-\frac{T_{in}+T_{out}}{2}）~~(12)\] 其中，$\frac{T_{in}+t_{out}}{2}$表示流體的平均溫度，$T_b$表示平均邊界溫度。 \[Q\delta({\Delta}T)=\delta(\phi_h)~~(13)\] 其中，${\Delta}T=T_b-\frac{T_{in}+T_{out}}{2}$表示溫差。 \\ 由（13）式可知，對于總邊界熱流量不變的情況，在熱傳遞區(qū)域，最小火積耗散率可以導出流體和邊界的最小 溫差。（the minimum entransy dissipation rate in the heat transfer domain leads to the least temperature difference between the fluid and the wall） 對于給定邊界溫度$T_b(T_b>T_{in})$,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。也就是說，當邊界溫度固定時，火積耗散最大導致熱流量最大 （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，如果對流傳熱發(fā)生在一個有內熱源的封閉系統(tǒng)，則，能量守恒方程可以表示為： \[{\rho}c_pU\cdot{\nabla}T={\nabla}{\cdot}(\lambda{\nabla}T)+q_v~~(16)\] 其中$q_v$表示熱源。假設只有一個邊界溫度是恒溫，其它邊界都是絕熱的，（16）式兩邊乘以T,有， \[\nabla\cdot{(\rho{c_p}UT^2/D)}-\frac{c_pT^2}{2}\nabla\cdot(\rho{U})=-\nabla\cdot{({\lambda}T{\nabla}T)}-{\lambda}\lvert{\nabla}T\rvert^2+q_vT~~(17)\] 對（17）式積分，并利用高斯公式和變分方法的，有， \[\phi_h=Q(T_f-T_b)~~(18)\] 其中$Q=q_vV$式總熱流量，$T_f$是平均溫度。這種情況，當 \[Q\delta(T_f)=\delta(\phi_h)~~(19)\] 從（19）式可知，在這種條件下，在腔中，最小火積耗散可以導致最小平均溫度。（it is clear that the minimum entransy dissipation in this condition leads to the minimum average temperature in the cavity.） 總的來說，在不同邊界條件下，最小火積耗散原則和最大火積耗散可以簡單的稱為EDEP，即火積耗散極值原理可以優(yōu)化傳熱性能。 （the extremumof entransy dissipation leads to the optimal heat transfer performance.） \zihao{-4}\ziti{B} 2.3\quad 基于歐拉方程的FSP\\ \[\Pi=\iiint_V\{{\rho}{c_p}U{\cdot}{\nabla}T+C_{\phi_m} +A[{\rho}{c_p}U\cdot{\nabla}T-{\nabla}T\cdot({\lambda}{\nabla}T)~~(21)] +B{\nabla}T\cdot(\rho{U})\}dV\] 由火積散極值原理得到的歐拉方程： \[\rho{U}\cdot{\nabla}U=-{\nabla}P+\mu{\nabla}^2U+(C_{\phi}A{\nabla}T+\rho{U}\cdot{\nabla}U)~~(29)\] \zihao{-4}\ziti{B} 2.4\quad 基于歐拉方程的EDEP（The EDEP-based Euler’s equation）\\ \[\Pi=\iiint_V\{{\lambda}{\nabla}T{\cdot}{\nabla}T+C^{'}_{\phi_m} +A^{'}[{\rho}{c_p}U\cdot{\nabla}T-{\nabla}T\cdot({\lambda}{\nabla}T)]+ B^{'}{\nabla}T\cdot(\rho{U})\}dV~~(30)\] \[C^{'}_{\phi}=\frac{\rho{c_p}}{2C^{'}}~~(33)\] \[F=C^{'}_{\phi}A^{'}{\nabla}T+\rho{U}\cdot{\nabla}U~~(34)\] 總的來說，場協(xié)同程度和火積耗散率兩個物理量不僅都可以作為評價傳熱性能的指標，而且都能指導我們通過變分法獲得 在約束條件下獲得最佳流場。\\ \zihao{4}\ziti{B} 3.\quad a fin-and-flat tube換熱器的優(yōu)化\\ \zihao{-4}\ziti{B} 3.1\quad 數值模型\\ \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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