حل تحلیلی انتقال حرارت در پوسته‌های مخروطی کامپوزیتی ناهمگن با ضرایب هدایت وابسته به دما

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی مکانیک دانشگاه صنعتی شاهرود

2 دانشیار دانشکده مهندسی مکانیک دانشگاه صنعتی شاهرود

چکیده

در این مقاله، برای اولین بار یک حل تحلیلی برای انتقال حرارت در پوسته‌های مخروطی کامپوزیتی ناهمگن وابسته به دما ارائه شده است. هندسه پوسته به‌طور کامل مخروطی شکل فرض شده است و الیاف به دور جسم، در جهات دلخواه پیچانده شده‌اند. به­منظور دستیابی به کلی‌ترین حل، شرایط مرزی حرارتی اعمال شده به صورت کلی در پایه پوسته و همچنین اثرات انتقال حرارت هدایتی، جابجایی با جریان سیال اطراف و تشعشع )صورت تقریبی تشعشع( در مرزها مدل شده‌اند. ناهمگن بودن در مسئله حاضر ناشی از وابستگی ضریب انتقال حرارت هدایتی به دما است. بنابراین می‌بایست، معادله انتقال حرارت را ابتدا با استفاده از تبدیل کیرشهف به معادله قابل حل به کمک سری انتگرالی محدود تبدیل کرد، سپس به کمک این تبدیل، معادله دیفرانسیل با مشتقات جزئی به یک معادله دیفرانسیل معمولی مبدل می‌گردد. درنهایت معادله دیفرانسیل حاصل به کمک روش توابع گرین قابل حل است. در آخر با اعمال معکوس تبدیل انتگرالی محدود و معکوس تبدیل کیرشهف توزیع دمای ناهمگن بدست آید. حل حاضر بر اساس مقایسه نتایج حل تحلیلی با حل عددی به روش مرتبه دوم تفاضلات محدود اعتبارسنجی شده است. مفروضات این مسئله به­گونه­ای انتخاب گردیده که  قابلیت حل حاضر برای رفع مشکلات صنعتی درزمینه تولید مخازن تحت فشار مخروطی کامپوزیتی مشخص گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analytical Solution of the Heat Transfer in Heterogeneous Composite Conical Shells with Temperature Dependent Conduction Coefficients

نویسندگان [English]

  • Babak Erfan Manesh 1
  • Mohammad Mohsen Shahmardan 2
  • Mahmood Norouzi 2
1 MSc student, Faculty of mechanical engineering, Shahrood university of technology
2 Associated professor, Faculty of mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
چکیده [English]

This paper presents an analytical solution for heat transfer in heterogeneous composite conical shells with temperature dependent conduction coefficients for the first time. The geometry of the shell is completely conical shaped and the fibers are winded around the laminate in the desired direction. In order to achieve the most general solution, the general boundary condition is considered  at the basis of shell and the effect of heat convection resulted from flow motion around the body and different kinds of non-axisymmetric radiative heat flux at the outer side of the shell is modeled. The heterogeneous effect in this case is the results of the dependency in conduction heat transfer coefficient on temperature. Therefore, the heat transfer equation should first be transformed using the Kirchhoff transform to a solvable equation using integral transformation, then, the partial differential equation becomes an ordinary differential equation Fourier transformation. Finally, the transformed differential equation can be solved Green’s functions. In the end, the reversal integral transformation and reversal Kirchhoff conversion are applied to obtain heterogeneous temperature distribution. Validation of this analytical solution is performed by comparing the analytical results with the solution of second-order finite difference method and some applied cases are considered to investigate the capability of current solution for solving the industrial problems in the production of composite conical pressure vessels.

کلیدواژه‌ها [English]

  • Analytical solution
  • Composite conical shell
  • Heterogeneous heat transfer
  • Integral transformation
  • Green functions
[1]  C.T. Herakovich, Mechanics of composites: a historical review, Mechanics Research Communications, 41 (2012) 1-20.
[2]  Z.-S. Guo, S. Du, B. Zhang, Temperature field of thick thermoset composite laminates during cure process, Composites science and technology, 65(3-4) (2005) 517- 523.
[3]  T. Behzad, M. Sain, Finite element modeling of polymer curing in natural fiber reinforced composites, Composites Science and Technology, 67(7-8) (2007) 1666-1673.
[4]  V. Antonucci, M. Giordano, K.-T. Hsiao, S.G. Advani, A methodology to reduce  thermal  gradients  due  to  the exothermic reactions in composites processing, International Journal of Heat and Mass Transfer, 45(8) (2002) 1675-1684.
[5]  A. Gilbert, K. Kokini, S. Sankarasubramanian, Thermal fracture of zirconia–mullite composite thermal barrier coatings under thermal shock: A numerical study, Surface and Coatings Technology, 203(1-2) (2008) 91-98.
[6]  A. Gilbert, K. Kokini, S. Sankarasubramanian, Thermal fracture of zirconia–mullite composite thermal barrier coatings under thermal shock: An experimental study, Surface and Coatings Technology, 202(10) (2008) 2152-2161.
 [7] I. Dlouhy, Z. Chlup, D. Boccaccini, S. Atiq, A. Boccaccini, Fracture behaviour of hybrid glass matrix composites: thermal ageing effects, Composites Part A: Applied Science and Manufacturing, 34(12) (2003) 1177-1185.
[8] F. Wang, Q. Hua, C.-S. Liu, Boundary function method for inverse geometry problem in two-dimensional anisotropic heat conduction equation, Applied Mathematics Letters, 84 (2018) 130-136.
[9]  F. Wang, W. Chen, W. Qu, Y. Gu, A BEM formulation in conjunction with parametric equation approach for three- dimensional Cauchy problems of steady heat conduction, Engineering Analysis with Boundary Elements, 63 (2016) 1-14.
[10]  Y. Gu, X. He, W. Chen, C. Zhang, Analysis of three- dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method, Computers & Mathematics with Applications, 75(1) (2018) 33-44.
 [11] I. Dülk, T. Kovácsházy, Steady-state heat conduction in multilayer bodies: An analytical solution and simplification of the eigenvalue problem, International Journal of Heat and Mass Transfer, 67 (2013) 784-797.
[12] O.O. Onyejekwe, Heat conduction in composite media: a boundary integral approach, Computers & chemical engineering, 26(11) (2002) 1621-1632.
[13] J. Miller, P. Weaver, Temperature profiles in composite plates subject to time-dependent complex boundary conditions, Composite Structures, 59(2) (2003) 267-278.
[14] S. Singh, P.K. Jain, Analytical solution to transient heat conduction in polar coordinates  with  multiple  layers  in radial direction, International Journal of Thermal Sciences, 47(3) (2008) 261-273.
[15] M. Kayhani, M. Norouzi, A.A. Delouei, A general analytical solution for heat conduction in cylindrical multilayer composite laminates, International Journal of Thermal Sciences, 52 (2012) 73-82.
[16] A.A. Delouei, M. Kayhani, M. Norouzi, Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates, International Journal of Heat and Mass Transfer, 55(15- 16) (2012) 4427-4436.
[17] M. Norouzi, A.A. Delouei, M. Seilsepour, A general exact solution for heat conduction in multilayer spherical composite laminates, Composite Structures, 106 (2013) 288-295.
[18] A.A. Delouei, M. Norouzi, Exact analytical solution for unsteady heat conduction in fiber-reinforced spherical composites under the general boundary conditions, Journal of Heat Transfer, 137(10) (2015) 101701.
[19]  J. Mahishi, R. Chandra, M. Murthy, Transient heat conduction analysis of laminated composite nose cone, Journal of Aeronautical Society of India, 32 (1980) 77-84.
 [20] S. Ray, A. Loukou, D. Trimis, Evaluation of heat conduction through truncated conical shells, International Journal of Thermal Sciences, 57 (2012) 183-191.
[21] M. Norouzi, H. Rahmani, On exact solutions for anisotropic heat conduction in composite conical shells, International Journal of Thermal Sciences, 94 (2015) 110-125.
[22] M. Norouzi, H. Rahmani, An exact analysis for transient anisotropic heat conduction in truncated composite conical shells, Applied Thermal Engineering, 124 (2017) 422-431.
[23] V.S. Arpaci, Conduction heat transfer, Addison-Wesley, 1966.
[24] Z.H. Khan, R. Gul, W.A. Khan, Effect of variable thermal conductivity on heat transfer from a hollow sphere with heat generation using homotopy perturbation method, in: ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences, American Society of Mechanical Engineers, 2008, pp. 301-309.
[25] C.W. Ohlhorst, W.L. Vaughn, P.O. Ransone, H.-T. Tsou, Thermal conductivity database of various structural carbon-carbon composite materials, NASA Technical Memorandum, (1997).
[26] T. Myint-U, L. Debnath, Linear partial differential equations for scientists and engineers, Springer Science & Business Media, 2007.
[27] J.R. Howell, M.P. Menguc, R. Siegel, Thermal radiation heat transfer, CRC press, 2015.