کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
297659 511763 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions
موضوعات مرتبط
مهندسی و علوم پایه مهندسی انرژی مهندسی انرژی و فناوری های برق
پیش نمایش صفحه اول مقاله
Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions
چکیده انگلیسی

The separation of variables (SOV) method has recently been applied to solve time-dependent heat conduction problem in a multilayer annulus. It is observed that the transverse (radial) eigenvalues for the solution in polar (r-θ) coordinate system are always real numbers (unlike in the case of similar multidimensional Cartesian problems where they may be imaginary) allowing one to obtain the solution analytically. However, the SOV method cannot be applied when the boundary conditions and/or the source terms are time-dependent, for example, in a nuclear fuel rod subjected to time-dependent boundaries or heat sources. In this paper, we present an alternative approach using the finite integral transform method to solve the asymmetric heat conduction problem in a multilayer annulus with time-dependent boundary conditions and/or heat sources. An eigenfunction expansion approach satisfying periodic boundary condition in the angular direction is used. After integral transformation and subsequent weighted summation over the radial layers, partial derivative with respect to r-variable is eliminated and, first order ordinary differential equations (ODEs) are formed for the transformed temperatures. Solutions of ODEs are then inverted to obtain the temperature distribution in each layer. Since the proposed solution requires the same eigenfunctions as those in the similar problem with time-independent sources and/or boundary conditions—a problem solved using the SOV method—it is also “free” from imaginary eigenvalues.

Research highlights▶ Analytical method to solve asymmetric multi-layer heat conduction in an annulus. ▶ Applicable for time-dependent source terms and/or time-dependent boundary conditions. ▶ “Free” from imaginary eigenvalues.▶ Mathematical formulation and solution for an illustrative problem is presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nuclear Engineering and Design - Volume 241, Issue 1, January 2011, Pages 144–154
نویسندگان
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