Periodic heat conduction in a solid homogeneous finite cylinder
ABSTRACT Analytic solution of the steady periodic, non-necessarily harmonic, heat conduction in a homogeneous cylinder of finite length and radius is given in term of Fourier transform of the fluctuating temperature field. The solutions are found for quite general boundary conditions (first, second and third kind on each surface) with the sole restriction of uniformity on the lateral surface and radial symmetry on the bases. The thermal quadrupole formalism is used to obtain a compact form of the solution that can be, with some exception, straightforwardly extended to multi-slab composite cylinders. The limiting cases of infinite thickness and infinite radius are also considered and solved.
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ABSTRACT: The radiant time series method (RTSM) takes advantages of the fact that design cooling load calculations are based on steady periodic excitations. The main difference between the RTSM and the other cooling load calculation methods is that the periodic response factors of the RTSM are restricted to calculating the conduction heat gain through building elements under periodic outdoor conditions, which simplifies the computational procedure significantly. It is vital to have a reliable method or procedure to accurately calculate the periodic response factors of various types of walls and roofs. In this study, a procedure, based on the frequency-domain regression (FDR) method, is developed to directly and accurately calculate the outside, across and inside periodic response factors of a multilayer wall or roof from its geometric and thermal properties. At first, a polynomial s-transfer function is established from the frequency characteristics of the wall or roof using the FDR method. The periodic response factors are then generated from the poles and residues of the polynomial s-transfer function. Computational tests show that the FDR method provides an accurate and hopefully better alternative procedure to calculate periodic response factors. Using this procedure, the periodic response factors of various representative wall and roof types are calculated and compared with those calculated by other conventional methods. Some results, particularly of the periodic response factors whose CTF coefficients tabulated in the ASHRAE Handbook are inaccurate, are presented and evaluated.International Journal of Thermal Sciences 01/2005; 44(4):382-392. · 2.47 Impact Factor
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ABSTRACT: The transient response of one-dimensional multilayered composite conducting slabs to sudden variations of the temperature of the surrounding fluid is analysed. The solution is obtained applying the method of separation of variables to the heat conduction partial differential equation. In separating the variables, the thermal diffusivity is retained on the side of the modified heat conduction equation where the time-dependent function is collected. This choice is the essence of composite medium analysis itself. In fact, it ‘naturally’ gives the relationship between the eigenvalues for the different regions and then yields a transcendental equation for the determination of the eigenvalues in a less complex form than the ones resulting from the application of traditional techniques. A new type of orthogonality relationship is developed by the author and used to obtain the final complete series solution. The errors, which develop when the higher terms in the series solution are neglected, are also investigated. Some calculated results of a numerical example are shown in a graphical form, by using dimensionless groups, and therefore discussed.International Journal of Heat and Mass Transfer. 01/2000;
- Journal of Heat Transfer-transactions of The Asme - J HEAT TRANSFER. 01/1996; 118(4).