Topic
Fourier number
About: Fourier number is a research topic. Over the lifetime, 637 publications have been published within this topic receiving 35296 citations. The topic is also known as: Fourier number.
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31 Dec 1959
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.
21,807 citations
TL;DR: In this article, the second law of thermodynamics is used as a basis for evaluating the irreversibility associated with simple heat transfer processes, such as heat augmentation techniques, heat exchanger design, and thermal insulation systems.
612 citations
TL;DR: In this article, an equation of phonon radiative transfer (EPRT) was developed which shows the correct limiting behavior for both purely ballistic and diffusive transport, and the solution of the EPRT for diamond thin films not only produces wall temperature jumps under ballistic transport but shows markedly different transient response from that of the Fourier law and the hyperbolic heat equation.
Abstract: Ballistic and diffusive phonon transport under small time and spatial scales are important in fast‐switching electronic devices and pulsed‐laser processing of materials. The Fourier law represents only diffusive transport and yields an infinite speed for heat waves. Although the hyperbolic heat equation involves a finite heat wave speed, it cannot model ballistic phonon transport in short spatial scales, which under steady state follows the Casimir limit of phonon radiation. An equation of phonon radiative transfer (EPRT) is developed which shows the correct limiting behavior for both purely ballistic and diffusive transport. The solution of the EPRT for diamond thin films not only produces wall temperature jumps under ballistic transport but shows markedly different transient response from that of the Fourier law and the hyperbolic heat equation even for predominantly diffusive transport. For sudden temperature rise at one film boundary, the results show that the Fourier law and the hyperbolic heat equat...
392 citations
TL;DR: In this article, the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out.
Abstract: The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.
385 citations