Abstract
Boundary conditions of high kinds (fourth and sixth kind) as defined by Carslaw and Jaeger are used in this work to model the thermal behavior of perfect conductors when involved in multi-layer transient heat conduction problems. In detail, two- and three-layer configurations are analyzed. In the former, a thin layer modeled as a lumped body is subject to a surface heat flux on the front side while it is in perfect (fourth kind) or in imperfect (sixth kind) thermal contact with a semi-infinite or finite body on the back side. When dealing with a semi-infinite body in imperfect contact, the temperature solution is derived by means of the Laplace transform method. Green’s function approach is also used but for solving the companion case of a finite body in perfect contact with the thin film. In the latter, a thin layer with internal heat generation is located between two semi-infinite or finite bodies in perfect/imperfect contact. For the sake of thermal symmetry, such a three-layer structure reduces to a two-layer configuration. Results are given in both tabular and graphical forms and show the effect of heat capacity and thermal resistance on the temperature distribution of conductive layers.
Highlights
Two or three-layer structures are used in a number of applications in engineering, such as in the field of thermoplastic shaping of polymers [1] and in the estimation of the thermal properties of solid materials [2,3]
One of these is the fourth kind (Carslaw) boundary condition [4] which takes the thermal capacity of the thin layer into account; it derives from the application of the first law of thermodynamics to the thin layer
The notation X40B1T00 denotes a one dimensional transient heat conduction problem concerning a rectangular semi-finite body in perfect contact with a thin layer at the surface x = 0 where a jump in heat flux is applied; T00 stands for a zero initial temperature for both layers
Summary
Two or three-layer structures are used in a number of applications in engineering, such as in the field of thermoplastic shaping of polymers [1] and in the estimation of the thermal properties of solid materials [2,3]. In order to identify which conductive problem is analyzed, the numbering system devised in [11] is used According to this notation the addressed problems may be listed as: (1) X40B1T00 for the case of a thin layer in perfect thermal contact with a semi-infinite body; (2) X60B1T00 when the contact between them is imperfect;. The notation X40B1T00 denotes a one dimensional transient heat conduction problem concerning a rectangular (by the “X”) semi-finite body (by the “0” in the “X40”) in perfect contact with a thin layer at the surface x = 0 (fourth kind boundary condition by the “4” in “X40”) where a jump in heat flux is applied (by the B1); T00 stands for a zero initial temperature for both layers. Three-layer structures involving a thin layer with internal heat generation, located between two semi-infinite bodies or two finite plates (slabs for short) are discussed
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