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Forced cooling of underground electric power transmission lines, pt.2, Forced-cooled systems for oil-filled pipe-type cable circuits have recently been considered. In such systems the conduction resistance through the paper insulation of the cables is the limiting thermal resistance. Assuming bilateral symmetry, steady-state conditions, and two-dimensional heat transfer, a FORTRAN IV computer program was written to solve the heat conduction problem in the cable insulation for arbitrary configurations of a three-cable system. For a steel pipe, a cable system is most susceptible to overheating in the equilateral configuration with the three cables touching. Proximity effects are very significant in forced cooling, especially when cables are not provided with a copper tape under the insulation moisture seal assembly, accounting for as much as 21% of the total oil temperature rise between refrigeration stations. This figure, however, is reduced to 8% when 0.005 inch thick copper tape is present., Consolidated Edison Co. of New York

Forced cooling of underground electric power transmission lines, pt.2, Forced-cooled systems for oil-filled pipe-type cable circuits have recently been considered. In such systems the conduction resistance through the paper insulation of the cables is the limiting thermal resistance. Assuming bilateral symmetry, steady-state conditions, and two-dimensional heat transfer, a FORTRAN IV computer program was written to solve the heat conduction problem in the cable insulation for arbitrary configurations of a three-cable system. For a steel pipe, a cable system is most susceptible to overheating in the equilateral configuration with the three cables touching. Proximity effects are very significant in forced cooling, especially when cables are not provided with a copper tape under the insulation moisture seal assembly, accounting for as much as 21% of the total oil temperature rise between refrigeration stations. This figure, however, is reduced to 8% when 0.005 inch thick copper tape is present., Consolidated Edison Co. of New York

Systems of contacting spheres are common in engineering applications. For such systems, the heat transfer analysis can be quite complicated due to the complex geometrical contact arrangement. As such, most of the previous works have typically applied a porous medium approach, which is only valid for resolution of two to three orders of magnitude larger than the sphere. Thus, for applications requiring a finer spatial resolution, porous medium approach is generally not applicable. If direct solving of energy equation is used as an alternative method, a high computational power is required due to its required iteration operation for coupling the temperature solutions at the interfaces between spheres. In this present work, a new formulation was developed to provide sufficient fine spatial resolution with any given packing structure. The computational efficiency of this new formulation has been shown. Furthermore, an experimental setup was designed and built for studying the contact resistance between spheres. The applicability of the new formulation was demonstrated with determination of effective conductivity of different packings. In addition, the effects of the contact resistance and the packing structure on the effective conductivity of sphere packings were studies. By using the new formulation, the effective conductivity of any packing with given packing structure can be determined.

Systems of contacting spheres are common in engineering applications. For such systems, the heat transfer analysis can be quite complicated due to the complex geometrical contact arrangement. As such, most of the previous works have typically applied a porous medium approach, which is only valid for resolution of two to three orders of magnitude larger than the sphere. Thus, for applications requiring a finer spatial resolution, porous medium approach is generally not applicable. If direct solving of energy equation is used as an alternative method, a high computational power is required due to its required iteration operation for coupling the temperature solutions at the interfaces between spheres. In this present work, a new formulation was developed to provide sufficient fine spatial resolution with any given packing structure. The computational efficiency of this new formulation has been shown. Furthermore, an experimental setup was designed and built for studying the contact resistance between spheres. The applicability of the new formulation was demonstrated with determination of effective conductivity of different packings. In addition, the effects of the contact resistance and the packing structure on the effective conductivity of sphere packings were studies. By using the new formulation, the effective conductivity of any packing with given packing structure can be determined.

Systems of contacting spheres are common in engineering applications. For such systems, the heat transfer analysis can be quite complicated due to the complex geometrical contact arrangement. As such, most of the previous works have typically applied a porous medium approach, which is only valid for resolution of two to three orders of magnitude larger than the sphere. Thus, for applications requiring a finer spatial resolution, porous medium approach is generally not applicable. If direct solving of energy equation is used as an alternative method, a high computational power is required due to its required iteration operation for coupling the temperature solutions at the interfaces between spheres. In this present work, a new formulation was developed to provide sufficient fine spatial resolution with any given packing structure. The computational efficiency of this new formulation has been shown. Furthermore, an experimental setup was designed and built for studying the contact resistance between spheres. The applicability of the new formulation was demonstrated with determination of effective conductivity of different packings. In addition, the effects of the contact resistance and the packing structure on the effective conductivity of sphere packings were studies. By using the new formulation, the effective conductivity of any packing with given packing structure can be determined.

Numerical investigations have been performed to study transient heat conduction in composite materials. Macroscopic unsteady equations in porous media consisting of solids and fluids of different thermal properties were derived under the assumption of non-thermal equilibrium. The derivation leads a two-equation system which requires the closure modeling of tortuosity term and interfacial heat transfer term. The closure model proposed recently by Hsu (1997) has been extensively reviewed since it is the main base of this study. The closure coefficients were determined to demonstrate the dependencies on the media geometry and thermal property. A numerical scheme is developed to solve the two-equation model in one dimension. Parametric study has been presented with three sets of initial and boundary conditions to discuss the departure from local thermal equilibrium and the applicability of the two-equation model. A three time domain numerical scheme has been adopted to study transient phase-change problem for pure substance. A numerical method has been constructed to obtain the solution of temperature distribution as well as the growth of the mushy zone, in which the solid and liquid phases co-exist at a definite phase change temperature. It can be seen that excellent agreement is observed between present numerical results and those of early works for pure substance. The three time domain method has been extended for two equation model to investigate the problem of transient heat conduction with solid-liquid phase-change effect in composite materials containing of solid and fluid, where only fluid is identified as phase change material. Parametric simulations via a finite difference method have been directed towards the response of the phase-change process in a slab to an imposed surface temperature, having a uniform temperature with or without a time dependent sinusoidally varying perturbation. The effects of relevant parameters on the phase-change behavior are investi

Numerical investigations have been performed to study transient heat conduction in composite materials. Macroscopic unsteady equations in porous media consisting of solids and fluids of different thermal properties were derived under the assumption of non-thermal equilibrium. The derivation leads a two-equation system which requires the closure modeling of tortuosity term and interfacial heat transfer term. The closure model proposed recently by Hsu (1997) has been extensively reviewed since it is the main base of this study. The closure coefficients were determined to demonstrate the dependencies on the media geometry and thermal property. A numerical scheme is developed to solve the two-equation model in one dimension. Parametric study has been presented with three sets of initial and boundary conditions to discuss the departure from local thermal equilibrium and the applicability of the two-equation model. A three time domain numerical scheme has been adopted to study transient phase-change problem for pure substance. A numerical method has been constructed to obtain the solution of temperature distribution as well as the growth of the mushy zone, in which the solid and liquid phases co-exist at a definite phase change temperature. It can be seen that excellent agreement is observed between present numerical results and those of early works for pure substance. The three time domain method has been extended for two equation model to investigate the problem of transient heat conduction with solid-liquid phase-change effect in composite materials containing of solid and fluid, where only fluid is identified as phase change material. Parametric simulations via a finite difference method have been directed towards the response of the phase-change process in a slab to an imposed surface temperature, having a uniform temperature with or without a time dependent sinusoidally varying perturbation. The effects of relevant parameters on the phase-change behavior are investi

Numerical investigations have been performed to study transient heat conduction in composite materials. Macroscopic unsteady equations in porous media consisting of solids and fluids of different thermal properties were derived under the assumption of non-thermal equilibrium. The derivation leads a two-equation system which requires the closure modeling of tortuosity term and interfacial heat transfer term. The closure model proposed recently by Hsu (1997) has been extensively reviewed since it is the main base of this study. The closure coefficients were determined to demonstrate the dependencies on the media geometry and thermal property. A numerical scheme is developed to solve the two-equation model in one dimension. Parametric study has been presented with three sets of initial and boundary conditions to discuss the departure from local thermal equilibrium and the applicability of the two-equation model. A three time domain numerical scheme has been adopted to study transient phase-change problem for pure substance. A numerical method has been constructed to obtain the solution of temperature distribution as well as the growth of the mushy zone, in which the solid and liquid phases co-exist at a definite phase change temperature. It can be seen that excellent agreement is observed between present numerical results and those of early works for pure substance. The three time domain method has been extended for two equation model to investigate the problem of transient heat conduction with solid-liquid phase-change effect in composite materials containing of solid and fluid, where only fluid is identified as phase change material. Parametric simulations via a finite difference method have been directed towards the response of the phase-change process in a slab to an imposed surface temperature, having a uniform temperature with or without a time dependent sinusoidally varying perturbation. The effects of relevant parameters on the phase-change behavior are investi

Sintering is a versatile process of powder metallurgy. It is typical for processing materials with high melting point such as ceramics. However, there exists a significant gap between the existing sintering theory and practical application. Consideration of the heating process is a crucial part of this gap. The underlying heat transfer analysis is tremendously complex. Since conduction is the dominant mode at the initial phase of the heating process, and is also the mode which always exists within any solid medium, the first step of the analysis is the study of heat conduction. In this work, the greenware is considered as a packing of spheres with finite contact areas. The objective of this work is to develop the fundamental ground for computing the transient temperature solution of conduction among spheres which are packed into contact. A finite volume formulation was developed for the investigation of computing the bulk temperature of individual spheres within a packing using thermal constriction resistance. The correlations were presented for the required constriction resistance. In addition, an artificial instantaneous diffusion effect was found with the transient computation of bulk temperature. As a result, a new governing equation was proposed and shown to be applicable for simple packed sphere system. The correlations for the required parameters for this new equation, such as thermal constriction capacitance and characteristic time, were presented as well. Furthermore, a numerical algorithm was developed for providing high computational efficiency with speed-up in the order of thousand which is generally greater than most existing methods.

Sintering is a versatile process of powder metallurgy. It is typical for processing materials with high melting point such as ceramics. However, there exists a significant gap between the existing sintering theory and practical application. Consideration of the heating process is a crucial part of this gap. The underlying heat transfer analysis is tremendously complex. Since conduction is the dominant mode at the initial phase of the heating process, and is also the mode which always exists within any solid medium, the first step of the analysis is the study of heat conduction. In this work, the greenware is considered as a packing of spheres with finite contact areas. The objective of this work is to develop the fundamental ground for computing the transient temperature solution of conduction among spheres which are packed into contact. A finite volume formulation was developed for the investigation of computing the bulk temperature of individual spheres within a packing using thermal constriction resistance. The correlations were presented for the required constriction resistance. In addition, an artificial instantaneous diffusion effect was found with the transient computation of bulk temperature. As a result, a new governing equation was proposed and shown to be applicable for simple packed sphere system. The correlations for the required parameters for this new equation, such as thermal constriction capacitance and characteristic time, were presented as well. Furthermore, a numerical algorithm was developed for providing high computational efficiency with speed-up in the order of thousand which is generally greater than most existing methods.

Sintering is a versatile process of powder metallurgy. It is typical for processing materials with high melting point such as ceramics. However, there exists a significant gap between the existing sintering theory and practical application. Consideration of the heating process is a crucial part of this gap. The underlying heat transfer analysis is tremendously complex. Since conduction is the dominant mode at the initial phase of the heating process, and is also the mode which always exists within any solid medium, the first step of the analysis is the study of heat conduction. In this work, the greenware is considered as a packing of spheres with finite contact areas. The objective of this work is to develop the fundamental ground for computing the transient temperature solution of conduction among spheres which are packed into contact. A finite volume formulation was developed for the investigation of computing the bulk temperature of individual spheres within a packing using thermal constriction resistance. The correlations were presented for the required constriction resistance. In addition, an artificial instantaneous diffusion effect was found with the transient computation of bulk temperature. As a result, a new governing equation was proposed and shown to be applicable for simple packed sphere system. The correlations for the required parameters for this new equation, such as thermal constriction capacitance and characteristic time, were presented as well. Furthermore, a numerical algorithm was developed for providing high computational efficiency with speed-up in the order of thousand which is generally greater than most existing methods.

Different models are proposed to evaluate the stagnant thermal conductivity of some 2D and 3D spatially periodic porous media. Based on a lumped-parameter model, algebraic expressions of the proposed geometries are obtained. The geometries under consideration include arrays of touching and non-touching in-line square, elliptic cylinders (2D), the touching and non- touching in-line cubes (3D) as well as in-line ellipsoids (3D) with connecting bars. A comparison of results based on these algebraic expressions with existing numerical solutions and experimental results shows that they are in excellent agreement. A modified Zehner-Schlunder model is proposed for calculation of the stagnant thermal conductivity of porous medium with spatially periodic structures. The modified model takes into consideration of finite contact area between spheres in a packed-sphere bed. It is shown that results based on the modified model is in better agreement with experimental data than those based on the original Zehner- SchIunder model, especially at high solid/fluid thermal conductivity ratios. By applying the lumped parameter model, algebraic expression of the stagnant thermal conductivity of a network of waived porous fibers are obtained. The geometry of the network includes parallel straight porous fibers aligning perpendicularly in different layers with small connecting bars. The results show good agreement with experimental data.

Different models are proposed to evaluate the stagnant thermal conductivity of some 2D and 3D spatially periodic porous media. Based on a lumped-parameter model, algebraic expressions of the proposed geometries are obtained. The geometries under consideration include arrays of touching and non-touching in-line square, elliptic cylinders (2D), the touching and non- touching in-line cubes (3D) as well as in-line ellipsoids (3D) with connecting bars. A comparison of results based on these algebraic expressions with existing numerical solutions and experimental results shows that they are in excellent agreement. A modified Zehner-Schlunder model is proposed for calculation of the stagnant thermal conductivity of porous medium with spatially periodic structures. The modified model takes into consideration of finite contact area between spheres in a packed-sphere bed. It is shown that results based on the modified model is in better agreement with experimental data than those based on the original Zehner- SchIunder model, especially at high solid/fluid thermal conductivity ratios. By applying the lumped parameter model, algebraic expression of the stagnant thermal conductivity of a network of waived porous fibers are obtained. The geometry of the network includes parallel straight porous fibers aligning perpendicularly in different layers with small connecting bars. The results show good agreement with experimental data.

Different models are proposed to evaluate the stagnant thermal conductivity of some 2D and 3D spatially periodic porous media. Based on a lumped-parameter model, algebraic expressions of the proposed geometries are obtained. The geometries under consideration include arrays of touching and non-touching in-line square, elliptic cylinders (2D), the touching and non- touching in-line cubes (3D) as well as in-line ellipsoids (3D) with connecting bars. A comparison of results based on these algebraic expressions with existing numerical solutions and experimental results shows that they are in excellent agreement. A modified Zehner-Schlunder model is proposed for calculation of the stagnant thermal conductivity of porous medium with spatially periodic structures. The modified model takes into consideration of finite contact area between spheres in a packed-sphere bed. It is shown that results based on the modified model is in better agreement with experimental data than those based on the original Zehner- SchIunder model, especially at high solid/fluid thermal conductivity ratios. By applying the lumped parameter model, algebraic expression of the stagnant thermal conductivity of a network of waived porous fibers are obtained. The geometry of the network includes parallel straight porous fibers aligning perpendicularly in different layers with small connecting bars. The results show good agreement with experimental data.