A thermal via has been used to enhance the heat transfer through the printed circuit board (PCB). Because the thermal conductivity of a dielectric material is very low, the array of metal vias is placed to make therma...A thermal via has been used to enhance the heat transfer through the printed circuit board (PCB). Because the thermal conductivity of a dielectric material is very low, the array of metal vias is placed to make thermal paths in the PCB. This paper describes the numerical analysis of the PCB having metal vias and focuses on the heat transfer characteristics under the nonisothermal boundary conditions. The mathematical model of the PCB has the metal vias between two metal sheets. Under 2nd and 3rd kinds of boundary conditions, the temperature distribution is obtained numerically by changing the design parameters. The discussion is also made on the effective thermal conductivity of the PCB. In industry, the use of effective thermal conductivity is convenient for thermal engineers because it simplifies the calculation process, that is, the composite board can be modeled as a homogeneous medium. From the numerical results, it is confirmed that the placement of metal sheets and the population of metal vias are important factors to dominate the heat transfer characteristics of the PCB. It is also shown that although the nonisothermal boundary conditions are applied at the boundary surface, the temperature difference between the heated and the cooled section is almost uniform when the metal vias are populated densely with the metal sheets. In this case, the effective thermal conductivity of the PCB is found to be the same irrespective of the boundary conditions, that is, whether the isothermal or the nonisothermal boundary conditions are applied.展开更多
In order to comply with the recent demand for downsizing of the electric equipment, the minia- turization and the improvement in heat transfer performance of a heat sink under natural air-cooling are increasingly requ...In order to comply with the recent demand for downsizing of the electric equipment, the minia- turization and the improvement in heat transfer performance of a heat sink under natural air-cooling are increasingly required. This paper describes the experimental and numerical investigations of heat sinks with miniature/micro pins and the effect of the pin size, pin height and the number of pins on heat transfer characteristics of heat sinks. Five types of basic heat sink models are investigated in this study. The whole heat transfer area of heat sinks having the different pin size, pin height and the number of pins respectively is kept constant. From a series of experiments and numerical analyses, it has been clarified that the heat sink temperature rises with increase in the number of pins. That is, the heat sink with miniaturized fine pins showed almost no effect on the heat transfer enhancement. This is because of the choking phenomenon occurred in the air space among the pin fins. Reflecting these results, it is confirmed that the heat transfer coefficient reduces with miniaturization of pins. Concerning the effects of the heat transfer area on the heat sink performance, almost the same tendency has been observed in other three series of large surface area, that is, higher pin height. Furthermore as a result of studying non-dimensional convection heat transfer performance, it was found that the relation between the Nusselt number (Nu) and the Rayleight number (Ra) is given by Nu = 0.16 Ra0.52.展开更多
By placing a sample between a heated and a cooled rod, a thermal conductivity of the sample can be evaluated easily with the assumption of a one-dimensional heat flow. However, a three-dimensional constriction/spreadi...By placing a sample between a heated and a cooled rod, a thermal conductivity of the sample can be evaluated easily with the assumption of a one-dimensional heat flow. However, a three-dimensional constriction/spreading heat flow may occur inside the rods when the sample is a composite having different thermal conductivities. In order to investigate the thermal resistance due to the constriction/spreading heat flow, the three-dimensional numerical analyses were conducted on the heat transfer characteristics of the rods. In the present analyses, a polymer-based composite board having thermal vias was sandwiched between the rods. From the numerical results, it was confirmed that the constriction/spreading resistance of the rods was strongly affected by the thermal conductivity of the rods as well as the number and size of the thermal vias. A simple equation was also proposed to evaluate the constriction/spreading resistance of the rods. Fairly good agreements were obtained between the numerical results and the calculated ones by the simple equation. Moreover, the discussion was also made on an effective thermal conductivity of the composite board evaluated with the heated and the cooled rod.展开更多
The 45。heat spreading angle is familiar among thermal designers. This angle has been used for thermal design of electronic devices, and provides a heat spreading area inside a board, e.g. printed circuit board, which...The 45。heat spreading angle is familiar among thermal designers. This angle has been used for thermal design of electronic devices, and provides a heat spreading area inside a board, e.g. printed circuit board, which is placed between a heat dissipating element and a relatively large heat sink. By using this angle, the heat transfer behavior can be estimated quickly without using high-performance computers. In addition, the rough design can be made easily by changing design parameters. This angle is effective in a practical situation;however, the discussion has not been made sufficiently on the applicability of the 45。heat spreading angle. In the present study, therefore, the extensive numerical investigation is conducted for the rational thermal design using the 45。heat spreading angle. The two-dimensional mathematical model of the board is considered;the center of the top is heated by a heat source while the bottom is entirely cooled by a heat sink. The temperature distribution is obtained by solving the heat conduction equation numerically with the boundary conditions. From the numerical results, the heat transfer behavior inside the board is shown and its relation with the design parameters is clarified. The heat transfer behavior inside the 45。heat spreading area is also evaluated. The applicability is moreover discussed on the thermal resistance of the board obtained by the 45。heat spreading angle. It is confirmed that the 45。heat spreading angle is applicable when the Biot number is large, and then the equations are proposed to calculate the Biot number index to use the 45。angle. Furthermore, the validity of the 45。heat spreading angle is also confirmed when the isothermal boundary condition is used at the cooled section of the board.展开更多
文摘A thermal via has been used to enhance the heat transfer through the printed circuit board (PCB). Because the thermal conductivity of a dielectric material is very low, the array of metal vias is placed to make thermal paths in the PCB. This paper describes the numerical analysis of the PCB having metal vias and focuses on the heat transfer characteristics under the nonisothermal boundary conditions. The mathematical model of the PCB has the metal vias between two metal sheets. Under 2nd and 3rd kinds of boundary conditions, the temperature distribution is obtained numerically by changing the design parameters. The discussion is also made on the effective thermal conductivity of the PCB. In industry, the use of effective thermal conductivity is convenient for thermal engineers because it simplifies the calculation process, that is, the composite board can be modeled as a homogeneous medium. From the numerical results, it is confirmed that the placement of metal sheets and the population of metal vias are important factors to dominate the heat transfer characteristics of the PCB. It is also shown that although the nonisothermal boundary conditions are applied at the boundary surface, the temperature difference between the heated and the cooled section is almost uniform when the metal vias are populated densely with the metal sheets. In this case, the effective thermal conductivity of the PCB is found to be the same irrespective of the boundary conditions, that is, whether the isothermal or the nonisothermal boundary conditions are applied.
文摘In order to comply with the recent demand for downsizing of the electric equipment, the minia- turization and the improvement in heat transfer performance of a heat sink under natural air-cooling are increasingly required. This paper describes the experimental and numerical investigations of heat sinks with miniature/micro pins and the effect of the pin size, pin height and the number of pins on heat transfer characteristics of heat sinks. Five types of basic heat sink models are investigated in this study. The whole heat transfer area of heat sinks having the different pin size, pin height and the number of pins respectively is kept constant. From a series of experiments and numerical analyses, it has been clarified that the heat sink temperature rises with increase in the number of pins. That is, the heat sink with miniaturized fine pins showed almost no effect on the heat transfer enhancement. This is because of the choking phenomenon occurred in the air space among the pin fins. Reflecting these results, it is confirmed that the heat transfer coefficient reduces with miniaturization of pins. Concerning the effects of the heat transfer area on the heat sink performance, almost the same tendency has been observed in other three series of large surface area, that is, higher pin height. Furthermore as a result of studying non-dimensional convection heat transfer performance, it was found that the relation between the Nusselt number (Nu) and the Rayleight number (Ra) is given by Nu = 0.16 Ra0.52.
文摘By placing a sample between a heated and a cooled rod, a thermal conductivity of the sample can be evaluated easily with the assumption of a one-dimensional heat flow. However, a three-dimensional constriction/spreading heat flow may occur inside the rods when the sample is a composite having different thermal conductivities. In order to investigate the thermal resistance due to the constriction/spreading heat flow, the three-dimensional numerical analyses were conducted on the heat transfer characteristics of the rods. In the present analyses, a polymer-based composite board having thermal vias was sandwiched between the rods. From the numerical results, it was confirmed that the constriction/spreading resistance of the rods was strongly affected by the thermal conductivity of the rods as well as the number and size of the thermal vias. A simple equation was also proposed to evaluate the constriction/spreading resistance of the rods. Fairly good agreements were obtained between the numerical results and the calculated ones by the simple equation. Moreover, the discussion was also made on an effective thermal conductivity of the composite board evaluated with the heated and the cooled rod.
文摘The 45。heat spreading angle is familiar among thermal designers. This angle has been used for thermal design of electronic devices, and provides a heat spreading area inside a board, e.g. printed circuit board, which is placed between a heat dissipating element and a relatively large heat sink. By using this angle, the heat transfer behavior can be estimated quickly without using high-performance computers. In addition, the rough design can be made easily by changing design parameters. This angle is effective in a practical situation;however, the discussion has not been made sufficiently on the applicability of the 45。heat spreading angle. In the present study, therefore, the extensive numerical investigation is conducted for the rational thermal design using the 45。heat spreading angle. The two-dimensional mathematical model of the board is considered;the center of the top is heated by a heat source while the bottom is entirely cooled by a heat sink. The temperature distribution is obtained by solving the heat conduction equation numerically with the boundary conditions. From the numerical results, the heat transfer behavior inside the board is shown and its relation with the design parameters is clarified. The heat transfer behavior inside the 45。heat spreading area is also evaluated. The applicability is moreover discussed on the thermal resistance of the board obtained by the 45。heat spreading angle. It is confirmed that the 45。heat spreading angle is applicable when the Biot number is large, and then the equations are proposed to calculate the Biot number index to use the 45。angle. Furthermore, the validity of the 45。heat spreading angle is also confirmed when the isothermal boundary condition is used at the cooled section of the board.
