A multi-scale homogenization approach for the effective thermal conductivity of dry lime–hemp concrete

2017 ◽  
Vol 11 (2) ◽  
pp. 179-189 ◽  
Author(s):  
T. Nguyen-Sy ◽  
A.D. Tran-Le ◽  
T. Nguyen-Thoi ◽  
T. Langlet
2016 ◽  
Vol 26 (3/4) ◽  
pp. 1157-1171 ◽  
Author(s):  
Sangbeom Cho ◽  
Venky Sundaram ◽  
Rao Tummala ◽  
Yogendra Joshi

Purpose – The functionality of personal mobile electronics continues to increase, in turn driving the demand for higher logic-to-memory bandwidth. However, the number of inputs/outputs supported by the current packaging technology is limited by the smallest achievable electrical line spacing, and the associated noise performance. Also, a growing trend in mobile systems is for the memory chips to be stacked to address the growing demand for memory bandwidth, which in turn gives rise to heat removal challenges. The glass interposer substrate is a promising packaging technology to address these emerging demands, because of its many advantages over the traditional organic substrate technology. However, glass has a fundamental limitation, namely low thermal conductivity (∼1 W/m K). The purpose of this paper is to quantify the thermal performance of glass interposer-based electronic packages by solving a multi-scale heat transfer problem for an interposer structure. Also, this paper studies the possible improvement in thermal performance by integrating a fluidic heat spreader or vapor chamber within the interposer. Design/methodology/approach – This paper illustrates the multi-scale modeling approach applied for different components of the interposer, including Through Package Vias (TPVs) and copper traces. For geometrically intricate and repeating structures, such as interconnects and TPVs, the unit cell effective thermal conductivity approach was used. For non-repeating patterns, such as copper traces in redistribution layer, CAD drawing-based thermal resistance network analysis was used. At the end, the thermal performance of vapor chamber integrated within a glass interposer was estimated by using an enhanced effective thermal conductivity, calculated from the published thermal resistance data, in conjunction with the analytical expression for thermal resistance for a given geometry of the vapor chamber. Findings – The limitations arising from the low thermal conductivity of glass can be addressed by using copper structures and vapor chamber technology. Originality/value – A few reports can be found on thermal performance of glass interposers. However thermal characteristics of glass interposer with advanced cooling technology have not been reported.


2016 ◽  
Vol 107 ◽  
pp. 127-134 ◽  
Author(s):  
S.T. Nguyen ◽  
A.D. Tran-Le ◽  
M.N. Vu ◽  
Q.D. To ◽  
O. Douzane ◽  
...  

2018 ◽  
Vol 35 (5) ◽  
pp. 2107-2123 ◽  
Author(s):  
Lucas Prado Mattos ◽  
Manuel Ernani Cruz ◽  
Julián Bravo-Castillero

Purpose The simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calculate an effective thermal conductivity for a multi-scale heterogeneous medium. Design/methodology/approach The methodology integrates the theory of reiterated homogenization with the finite element method, leading to a renewed calculation algorithm. Findings The effective thermal conductivity gain of the considered three-scale array relative to the two-scale array has been evaluated for several different values of the global volume fraction. For gains strictly above unity, the results indicate that there is an optimal local volume fraction for a maximum heat conduction gain. Research limitations/implications The present approach is formally applicable within the asymptotic limits required by the theory of reiterated homogenization. Practical implications It is expected that the present analytical-numerical methodology will be a useful tool to aid interpretation of the gain in effective thermal conductivity experimentally observed with some classes of heterogeneous multi-scale media. Originality/value The novel aspect of this paper is the application of the integrated algorithm to calculate numerical bulk effective thermal conductivity values for multi-scale heterogeneous media.


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