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DOI | 10.1002/2017WR021040 |
Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion | |
Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T. | |
2017-11-01 | |
发表期刊 | WATER RESOURCES RESEARCH
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ISSN | 0043-1397 |
EISSN | 1944-7973 |
出版年 | 2017 |
卷号 | 53期号:11 |
文章类型 | Article |
语种 | 英语 |
国家 | USA |
英文摘要 | There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10(-7) relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes. |
英文关键词 | diffusion analytical solution heat transfer mass transfer fracture and matrix numerical simulation |
领域 | 资源环境 |
收录类别 | SCI-E |
WOS记录号 | WOS:000418736700072 |
WOS关键词 | CONVERGENT RADIAL DISPERSION ; FRACTURED POROUS-MEDIA ; MATRIX DIFFUSION ; CONTAMINANT TRANSPORT ; TRACER EXPERIMENTS ; POROSITY MODELS ; SINGLE FRACTURE ; FISSURED ROCKS ; CONDUCTION ; TIME |
WOS类目 | Environmental Sciences ; Limnology ; Water Resources |
WOS研究方向 | Environmental Sciences & Ecology ; Marine & Freshwater Biology ; Water Resources |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://119.78.100.173/C666/handle/2XK7JSWQ/21537 |
专题 | 资源环境科学 |
作者单位 | Lawrence Berkeley Natl Lab, Energy Geosci Div, Berkeley, CA 94720 USA |
推荐引用方式 GB/T 7714 | Zhou, Quanlin,Oldenburg, Curtis M.,Rutqvist, Jonny,et al. Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion[J]. WATER RESOURCES RESEARCH,2017,53(11). |
APA | Zhou, Quanlin,Oldenburg, Curtis M.,Rutqvist, Jonny,&Birkholzer, Jens T..(2017).Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion.WATER RESOURCES RESEARCH,53(11). |
MLA | Zhou, Quanlin,et al."Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion".WATER RESOURCES RESEARCH 53.11(2017). |
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