MODIFIED APPROXIMATE SOLUTION FOR GRAETZ AND LEVEQUE PROBLEMS FROM ADVANCINGFRONT THEORY

张国亮; 王绍亭

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MODIFIED APPROXIMATE SOLUTION FOR GRAETZ AND LEVEQUE PROBLEMS FROM ADVANCINGFRONT THEORY

更新时间：2025-12-16

- MODIFIED APPROXIMATE SOLUTION FOR GRAETZ AND LEVEQUE PROBLEMS FROM ADVANCINGFRONT THEORY
- CIESC Journal Issue 4, (1992)
- 作者机构：
  
  天津大学生物医学工程研究所,天津大学生物医学工程研究所天津300072,天津,300072
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Online First：25 August 1992，
  
  Published：25 August 1992
- 稿件说明：
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张国亮, 王绍亭. MODIFIED APPROXIMATE SOLUTION FOR GRAETZ AND LEVEQUE PROBLEMS FROM ADVANCINGFRONT THEORY[J]. CIESC Journal, 1992, (4).
DOI：

张国亮, 王绍亭. MODIFIED APPROXIMATE SOLUTION FOR GRAETZ AND LEVEQUE PROBLEMS FROM ADVANCINGFRONT THEORY[J]. CIESC Journal, 1992, (4). DOI：

摘要

1引言氧合器的开发设计，需要计算血液中O2的传质速率。一般地，由于趴在血液中溶解度的非线性特点，使得趴传质的数学模型为一非线性偏微分方程”，“。但在体外氧合装置中，血液的流道远大于单一红细胞尺寸，故可认为O南血红蛋自（Hb）的反应是瞬时的，据此可用可逆反应理论和前进边界理论“－“两种方法近似描述o。的溶解度曲线，进而求出方程的分析解。对于传质界面固定的膜式氧合器，宜应用前进边界理论，但其解仍为较复杂的级数形式。为简化数学处理，Stfoeve等”’提出了1个求解该模型的近似方法。但与精确解比较，其偏差较大（约15％）。本文对Stroeve的近似解法进行了修正，修正后的结果与精确解的偏差可减小到4．36％。

Abstract

The advancing front theory is an approximate solution for mass transfer of O2 within blood when the reaction of O2 with homoglobin can be assumed to be very fast. An approximate solution for the Graetz and Leveque problems from the advancing front theory is modified according to the analogy between momentum and mass transfer in this study. By substituting third order polynomial for linear relationship of O2 concentration profile in the saturated region

the deviation of the modified approximate solution from that of exact solution is decreased to 4.36% from Stroeves 15.1%.

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