Semi-Analytical Solution of the Graetz Problem With Uniform Wall Heat Flux Utilizing the Transversal Method of Lines

被引:3
|
作者
Campo, Antonio [1 ]
Arici, Muesluem [2 ]
机构
[1] Univ Vermont, Dept Mech Engn, Burlington, VT 05405 USA
[2] Kocaeli Univ, Dept Mech Engn, Umuttepe Campus, TR-41380 Kocaeli, Turkey
来源
关键词
Passive solar - Heat flux - Ordinary differential equations - Solar heating;
D O I
10.1115/1.4045754
中图分类号
O414.1 [热力学];
学科分类号
摘要
This study addresses the second Graetz problem with prescribed wall heat flux employing the transversal method of lines (TMOL), which deviates significantly from the traditional mathematical procedures employed in the past. The wall heat flux is customarily provided by electrical, radiative or solar heating in engineering applications. The TMOL transforms the governing two-dimensional energy equation with temperature-invariant thermo-physical properties into a sequence of adjoint ordinary differential equations of second order with the radial variable as the independent variable. The singular feature in those equations is the embedded axial variable interval. For the implementation of TMOL, a special computational domain consists in a condensed set of transversal lines displayed in the cross section of the tube. An approximate, semi-analytical temperature distribution is obtained with the solution of the first adjoint ordinary differential equation of second order, which is expressed in terms of the Kummer function of first kind M(a,b,c). From here, the approximate, semi-analytical wall and center temperature distributions exhibit excellent quality because the two compare favorably with the exact, analytical wall and center temperature distributions given by the classical Graetz infinite series. As a beneficial consequence, usage of the second adjoint ordinary differential equation of second order having more complex structure becomes unnecessary.
引用
收藏
页数:5
相关论文
共 50 条
  • [31] On the computation of moving mass/beam interaction utilizing a semi-analytical method
    Ali Nikkhoo
    Ali Farazandeh
    Mohsen Ebrahimzadeh Hassanabadi
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016, 38 : 761 - 771
  • [32] A semi-analytical locally transversal linearization method for non-linear dynamical systems
    Roy, D
    Ramachandra, LS
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2001, 51 (02) : 203 - 224
  • [33] A semi-analytical model of heat transfer and pressure drop in annular flow regime for flow boiling in a horizontal microtube at uniform heat flux
    Younes, Amen
    Hassan, Ibrahim
    Kadem, Lyes
    TRANSACTIONS OF THE CANADIAN SOCIETY FOR MECHANICAL ENGINEERING, 2020, 44 (03) : 362 - 384
  • [34] Semi-analytical solution for fully developed forced convection in metal-foam filled tube with uniform wall temperature
    ZHANG Jia Jie
    QU Zhi Guo
    XU Hui Jin
    TAO Wen Quan
    Science China(Technological Sciences), 2014, 57 (12) : 2487 - 2499
  • [35] Semi-Analytical Solution for a Multi-objective TEAM Benchmark Problem
    Karban P.
    Pánek D.
    Orosz T.
    Doležel I.
    Periodica polytechnica Electrical engineering and computer science, 2021, 65 (02): : 84 - 90
  • [36] A semi-analytical solution for a newsboy problem with mid-period replenishment
    Lau, HS
    Lau, AHL
    JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, 1997, 48 (12) : 1245 - 1253
  • [37] Semi-analytical solution for fully developed forced convection in metal-foam filled tube with uniform wall temperature
    JiaJie Zhang
    ZhiGuo Qu
    HuiJin Xu
    WenQuan Tao
    Science China Technological Sciences, 2014, 57 : 2487 - 2499
  • [38] Semi-analytical solution for fully developed forced convection in metal-foam filled tube with uniform wall temperature
    ZHANG Jia Jie
    QU Zhi Guo
    XU Hui Jin
    TAO Wen Quan
    Science China(Technological Sciences), 2014, (12) : 2487 - 2499
  • [39] Semi-analytical solution for fully developed forced convection in metal-foam filled tube with uniform wall temperature
    Zhang JiaJie
    Qu ZhiGuo
    Xu HuiJin
    Tao WenQuan
    SCIENCE CHINA-TECHNOLOGICAL SCIENCES, 2014, 57 (12) : 2487 - 2499