JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (9): 83-90.doi: 10.6040/j.issn.1671-9352.0.2019.010

Previous Articles     Next Articles

Reconstruction of unknown surface heat flux from an internal temperature history

REN Jian-long   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Online:2019-09-20 Published:2019-07-30

PDF (PC)

329

Abstract: An inverse heat conduction problem is discussed by using the temperature observed at a certain point in the interior of the heater to recover the surface heat flux of heater wall. The forward problem is solved with the method of variable separation, then the original problem is transformed into Volterra integral equation of the second kind and the uniqueness of the solution of integral equation is proved. Numerical simulation is conducted with the direct solving method. The numerical results are carried out to confirm the feasible and effective of the aforementioned method,and the heat flux is recovered very well.

Key words: heat flux, inverse problem, Volterra integral equation, uniqueness, numerical simulation

CLC Number: 

  • O175.26
[1] ALIFANOV O M. Inverse heat transfer problems[M]. Berlin: Springer-Verlag, 1994.
[2] CHEN W L, YANG Y C. Inverse prediction of frictional heat flux and temperature in sliding contact with a protective strip by iterative regularization method[J]. Applied Mathematical Modelling, 2011, 35(6):2874-2886.
[3] ZHUO Lijun, YI Fajun, MENG Songhe. An inverse method for the estimation of a long-duration surface heat flux on a finite solid[J]. International Journal of Heat and Mass Transfer, 2016, 106:1087-1096.
[4] DUDA P. A general method for solving transient multidimensional inverse heat transfer problems[J]. International Journal of Heat and Mass Transfer, 2016, 93:665-673.
[5] UDAYRAJ, CHAKRABORTY S, GANGULY S, et al. Estimation of surface heat flux in continuous casting mould with limited measurement of temperature[J]. International Journal of Thermal Sciences, 2017, 118:435-447.
[6] WOOBURY K A, BECK J V. Estimation metrics and optimal regularization in a Tikhonov digital filter for the inverse heat conduction problem[J]. International Journal of Heat and Mass Transfer, 2013, 62:31-39.
[7] TIAN J M, CHEN B, ZHOU Z F. Methodology of surface heat flux estimation for 2D multi-layer mediums[J]. International Journal of Heat and Mass Transfer, 2017, 114:675-687.
[8] MYRICK J A, KEYHANI M, FRANKEL J I. Determination of surface heat flux and temperature using in-depth temperature data: experimental verification[J]. International Journal of Heat and Mass Transfer, 2017, 111:982-998.
[9] FABIOLA S, RODRIGUEZ D R P, RODRIGUEZ D R M, et al. Mathematical model for localised and surface heat flux of the human body obtained from measurements performed with a calorimetry minisensor[J]. Sensors, 2017, 17(12): 2749.
[10] SU J, HEWITT G F. Inverse heat conduction problem of estimating time-varying heat transfer coefficient[J]. Numerical Heat Transfer, 2004, 45(8):777-789.
[11] SU J, NETO A J S. Heat source estimation with the conjugate gradient method in inverse linear diffusive problems[J]. Journal of the Brazilian Society of Mechanical Sciences & Engineering, 2001, 23(3):321-334.
[12] ONYANGOA T T M, INGHAMA D B, LESNIC D. Reconstruction of heat transfer coefficients using the boundary element method[J]. Computers & Mathematics with Applications, 2008, 56(1):114-126.
[13] FAZELI H, MIRZAEI M. Shape identification problems on detecting of defects in a solid body using inverse heat conduction approach[J]. Journal of Mechanical Science and Technology, 2012, 26(11):3681-3690.
[14] LIU F B. Particle swarm optimization-based algorithms for solving inverse heat conduction problems of estimating surface heat flux[J]. International Journal of Heat and Mass Transfer, 2012, 55(7/8):2062-2068.
[15] LI Ran, HUANG Zhongwei, LI Gensheng, et al. A modified space marching method using future temperature measurements for transient nonlinear inverse heat conduction problem[J]. International Journal of Heat and Mass Transfer, 2016, 106:1157-1163.
[1] LI Hai-xia. Qualitative analysis of a diffusive predator-prey model with density dependence [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 54-61.
[2] ZHANG Wei-jie, WANG Xin-li, WANG Han-jie. Uniqueness of differential polynomials of meromorphic functions IM sharing a value [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 90-96.
[3] . Inverse spectral results for AKNS systems with partial information on the potentials [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 50-54.
[4] . Uniqueness of positive solutions of singular p-biharmonic equations with Hardy terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 75-80.
[5] WANG Su-yun, LI Yong-jun. Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 53-56.
[6] XIAO Xin-ling. Forward-backward stochastic differential equations on Markov chains [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 46-54.
[7] ZHEN Wei-wei, ZENG Jian, REN Jian-long. Time dependent parabolic inverse source problem based on variational theory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 61-71.
[8] CAO Wei-dong, DAI Tao, YU Jin-biao, WANG Xiao-hong, SHI An-feng. Improvement on the solution of pressure equation based on alternating direction in chemical flooding model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 88-94.
[9] ZHANG Tai-nian, LI Zhao-xing. Convergence analysis for inverse problems in a degenerate parabolic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 35-42.
[10] . Uniqueness of solution for singular boundary value problems of fourth-order differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 73-76.
[11] ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72.
[12] HU Pei-chu, WU Ai-di. Topics in L-functions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 1-15.
[13] CAI Chao. An inverse problem of identifying the coefficient in a Kolmogorov type equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 127-134.
[14] DONG Jian-wei, LOU Guang-pu, WANG Yan-ping. Uniqueness of stationary solutions to a simplified energy-transport model for semiconductors [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 37-41.
[15] WANG Xian-fei, JIANG Long, MA Jiao-jiao. Multidimensional backward doubly stochastic differential equations with generators of Osgood type [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 24-33.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] TANG Feng-qin1, BAI Jian-ming2. The precise large deviations for a risk model with extended negatively upper orthant dependent claim  sizes[J]. J4, 2013, 48(1): 100 -106 .
[2] QIU Tao-rong, WANG Lu, XIONG Shu-jie, BAI Xiao-ming. A granular computing approach for knowledge hiding[J]. J4, 2010, 45(7): 60 -64 .
[3] XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1. Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method[J]. J4, 2013, 48(4): 65 -71 .
[4] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[5] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[6] REN Min1,2, ZHANG Guang-hui1. Absorbing probabilities of random walks in an independent random  environment convergence in distribution on the half-line[J]. J4, 2013, 48(1): 93 -99 .
[7] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[8] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63 -67 .
[9] LI Min1,2, LI Qi-qiang1. Observer-based sliding mode control of uncertain singular time-delay systems#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 37 -42 .
[10] SHI Ai-ling1, MA Ming2*, ZHENG Ying2. Customer lifetime value and property with #br# homogeneous Poisson response[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 96 -100 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd