Wärme - und Stoffübertragung

, Volume 23, Issue 4, pp 229–233 | Cite as

Approximate solution of nonlinear transient heat conduction in one dimension

  • S. P. Venkateshan
  • O. Solaiappan


Three approximate methods, viz. the Heat Balance Integral method (HBI), the Modified Heat Balance Integral method (MHBI) and the Double Integral Method (DIM) in combination with hybrid profiles (HP - consisting of an exponential and polynomial) are evaluated for relative merits in solving the onedimensional heat diffusion equation. Applications to two linear test problems (TP1 - semi-infinite solid with constant heat flux at its boundary, TP 2 - semi-infinite solid with step change in its surface temperature) yield the HP-MHBI as the most desirable combination. Applications to nonlinear problems show that these combinations are ideally suited for obtaing reliable and accurate appoximate solutions.


Heat Flux Diffusion Equation Step Change Relative Merit Constant Heat 
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Näherungslösung von eindimensionaler nicht linearer transienter Wärmeleitung


Es wurden drei Näherungsmethoden, die Heat Balance Integral-Methode (HBI), die Modified Heat Balance IntegralMethode (MHBI) und die Double Integral-Methode (DIM) in Verbindung mit hybriden Profilen (HP - bestehend aus Exponentialund Polynomfunktionen) ausgewählt, um die eindimensionale Wärmediffusionsgleichung zu lösen. Anwendungen auf zwei lineare Testprobleme (TP 1 - halb-unendlicher Festkörper mit konstantem Wärmestrom an dessen Grenze, TP2 - halb-unendlicher Festkörper mit sprunghaftem Wechsel der Oberflächentemperatur) ergaben, daß die HP-MHBI-Methode die erwünschte Kombination darstellt. Anwendungen auf nichtlineare Probleme zeigen, daß diese Kombination ideal für das Erzielen zuverlässiger und aussagekräftiger Näherungslösungen ist.


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • S. P. Venkateshan
    • 1
  • O. Solaiappan
    • 1
  1. 1.Regional Sophisticated Instrumentation Centre and Department of Mechanical EngineeringIndian Institute of TechnologyMadrasIndia

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