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Abstract

Advancements in Civil Engineering & Technology

Analytical Solutions of a Conduction Problem with Two Different Kinds of Boundary Conditions

  • Open or Close Zhongzhi Fu2*, Qiming Zhong1 and Shengshui Chen2

    1Department Geotechnical Engineering, Nanjing Hydraulic Research Institute, China

    2Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dams, Ministry of Water Resource, China

    *Corresponding author: Zhongzhi Fu, Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dams, Ministry of Water Resource, China

Submission: May 30, 2018; Published: August 28, 2018

DOI: 10.31031/ACET.2018.02.000532

ISSN 2639-0574
Volume2 Issue2

Abstract

A heat transfer problem was taken as an example to provide the analytical solutions of a one-dimensional conduction problem with two different kinds of boundary conditions. The theoretical solutions were obtained by using the method of separation of variables for solving partial differential equations. Temperature distribution in two simple cases were studied using the analytical solutions and were compared with corresponding numerical results. Reliability of the analytical results were shown by their excellent agreement with those numerical ones. The solutions presented in this note can be used for the verification of new numerical algorithms.

Keywords: Heat transfer; Conduction problem; Analytical solution; Boundary condition

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