Graphical Solution of the Transient Heat Transfer Problem


Dilsiz R., Devres Y. O.

International Conference on Numerical Analysis and Applied Mathematics, Psalidi, Greece, 16 - 20 September 2008, vol.1048, pp.855-858 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1048
  • City: Psalidi
  • Country: Greece
  • Page Numbers: pp.855-858

Abstract

In literature, both analytical and numerical solutions to the time-dependent multi-dimensional heat transfer problem can be found. Unfortunately, in order to apply these solution methods, fundamentals of differential equations and numerical analysis methods must be well known. These subjects are not satisfactorily covered in undergraduate level of engineering education, so that, alternative solutions such as reading values from charts (Heisler charts) are introduced. In this study, foremost problems in using graphic solution which are being followed by almost every textbook of heat transfer are discussed and misreading during application of these charts is highlighted. For this purpose, functions which analytically solve heat transfer equation are developed in numerical analysis tool (MATLAB). Furthermore, programs that will more accurately regenerate the charts of Heisler, with high-precision, which was drawn in 1947 with only one-term of the series expansion, were developed. To solve transient heat transfer problem, separation of variables method is employed for four main geometries (slab, semi-infinite slab, cylinder, and sphere) with three of the boundary conditions. Functions are coded in numerical analysis tool which will solve problems with high precision. In order to improve the access to the functions developed in numerical analysis tool and to have a more user-friendly interface, a web site is coded. By running MATLAB Web Server integrated to an Apache 2.1 HTTPD server with PHP 5.1, results of this study were made available online. A Web page for reading accurate data from Heisler charts was coded and values extracted by that tool were compared to the real values in order to express the errors made during chart reading. Comparison between the results of the functions developed and the examples on the common textbooks of heat transfer education are given. In this comparison, it was concluded that solutions with chart reading have errors up to 20%.