Introduction to the Slide Modeling Method for the Efficient Solution of Heat Conduction Calculations

Abstract

Determination of the maximum temperature and its location is the matter of the greatest importance in many technological and scientific engineering applications. In terms of numerical calculations of the heat conduction equation by using uniform mesh increments in space, large computational cost is sometimes countered. However, adaptive grid refinement method could be computationally efficient both in terms of accuracy and execution time. In this work, the numerical solution of the heat conduction equation based on the slide modeling method (SMM) is introduced. This method is based on a pre-determined mesh density approach which divides each homogeneous region into different slides and then assigns higher mesh point densities to slides of interest regarding their relative importance by performing some mathematical calculations. The importance of each region is determined by some formulated weighting factors which rely on the estimation of temperature profiles in all regions and slides. To investigate the accuracy and efficiency of the proposed method, a number of different case studies have been considered. The results all revealed the strength of the proposed SMM in comparison with the conventional method (based on uniform mesh point distribution).