Mathematical modelling for solving nonlinear heat diffusion problems of pavement spherical roads in Makkah

Abstract

Pavement temperature is one of the most important factors affecting the design and performance of roads. Actual pavement temperature is required to be considered in design standards for pavements roads which have spherical shapes. The heat distribution is highly influential in pavement structural design and have a large effect on indirect tensile stiffness modulus. This importance calls for special attention and interest in research to develop procedures for design and analysis that account for temperature considerations. However, temperatures at different depths in the pavement are difficult to measure. Therefore, a mathematical model for pavement temperature estimation from climatic data such as air temperature and solar radiation is presented. Maximum and minimum pavement temperatures are usually needed for design, evaluation and analysis of pavements. In this study, these temperatures are both calculated from the air temperatures.

Keywords:

• pavement roads
• composite media
• spherical coordinate
• integral transform method
• nonlinear problems

Acknowledgements

The authors would like to express their high appreciation to the referees of this paper for their critical review as well as their valuable comments that improved the paper to its present form.