A mathematical model for the distribution of heat through pavement layers in Makkah roads

Pavement layers are the predominant type used in Saudi Arabian roads, it is necessary to have roads with excellent pavements from the structural and functional points of view. The heat distribution is highly influential in the pavement’s structural design and has a large effect on indirect tensile stiffness modulus (ITSM). In this study, heat distribution through all the layers of the pavement will be studied. The mathematical technique used in the present analysis is the parameter-group transformation, the linear transformation group approach is developed to solve the heat diffusion problems in the presence of thermal conductivity and heat capacity. These problems obeyed an unusual power law relation, subject to nonlinear boundary conditions due to radiation exchange at the interface according to the fourth power law. The group theoretic approach shrinks the number of independent variables by one, therefore a nonlinear ordinary differential equation is obtained instead of the given nonlinear partial differential. The Runge–Kutta shooting method is used to solve the resulting nonlinear ordinary differential equation to determine heat distribution in the pavement layers of “Makkah” roads.