The building sector accumulates approximately a third of the final energy consumption. Consequently, the improvement of the energy efficiency in buildings has become an essential ins trument in the energy policies to ensure the energy supply in the mid to long term moreover is the mos t cos t-effective s trategy available for reducing carbon dioxide emissions This paper is s tudying the main objectives for an effective sus tainable building taking into account the environmental sus tainability aspect, where it has introduced the main principles for developing building concept and the governor concepts for this development for forming sus tainable building skins, also it is focusing on the different techniques in terms of natural ventilation, shading techniques, and energy conservation and its role in enhancing the internal environment. The main objective of the paper is to investigate the impact of different ventilation strategies that can be implemented in new and exis ting buildings in hot climates So that it can reduce the amount of energy needed for building and sustainability in this climate.

In this paper group-invariant properties of the Dym equation are studied. Lie symmetries are given and some group-invariant solutions are found with the use of similarity variables obtained from these operators. Conservation laws are computed via three methods. Direct method for construction of conservation laws is introduced by the concept of multipliers and Euler-Lagrange operator. Next, the non-linearly self-adjointness of the considered PDE is stated. Then, the modi, ed Noether's theorem is used for , nding conservation laws. Finally, the third method is established via the Hereman-Pole method by using the evolutionary form of the equation.

In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation.

In this paper, Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. Complete analysis of symmetries and nonclassical symmetries is discussed. Furthermore, optimal system, preliminary classification of its group invariant solutions and symmetry reduction are investigated. Finally conservation laws for the higher order Camassa-Holm equation which conserved quantities arise from multipliers by using homotopy operator are presented.