The Ground Air Heat Exchanger (EAHE) is an integrated passive heating and cooling system for many greenhouses, industrial and residential building applications. Reduces heating and cooling loads by transferring heat between ventilated air and the ground. In this paper, the performance of EAHE was studied numerically using the ESP-r program under weather and soil conditions in Al-Diwaniyah city (southern Iraq), connecting the pipe to a building model and testing it during the summer and winter months. In the case of summer, the results indicated a decrease in the temperature of the air supplied to the air-conditioned space, where the temperature reached 37.42 ° C, 40.09 ° C and 39.93 ° C, while the temperature of the outside air was 47.09 ° C, 47.45 ° C and 48.48 ° C during the summer. July, August and September respectively. In the case of the winter months, the air leaving the tube is heated to a temperature of 16.38°C, 13.99°C, 16.42°C, and 16.42°C, when the outside air temperature is 3.33°C, -0.01°C and 5.37° percentage during December, January and February, respectively. The use of this type of heat exchanger achieved a reduction of more than 10 ° C during the summer and an increase of more than 13 ° C in the winter.

In this paper, a new approach for solving partial differential equations was introduced. The collocation method based on LA-transform and proposed the solution as a power series that conforming Taylor series. The method attacks the problem in a direct way and in a straightforward fashion without using linearization, or any other restrictive assumption that may change the behavior of the equation under discussion. Five illustrated examples are introduced to clarifying the accuracy, ease implementation and efficiency of suggested method. The LA-transform was used to eliminate the linear differential operator in the differential equation.