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In this article, the fractional third‐order dispersive partial differential equations were investigated by using Shehu decomposition and variational iteration transform methods. The well known Riemann‐Liouville fraction integral, Caputo's fractional‐order derivative, Shehu transform for fractional‐order derivatives and Mittag‐Leffler function were used as the major basis of the methodology. The graphs and table show the solution behavior for various fractional order values. The comparison provided the signed agreement of the solutions to each other as well as with the exact result. The accurateness and efficiency of the suggested techniques are examined using two numerical experiments. The reliability and validity tests show that for various fractional‐order values, the newly proposed method is reliable, accurate, and efficient.

This research is proposed to fully investigate the performance of a single‐effect water/lithium bromide absorption chiller driven by geothermal energy. Since absorption cycles are considered as low‐grade energy cycles, this innovative idea of rejecting fluid from a single‐flash geothermal power plant with low‐grade energy would serve as efficient, economical, and promising technology. In order to examine the feasibility of this approach, a residential building which is located in Sharjah, UAE, considered to evaluate its cooling capacity of 39 kW which is calculated using MATLAB software. Based on the obtained cooling load, modeling of the required water/lithium bromide single‐effect absorption chiller machine is implemented and discussed. A detailed performance analysis of the proposed model under different conditions is performed using Engineering Equation Solver software (EES). Based on the obtained results, the major factors in the design of the proposed system are the size of the heat exchangers and the input heat source temperature. The results are presented graphically to find out the geofluid temperature and mass flow and solution heat exchanger effectiveness effects on the chiller thermal performance. Moreover, the effects of the size of all components of the absorption chiller on the cooling load to meet the space heating are presented. The thermal efficiency of the single‐flash geothermal power plant is about 13% when the power plant is at production well temperature 250℃, separator pressure 0.24 MPa, and condenser pressure 7.5 kPa. The results show that the coefficient of performance (COP) reaches about 0.87 at solution heat exchanger effectiveness of 0.9, when the geofluid temperature is 120℃.