As the world fights climate change challenges and the soaring demand for energy-efficient solutions, the need for sustainable heating and cooling systems in residential buildings has become paramount. Traditional systems rely on fossil fuels and contribute significantly to greenhouse gas emissions. Ground source heat pumps (GSHPs) have emerged as a promising technology, offering a sustainable alternative to conventional space conditioning systems. Central to the success of GSHPs is the efficient and reliable operation of their ground heat exchangers, with lower installation costs, as a prospective solution for future residential applications. This paper presents a numerical axisymmetric (r-z) finite volume method solution of the thermal performance of coaxial ground heat exchangers (CGHE) that incorporate phase change material (PCM) in the ground for GSHP applications. An analysis of the CGHE with PCM grout is presented, highlighting the advantages of heat exchange performance over normal grouts. The temperature comparison on three different points in the grout with different grouting materials was carried out to analyse the behaviour of different grouting materials during the heat exchange process. The investigation from a temperature point of view showed that the inclusion of PCM in the grouting material improves the thermal performance of the CGHE.