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Nanodielectrics have been extensively researched in recent years with the expectation that they may enhance electrical performance. In this paper we have studied the electrical conduction processes in linear low density polyethylene (LLDPE) filled with nano alumina particles. The electrical conduction was measured at various applied electric fields. It has been found that the conduction current shows a minimum at a 1% b.w. concentration nano alumina particles. To aid an understanding of conduction processes in the nanodielectric, differential scanning calorimetry (DSC) was used to analyse the interaction between nano alumina particles and the host matrix. Initial findings suggest that there is an interaction zone around the nano alumina particles. Neighbouring interaction zones are expected to overlap when the percentage of nano alumina particles exceeds 5% in LLDPE.