Using a Landau-de-Gennes-type free-energy density expansion, we have analyzed the effect of high pressure on the smectic A-isotropic () phase transition temperature and nonlinear dielectric effect (NDE) of a homologous series 5-n-alkyl-2(4’-isothiocyanatophenyl)-1,3-dioxanes (nDBT). The pressure dependence of () transition temperature () is explained in terms of the pressure-dependent Landau coefficients associated with the order parameter coupling terms of the free-energy density expansion. We have shown that the transition remains first order even at the elevated pressures. We have investigated the temperature and pressure dependence of the NDE in the isotropic phase of transition. The role of alkyl chain length of the homologous series on the transition and NDE has been studied and has been found to be substantial. A close agreement between the theoretical and experimental results has been found.