In this work, we have investigated the magnetic and magnetocaloric properties of Pr$_{0.8−x}$Bi$_x$Sr$_{0.2}$MnO$_3$ ($x = 0$, 0.05 and 0.1) polycrystalline manganites prepared by sol–gel route on the basis of a phenomenological model. Temperature dependence of magnetization indicates that all our samples exhibit a second order paramagnetic to ferromagnetic transition with a decrease in temperature. A correlation between experimental results and theoretical analysis based on a phenomenological model is investigated. The magnetic and magnetocaloric measurements are well simulated by this model. Under a magnetic applied field of 5 T, the theoretical absolute values of the maximum of magnetic entropy change $\Delta S_{\rm Max}$ are found to be equal to 5.33, 3.33 and 2.97 J kg$^{−1} K$^{−1}$ for $x = 0$, 0.05 and 0.1 respectively. The relative cooling power and the specific heat capacity values are also estimated. The predicted results permit us to conclude that our compounds may be promising candidates for magnetic refrigeration at low temperatures.

In this study, we have tried to simulate both temperature and magnetic field dependence of electrical resistivity for polycrystalline La$_{0.75}$Ho$_{0.05}$Sr$_{0.2}$MnO$_3$. The studied sample was elaborated by sol–gel method. The energydispersiveX-ray confirms the presence of Ho element. The temperature dependence of resistivity in the whole temperature range (100–300 K) was successfully fitted by phenomenological percolation model, testifying the percolative natureof the electrical transition. The evolution of the volume fraction of the ferromagnetic phase is in agreement with the magnetic properties. The magnetic field dependence of resistivity follows the recently established universal behaviour of resistivity, which may confirm the validity of this model.