The encapsulation technique of phase change materials in the nanodimension is an innovative approach to improve the heat transfer capability and solve the issues of corrosion during the melting process. This new type of nanoparticle is suspended in base fluids call NEPCMs, nanoencapsulated phase change materials. The goal of this work is to analyze the impacts of pertinent parameters on the free convection and entropy generation in an elliptical-shaped enclosure filled with NEPCMs by considering the effect of an inclined magnetic field. To reach the goal, the governing equations (energy, momentum, and mass conservation) are solved numerically by CVFEM. Currently, to overcome the low heat transfer problem of phase change material, the NEPCM suspension is used for industrial applications. Validation of results shows that they are acceptable. The results reveal that the values of
N
u
ave
descend with ascending Ha while
N
gen
has a maximum at
Ha
=
16
. Also, the value of
N
T
,
MF
increases with ascending
Ha
. The values of
N
u
ave
and
N
gen
depend on nondimensional fusion temperature where good performance is seen in the range of
0.35
<
θ
f
<
0.6
. Also,
Nu
ave
increases 19.9% and ECOP increases 28.8% whereas
N
gen
descends 6.9% when
ϕ
ascends from 0 to 0.06 at
θ
f
=
0.5
.
Nu
ave
decreases 4.95% while
N
gen
increases by 8.65% when
Ste
increases from 0.2 to 0.7 at
θ
f
=
0.35
.