  To understand the nature of magnetic phase transition in nano-crystalline
Pr$_2$CoMnO$_6$, in present study we have investigated the critical behavior
and magnetocaloric effect. To estimate the critical exponents, various methods
have been adopted like; the modified Arrott plots (MAP), the Kouvel-Fisher
method (KF) and the critical isotherm analysis. This material shows a second
order type a paramagnetic (PM) to ferromagnetic (FM) phase transition around
160 K. The critical exponents obtained from modified Arrott plots are $\beta$ =
0.531, $\gamma$ = 0.935 and $T_c$ = 160 K. Kouvel-Fisher method gives the
exponents as $\beta$ = 0.533$\pm$0.001 with $T_c$ = 160.72$\pm$0.03 K and
$\gamma$ = 0.932$\pm$0.003 with $T_c$ = 160.15$\pm$0.05 K. The third exponent
$\delta$ = 2.763$\pm$0.005 obtained from critical isothermal is in agreement
with Wisdom scaling rule. The estimated critical exponents do not exactly match
with any established universality class, however, the deduced exponent values
suggest that spin interaction in the present material is close to mean-field
model which suggests the existence of long-range ferromagnetic order in
nano-crystalline Pr$_2$CoMnO$_6$. The reliability of critical exponents is
checked by universal scaling hypothesis on magnetic data across T$_c$. We have
calculated the magnetic entropy change from magnetic data and found maximum
value of -$\Delta$S = 2.05 (J kg$^{-1}$ K$^{-1}$) for 50 kOe at 180 K.
Moreover, field dependent change in magnetic entropy obeys scaling and also
indicates that the magnetic interaction is close to mean-field type.
