In this research, a new heat transfer model for ternary nanofluid (Al₂O₃-CuO-Fe₃O₄)/C₂H₆O₂ inside slippery converging/diverging channel is reported with innovative effects of dissipation function. This flow situation described by a coupled set of PDEs which reduced to ODEs via similarity and effective ternary nanofluid properties. Then, LSM is successfully coded for the model and achieved the desired results influenced by $\alpha ,Re,{\gamma }_1$ and $Ec$. It is examined that the fluid movement increases for $Re$ in the physical range of 30–180 and it drops for diverging channel ( $\alpha >0$) when the slippery wall approaches to $\alpha ={60}^o$. The fluid movement is very slow for increasing concentration factor ${\phi }_i$ for $i=1,2,3$ up to 10%. Further, ternary nanofluid temperature boosts rapidly due to inclusion of trinanoparticles thermal conductivity and dissipation factor ( $Ec=0.1,0.2,0.3,0.4,0.6$) also contributes significantly. Moreover, the temperature is maximum about the center of the channel ( $\eta =0$) and slip effects ( ${\gamma }_1=0.1,0.2,0.3,0.4,0.5,0.6$) on the channel walls lead to decrement in the temperature $\beta \left(\eta \right)$.

The objective of the current examination is to present new sub-classes of $q$-convex and $q$-starlike functions inside $\mathcal{E}=\left\{z\in \mathbb{C}:\left|z\right|<1\right\}$, by $q$-difference operator. We determined connections of these classes and acquired a few fundamental properties, for instance, inclusion relation, subordination properties and $q$-limits on real part.