<p>In this paper, the ultraspherical wavelet operational matrix of derivative method is proposed for the solution of non-linear ordinary differential equation arising in the study of heat transfer through a ternary hybrid nanofluid flow over a moving wet porous fin under the influence of magnetic field with natural convection and radiation. The proposed technique is applied to the test problem having the exact solution and the solution obtained is very close to the exact solution. The considered fin problem is solved using UWOMDM and the result obtained for certain fixed parameters are compared and found to be in good agreement with the result given in the literature. The comparisons validate the UWOMDM. The influence of various physical aspects on thermal distribution and heat transmission rate of the ternary hybrid nanofluid over the straight moving fin is studied. It is inferred that the ternary hybrid nanofluid provides better heat transfer followed by hybrid and mono nanofluids. Ternary hybrid nanofluid with platelet shape allows more heat transfer followed by cylindrical and spherical shapes. Improving Peclet number by 800% increases the fin tip temperature by 2.955%. Hartmann number, convective and radiation parameters help for faster cooling the fin. The heat transmission rate at the fin base escalates for higher Hartmann number, wet porous parameter, convective parameter and radiation parameter and declines for higher Peclet number.</p>