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The alloys with 8/18/24 valence electron count (VEC) are promising candidatesfor efficient energy conversion and refrigeration applications at low as wellas high temperatures. The full potential linearized augmented plane wave methodas implemented in WIEN2k code was used to investigate electronic structure andTE transport properties with the PBE$-$GGA and TB$-$mBJ exchange potentials andBoltzmann transport theory. The calculated single crystal elastic constants,phonon dispersion and phonon density of states confirm that these systems aremechanically and dynamically stable. The TE transport properties is calculatedby including the lattice part of thermal conductivity ($\kappa_{L}$) obtainedfrom two methods one from the calculated elastic properties calculation($\kappa^{elastic}_{L}$) and the other from phonon dispersion curve($\kappa^{phonon}_{L}$). The strong phonon$-$phonon scattering by large massdifference/strain fluctuation of isovalent/aliovalent substitution at Ti/Snsites of Fe$_{2}$TiSn reduces the lattice thermal conductivity which results inhigh \textit{ZT} value of 0.81 at 900\,K forFe$_{2}$Sc$_{0.25}$Ti$_{0.5}$Ta$_{0.25}$Al$_{0.5}$Bi$_{0.5}$. The comparativeanalysis of TE transport properties using the band structures calculated withthe PBE$-$GGA and TB$-$mBJ functional shows that the \textit{ZT} value obtainedfrom TB$-$mBJ scheme is found to be significantly higher than that based onPBE$-$GGA. The calculated relatively low lattice thermal conductivity and high\textit{ZT} values suggest that isovalent/aliovalent substituted Fe$_{2}$TiSnare promising candidates for medium to high temperature waste heat recovery.

First principle studies on electronic and thermoelectric properties of Fe$_{2}$TiSn based multinary Heusler alloys