A mathematical model of coupled thermoelectricity is presented to investigate the transient and steady-state behaviour of thermoelectric bulk material. Governing partial differential equations (PDEs) for the coupled thermal and electrical behaviour of the thermoelectric model are discretised using the explicit finite-difference method. Differencing schemes like Upwind and Lax–Wendroff methods are employed to obtain solutions for the first-order hyperbolic PDEs, whereas FTCS (Forward Time, Centred Space) scheme is employed to solve second-order parabolic PDEs. Courant-Friedrichs-Lewy and Von Neumann stability analyses are done to ensure the stability and convergence of the model. The model considers the temperature dependency of thermal conductivity, electrical conductivity, and Seebeck coefficient of the P/N materials separately. and accounts for the Seebeck, Peltier, and Joule-Thomson effects in thermoelectric materials. The new model is practically useful to predict the transient and steady-state behaviours of a thermoelectric device with multiple P-N elements. The results of the presented finite-difference model are proven to agree well with experimental values as well as 3-D simulations with ANSYS®.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.