  We investigate the thermoelectric effect, which describes the generation of
an electric field induced by temperature and conserved charge chemical
potential gradients, in the hot and dense hadronic matter created in heavy-ion
collisions. Utilizing the Boltzmann kinetic theory within the repulsive
mean-field hadron resonance gas model, we evaluate both the diffusion
thermopower matrix and diffusion coefficient matrix for the baryon number
($B$), electric charge ($Q$), and strangeness ($S$). The Landau-Lifshitz choice
for the rest frame of the fluid is enforced in the derivation. We find that the
thermoelectric effect hinders the diffusion processes of multiple conserved
charges, particularly reducing the coupling between electric charge and baryon
number (strangeness) in baryon (strangeness) diffusion. Given that the
repulsive mean-field interactions between hadrons have a significant effect on
the diffusion thermopower matrix and diffusion coefficient matrix in the
baryon-rich region, we extend the investigation to include the impact of
magnetic fields, analyzing the magneto-thermoelectric effect on both the
diffusion coefficient matrix and the Hall-like diffusion coefficient matrix.
The sensitivities of the magnetic field-dependent diffusion thermopower matrix
and magneto-thermoelectric modified diffusion coefficient matrix to the choices
of various transverse conditions are also studied.
