where q is the heat flux density vector, J is the electric current density vector, E is the electric field intensity vector, [[PI]] is the Peltier coefficient
matrix, [k] is the thermal conductivity matrix, [[sigma]] is the electrical conductivity matrix, [[alpha]] is the Seebeck coefficient matrix .
The Peltier coefficient is a measure of the amount of heat carried by electrons or holes.
When two different materials are joined together to form a loop, as shown in Figure 2, there will be an abrupt change in heat flow at the junctions because the two materials have different Peltier coefficients. The excess energy released to the lattice causes heating; the deficiency in energy supplied by the lattice causes cooling.