Effect of heat exchange at the hot junction of a thermoelectric element on the optimum current-carrier density distribution along its branches

The optimum current-carrier density distribution along the height of the branches of a thermoelectric element is obtained, which ensures minimum temperature at the cold junction taking into account the heat transfer at the hot junction.Notation T absolute temperature - T temperature drop between the cold junction and the medium - q temperature gradient - n current-carrier density - u density gradient - a heat-transfer coefficient - x coordinate of the length - d height of the thermoelectric element - , , thermal conductivity, the electrical conductivity, and the thermoelectric coefficient respectively - j current density Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 125–130, July, 1984.