单级半导体制冷器设计中常用公式的推导

Derivation of equation used in designing single-stage semiconductor coolers

利用数学方法分析了半导体制冷器的最大制冷量、最大制冷温差和最大制冷系数,讨论了半导体制冷器工作电流和使用参数的关系,并归纳总结出一组公式,如最大制冷量工况I=aTc/R,U=αTh;最佳制冷效率工况I0=α△T/R(M-l),U=α△TM/M-l,其中M=(√1+0.5z(Th+Tc))等.用该组公式对某制冷件进行计算,计算值与实测结果非常接近,说明公式的推导合理,可信度较高.

Maximum refrigeration capacity, maximum refrigeration temperature difference, and maximum refrigeration coefficient of semiconductor refrigerator are analyzed by mathe- matics, and the relationship between working current and parameter is discussed. Finally, some equations, such as I=(αT_c)/R,U=αT_h in a condition of maximum refrigeration capacity, and I_0=(α△T)/(R(M-1)), U=(α△TM)/(M-1) in a condition of maximum refrigeration efficiency, are ab- tained. Calculation values from the equations are coincident with results from actual mea- surement,which shows that the derivation is reasonable, and the equations are reliable.