第2期黄晓齐等：对流简谐环境温度边界条件下多集总热容系统导热微分方程组的复数倒算法T门 1 R2 Ray2R2)2 (15) X2 X3 X2 X3'X3 R2= (16) h2A2 R2+R3+R2 X2'X3'X3 P1b=arctg (17) R2 R3 X2 X3 Q6==是+袋+影+-袋 =名k1-+会++ (18) X=ficiv (19) 0=Q+Qw=一只是名++太)袋+太袋++名+)-太是是器 R2R3] 只+宗+妇袋+名++名+名-，品 (20) 6=ac8-〔 宝+名+名)名是是 (21) 袋+名+安名+ 则倒算出的环境流体温度的复数表达式为 TB=T1b十Q6R1 =1-是是-是是-是+是是-是+是+是2+学+是+是+是是是 = -安学-是++++务 (22) 1 R1= (23) hA1 +：+是+是+是-是器是 =arctg- (24) 名是；经+0会 于是，由式(3)与式(22)之比，得修正系数为 To -是-会，+尝g名4+名+安+名+，+ (25) 以此5值分别乘以式2918,5138,6，凸刚实际条准稳态热流量和温度的复数表达式= (1 - R 2 X 2 R 3 X 3 )2 +( R 2 X 2 + R 3 X 3 + R 2 X 3 )2 e iφ1b (15) R 2 = 1 h2 A2 (16) φ1b =arctg R 2 X 2 + R 3 X 3 + R 2 X 3 1 - R2 X 2 R 3 X 3 (17) Q﹒ 1b = T﹒ 1b -iX 1 =-1 X 1 ( R 2 X 2 + R 3 X 3 + R 2 X 3 )+ i X 1 (1 - R 2 X 2 R3 X 3 ) = 1 X 1 (1 - R 2 X 2 R 3 X 3 ) 2 +( R 2 X 2 + R 3 X 3 + R 2 X 3 ) 2 e i(φ1b +π 2 ) (18) X 1 = 1 2πfρ1 c1 V1 (19) Q﹒ b =Q﹒ 12b +Q﹒ 1b =-〔 1 X 1 R2 X 2 +(1 X 1 + 1 X 2 ) R 3 X 3 + 1 X 1 R 2 X 3 〕 +i〔(1 X 1 + 1 X 2 + 1 X 3 )- 1 X 1 R2 X 2 R 3 X 3 〕 = 〔 1 X 1 R 2 X 2 +( 1 X 1 + 1 X 2 ) R3 X 3 + 1 X 1 R 2 X 3 〕 2 +〔( 1 X 1 + 1 X 2 + 1 X 3 )- 1 X 1 R 2 X 2 R 3 X 3 〕 2 e iφb (20) φb =arctg ( 1 X 1 + 1 X 2 + 1 X 3 )- 1 X 1 R 2 X 2 R 3 X 3 -〔 1 X 1 R 2 X 2 +( 1 X 1 + 1 X 2 ) R 3 X 3 + 1 X 1 R 2 X 3 〕 (21) 则倒算出的环境流体温度的复数表达式为 ﹒Tfb = ﹒T 1b +﹒QbR 1 =〔1 - R 1 X 1 R 2 X 2 - R 2 X 2 R 3 X 3 -( R 1 X 1 + R1 X 2 ) R 3 X 3 - R 1 X 1 R 2 X 3 〕 +i〔( R 1 X 1 + R 2 X 2 + R 3 X 3 )+ R 1 X 2 + R 1 X 3 + R 2 X 3 - R 1 X 1 R 2 X 2 R 3 X 3 〕 = 〔1 - R1 X 1 R 2 X 2 - R 2 X 2 R 3 X 3 -( R 1 X 1 + R 1 X 2 ) R 3 X 3 - R1 X 1 R 2 X 3 〕 2 +〔( R 1 X 1 + R 2 X 2 + R 3 X 3 )+ R 1 X 2 + R 1 X 3 + R 2 X 3 - R 1 X 1 R 2 X 2 R 3 X 3 〕 2 e iφfb (22) R 1 = 1 h1A 1 (23) φfb =arctg ( R 1 X 1 + R 2 X 2 + R3 X 3 )+ R1 X 2 + R 1 X 3 + R 2 X 3 - R 1 X 1 R 2 X 2 R 3 X 3 1 - R 1 X 1 R2 X 2 - R 2 X 2 R 3 X 3 -( R 1 X 1 + R1 X 2 ) R 3 X 3 - R 1 X 1 R 2 X 3 (24) 于是 ,由式(3)与式(22)之比, 得修正系数为 K﹒ = ﹒Tf ﹒T fb = T fm 〔1 - R 1 X 1 R 2 X 2 - R 2 X 2 R 3 X 3 -( R 1 X 1 + R 1 X 2 ) R 3 X 3 - R 1 X 1 R 2 X 3 〕 2 +〔( R 1 X 1 + R 2 X 2 + R 2 X 3 )+ R1 X 2 + R 1 X 3 + R 2 X 3 - R 1 X 1 R 2 X 2 R 3 X 3 〕 2 e -iφfb (25) 以此 K﹒ 值分别乘以式(20 , 18 , 15 , 13 , 11 , 8 , 6 , 5), 则实际各准稳态热流量和温度的复数表达式 第 2 期 黄晓齐等 :对流简谐环境温度边界条件下多集总热容系统导热微分方程组的复数倒算法 77