* Bilinear heat exchanger problem * Floudas and Ciric (1988) * Refer to Figure 5.11 in test problem collection. * f denotes a flowrate * T denotes a temperature VARIABLES dT11 temperature difference at hot end of exchanger H1-C dT12 temperature difference at cold end of exchanger H1-C dT21 temperature difference at hot end of exchanger H2-C dT22 temperature difference at cold end of exchanger H2-C dT31 temperature difference at hot end of exchanger H3-C dT32 temperature difference at cold end of exchanger H3-C f11 f12 f13 f14 f15 f21 f22 f23 f24 f25 f31 f32 f33 f34 f35 t1i t1o t2i t2o t3i t3o objval Automatically generated objective function variable; FREE VARIABLES objval; EQUATIONS g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g11 g12 g13 g14 g15 g16 g17 g18 g19 f Objective function; f .. objval =e=1300*(2000/(1/3*dT11*dT12+1/6*(dT11+dT12)))**0.6+1300*(1000/(2/3*dT21*dT22+1/6*(dT21+dT22)))**0.6+1300*(1500/(2/3*dT31*dT32+1/6*(dT31+dT32)))**0.6; g1 .. f11+f21+f31 =e= 45; g2 .. f11+f23+f34-f12 =e= 0; g3 .. f21+f13+f33-f22 =e= 0; g4 .. f31+f14+f24-f32 =e= 0; g5 .. f15+f13+f14-f12 =e= 0; g6 .. f25+f23+f24-f22 =e= 0; g7 .. f35+f33+f34-f32 =e= 0; g8 .. 100*f11+t2o*f23+t3o*f34-t1i*f12 =e= 0; g9 .. 100*f21+t1o*f13+t3o*f33-t2i*f22 =e= 0; g10 .. 100*f31+t1o*f14+t2o*f24-t3i*f32 =e= 0; g11 .. f12*t1o-f12*t1i =e= 2000; g12 .. f22*t2o-f22*t2i =e= 1000; g13 .. f32*t3o-f32*t3i =e= 1500; g14 .. dT11+t1o =e= 210; g15 .. dT12+t1i =e= 130; g16 .. dT21+t2o =e= 210; g17 .. dT22+t2i =e= 160; g18 .. dT31+t3o =e= 210; g19 .. dT32+t3i =e= 180; * Bounds dT11.LO = 10; dT11.UP = 110; dT12.LO = 10; dT12.UP = 110; dT21.LO = 10; dT21.UP = 110; dT22.LO = 10; dT22.UP = 110; dT31.LO = 10; dT31.UP = 110; dT32.LO = 10; dT32.UP = 110; f11.LO = 0; f11.UP = 45; f12.LO = 0; f12.UP = 45; f13.LO = 0; f13.UP = 45; f14.LO = 0; f14.UP = 45; f15.LO = 0; f15.UP = 45; f21.LO = 0; f21.UP = 45; f22.LO = 0; f22.UP = 45; f23.LO = 0; f23.UP = 45; f24.LO = 0; f24.UP = 45; f25.LO = 0; f25.UP = 45; f31.LO = 0; f31.UP = 45; f32.LO = 0; f32.UP = 45; f33.LO = 0; f33.UP = 45; f34.LO = 0; f34.UP = 45; f35.LO = 0; f35.UP = 45; t1i.LO = 100; t1i.UP = 200; t1o.LO = 100; t1o.UP = 200; t2i.LO = 100; t2i.UP = 200; t2o.LO = 100; t2o.UP = 200; t3i.LO = 100; t3i.UP = 200; t3o.LO = 100; t3o.UP = 200; * Starting point (global solution) * dT11.L = 52.86; dT12.L = 30; * dT21.L = 10; dT22.L = 60; * dT31.L = 10; dT32.L = 22.86; * f11.L = 35; f12.L = 35; f13.L = 0; f14.L = 35; f15.L = 0; * f21.L = 10; f22.L = 10; f23.L = 0; f24.L = 0; f25.L = 10; * f31.L = 0; f32.L = 35; f33.L = 0; f34.L = 0; f35.L = 35; * t1i.L = 100; t1o.L = 157.14; * t2i.L = 100; t2o.L = 200; * t3i.L = 157.14; t3o.L = 200; MODEL test /ALL/; SOLVE test USING NLP MINIMIZING objval;