Problemas De Fisica

13-87 Una sustancia química se calienta por el agua en un intercambiador de calor. Se dan las tasas de flujo de masa y las tempera turas de entrada. Las temperaturas de salida de ambos fluidos se han de determinar.

Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes in the kinetic and potential energies of fluid streams are negligible. 4 The thickness of the tube is negligible since tube is thin-walled. 5 The overall heat transfer coefficient is constant and uniform.

Properties The specific heats of the water and chemical are given to be 4.18 and 1.8 kJ/kg.C, respectively.

Analysis The heat capacity rates of the hot and cold fluids are

Ch  m h C ph  (2 kg / s)(4.18 kJ / kg. C) = 8.36 kW/ C

Cc  m c C pc  (3 kg / s)(1.8 kJ / kg. C) = 5.40 kW/ C

Therefore, Cmin  Cc  5.4 kW/ C

Chemical

20C

3 kg/s

and C  Cmin

Cmax

 5.40  0.646

8.36

Hot Water

110C

2 kg/s

Then the maximum heat transfer rate becomes

Q max  Cmin (Th,in  Tc,in )  (5.4 kW/ C)(110 C - 20 C)  486 kW

The NTU of this heat exchanger is

UA NTU 

 (1.2 kW/m

2 .C) (7 m 2 )

 1.556

C min

5.4 kW/C

Then the effectiveness of this parallel-flow heat exchanger corresponding to C = 0.646 and NTU=1.556 is determined from

  1  exp[ NTU (1  C)]  1  exp[1.556(1  0.646)]  0.56

1  C

1  0.646

Then the actual rate of heat transfer rate becomes

Q  Q max  (0.56)(486 kW)  272.2 kW

Finally, the outlet temperatures of the cold and hot fluid streams are determined to be

Q  C c

(Tc,out

 Tc,in

)  T

c,out

 Tc,in

 Q

C c

 20C +

272.2 kW

5.4 kW / C

 70.4C

Q  C h

(Th,in

 Th,out

)  T

...