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Heat Transfer
Convection & Radiation
GATE 2008
Hard

The logarithmic mean temperature difference (LMTD) of a counterflow heat exchanger is 20°C. The cold fluid enters at 20°C and the hot fluid enters at 100°C. The mass flow rate of the cold fluid is twice that of the hot fluid; the specific heat of the hot fluid is twice that of the cold fluid. The exit temperature of the cold fluid

  • Ais 40°C
  • Bis 60°C
  • is 80°C
  • Dcannot be determined

Explanation

C_cold=ṁc·cpc=(2ṁh)(cph/2)=ṁh·cph=C_hot — the heat capacity rates are EQUAL, so the temperature difference is constant throughout the exchanger and LMTD equals that constant approach temperature: Thot,in-Tcold,out=20°C ⟹ Tcold,out=100-20=80°C.

Source: GATE ME 2008 (2008)

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