Question

A small workboat is fitted with a diesel engine that develops its maximum power of 300 kW with a corresponding specific fuel consumption of 0.21 kg/kW h. At maximum power, the air-fuel ratio of the engine is 20 and the exhaust pressure is 1.01 bar. It is proposed to provide hot water for the vessel by using a shell and tube heat exchanger to extract waste heat from the engine exhaust gases. Calculate the:

(i) tube length required.

The following information has already been established. The exhaust gases flow through 25 mm diameter tubes with a velocity of 12 m/s, entering at 340oC and leaving at 90oC. The water enters the heater at l0oC and leaves at 90oC, flowing in a counter-flow direction to the hot gases. The overall heat transfer coefficient of the heat exchanger has been calculated as 56 W/m2 K. The specific heat capacity and the gas constant for the exhaust gases as 1.11 kJ/kg K and 0.29 kJ/kg K, and the specific heat capacity for the water as 4.19 kJ/kg K,

Answer 1

GIVEN:- EXHAUST PRESSURE P. =:1-01 bar: OVERALL HEAT TRANSFER.COEFFICIENT 'U'=560469? SPECIFIC HEAT CAPACITY OF EXHAUST GASES a kpe1.11 KJ/kg R. GAS CONSTANT OF EXHAUST GASES R=0.29 kJ/ kg DIAMETER OF TUBES 'D' = 0.025. VELOCITY. OF EXHAUST GASES = 12mys: Has MASS FLOW RATE OF EXHAUST GASES :- isos 3x AxV. . T- INLET TEMPERATURE 33.p OF EXHAUST GAS RT ::- 1.01 X1D? 10.29)(613) =0:56811 ise = 0.5661X II x(0.025) 2 12 . = 3.346X163 kg/s. COUNTER FLOW HEAT EXCHANGER:- ENERGY EQUATION : Q melp)e(Thi- The) .= Mulepos (T676). Thu : INLET TEMPERATURE OF EXHAUST : GASES. Th.:: OUTLET TEMPERATURE OF EXHAUST GASES.

TG: INLET TEMPERATURE OF WATER. The ! OUTLET TEMPERATURE OF WATER: Q = Melle (The Thy) = 3:346X163x i11 * ( 340 - 90). = :0.9287 kw Q3.928.7 watts. The = 340 c . The =90c. Tu = 10c .. Tg = 90c. Thik T S STI = Thy - The = 340-90 9= 250°C. L ST2 = Thy - T4 = 90-10 = 80C. LMTD = ATA-A12: 230-80 : ex A) 10120). = 149.19°C. RE: DALMTD 928.7=56x TTX 0-0 25x Lx 149-19. Le loumi :: LENGTH OF TUBE = 1.41 metres.