Question

3. Applesauce at a food processing plant exits a tank at an initial temperature of 90°C. It flows through a 6 m section of 40 mm diameter pipe at speed of 1 cm/sec. The pipe is wrapped in 5 mm of insulation (k 0.3 W/mK), and has an inside heat transfer coefficient of hi = 100 W/m2K and an outside heat transfer coefficient of 8 W/m2K. losing heat to the environment at To10°C. The applesauce next enters a 1 m long section of pipe with negligible heat loss where a resistance heater delivers a constant heat flux of 5000 W/m2, and finally flows through a second insulated section 5 m long. The properties of applesauce are: k # 0.6 w/mK, ? 958 kg/m3, and cp-4217 J/kg-K Find the temperature of the applesauce at locations A. B and C. lout

Answer 1

1)
Diameter of pipe = 40 mm K_insulation = 0.3 w/mk speed = 1 cm/sec Thickness of insulation = 5 mm having k = thermal conductivity = 0.3 w/mk Ambient condition = T_infinity = 10 degree C for section 0 - A of pipe heat lost to Environment = decrease in Energy of the fluid (Internal Energy) q = T - T_infinity/Resistance = heat lost to Environment taking element of dx along the pipe OA So Resistance = 1/h_iA_i + ln(r_2/r_1)/2 pi k dx + 1/h_0 A_0 where A_i = pi D_i dx A_0 = pi D_0 dx D_i = 40 mm D_0 = 50 mm = 40 + 2 times 5 = 50 mm \r\n Resistance = 1/100 times pi times 40 times 10^- 3 x dx + ln(25/20)/2 pi times 0.3 times dx + 1/8 times pi times 50 times dx times 10^- 3 Resistance = 0.07957/dx + 0.11838/dx + 0.79577/dx = 0.99373/dx w/k So q = (T.T_infinity)dx/0.99373 = -m^.c_p dT(decrease in Energy of the fluid) Also m^. = mass flow rate = rho AV where rho = 958 kg/m^3 A = pi/4 times(40 times 10^- 3)^2 T_infinity = 10 degree c
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