momentum heat mass and transfer

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Problem 1) Heating oil in pipes Learning Objective: Application of the derivation in example 1 in Chapter 19 to a common problem for heating fluids flowing through pipes. Oil at 300 K is heated by pumping 1.47 kg/s though steel pipes 2.5 m long with ID = 2.09 cm and OD = 2.67 cm. T.K . kg/ml CJ/kg-K kW/ mK M. Pas This flow is split between six identical but separate pipes. 300 1.84 x 10 0.133 0.0414 Steam condenses on the outside of the pipes to keep the 1.92 10 0.131 surface temperature at a constant at 372 K. The physical 340 2.00 x 10 0.130 7.89 x 10- properties of the oil are given in the table. 370 2.13 x 100 0.128 3.72 x 10- 310 910 897 870 0.0228 865 The goal of this problem the heat requirement of this process. Solve this problem in the following steps: Because the temperature of the oil increases continuously as it moves through the tubes, a differential energy balances must be integrated from the inlet to the outlet to make the required calculation. The derivation of the necessary equation is given in Chapter 19, equation 19.62. a) What assumptions are made in the derivation of Equation 19.62 that are not strictly true considering the information in the table? b) Rewrite equation 19.62 in terms of dimensionless variables for temperature, position, and Stanton Number. That is, the final form would be comparable to the dimensionless form of the lumped parameter model (Eq. 18-9) c) Select an appropriate correlation for flow through the pipe and use this to find the Stanton Number for the flow. d) Calculate the temperature of the oil leaving the pipes. e) Find the total heat transfer rate required to heat the oil to this temperature