A smooth thin-walled cylindrical copper pipe made up of a pipe length L = 3m, diameter D=10 cm is used to transfer industrial hot water. The hot water enters the copper pipe at a temperature T_h = 90 degree C and mass flow rate m = 0.2 kg/s. The water has the constant physical properties rho_w 1000 kg/m^3, v_w = 1.0 * 10^6 m^2/s, gama_w = 0.654 W/(mK), c_w = 4200 J/(kgK) as well as the Prandtl number Pr_w = 7.0. On the outer surface, air at 1 atmospheric pressure and temperature T_infinity = 20 degree C flows over the copper pipe. The convective heat transfer coefficient between the air and the outer surface of the copper pipe alpha_a is described as 20 W/(m^2 K). Contact resistances do not occur. Additionally, all effects of thermal radiation may be neglected. Calculate the convective heat transfer coefficient alpha_i between the water and the inner surface of the pipe. What is the overall heat transfer coefficient U between the water and the ambient air based on the outer surface area A of the copper pipe. Consider the copper pipe as a heat exchanger, draw the temperature profiles of the water and air on the same graph. Carry out the calculation using the operating characteristic of a heat exchanger, and determine the number of transfer units N of the heat exchanger.
1. calculate the convective heat transfer coefficient between the water and the inner surface of the pipe.
2. what is the overall transfer coefficient U between the water and the ambient air based on the outer surface area A of the pipe.
3. consider the copper pipe as a heat exchanger, draw the temperature profiles of the water and air on the same graph.
4. carry out the calculations using the operating characteristic of a heat exchanger, and determine the number of transfer units N of the heat exchanger.
5. determine the efficiency of the heat exchanger.
6. determine the heat transfer rate from the water to the ambient air
7. find the temperature of the water at the exit of the pipe
8. what is the new exit temperature of the water, if the inlet temperature Th increases from 90 to 95 degree celcius
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