Question

6. Water steadily enters an extremely thin 100 m stainless steel pipe with a diameter of 10 cm at a mass flow rate of 31.4 kg/s at 80 °C at 100 kPa. The convection heat transfer coefficient between the ambient air (20 °C) and water pipe is ℎ = 120 ?/(?^2)?. You can ignore the heat loss by radiation and assume the temperature of the water and pipe surface are almost same but the temperature Difference is very small but enough for conduction heat transfer. Please find the variation of the water Temperature with length of pipe (from entrance), the heat loss from water to ambient air when passing through this pipe. You can assume the specific heat of water is 4.2 kJ/(kg*Celsius). Please keep in mind that the temperature of the pipe surface is a function of the length, so that heat loss through convection is not constant but a function of pipe surface temperature. In solving this question, you can assume the water in this pipe consists of a series of small elements (discs). For each element (disc), the heat loss through side (pipe) surface by convection is equal to the change of thermal energy (temperature change noted as dT) of water flowing through this element (disc). This will lead to the development of a differential equation: ?? ?? = ?? + ?. You can find the temperature as a function of x noted as ? = ?(?), and heat transfer as a function of ?(?) = ?(?).

Answer 1