2 A shell-and-tube heat exchanger must be designed to heat 2.5 kg/s of water from 15 to 85°C. The heating is to be accomplished by passing hot engine oil, which is available at 160°C, through the shell side of the exchanger. The oil is known to provide an average convection coefficient of h, = 400 W/m² K on the outside of the tubes. Ten tubes pass the water through the shell. Each tube is thin walled, of diameter D = 25 mm, and makes eight passes through the shell. If the oil leaves the exchanger at 100°C, what is its flow rate? How long must the tubes be to accomplish the desired heating?

A shaft of 0.06-m diameter is heat treated in a gas-fired furnace whose gases is at 1200 K and provide a convection coefficient of 125 W/m² K. If the shaft enters the furnace at 300 K and stays in the furnace. (1) What is the centerline temperature (in K) of the shaft after 900 seconds? (2) What is the value of the dimensionless Fourier number? The shaft material has a density of 7000 kg/m², thermal conductivity of 50 W/m.K, and specific heat capacity 500 J/kg.K. Please show your work and assumptions.

A metallic sphere of radius R is heated in an oven to a temperature of 600 ° F throughout, and then removed from the oven and allowed to cool in ambient air to T∞ = 75 ° F, by convection and radiation (see attached figure). The thermal conductivity of the ball material is known to vary linearly with temperature. Assuming that the ball is uniformly cooled starting from the entire outer surface, obtain the differential equation that describes the change in temperature in the sphere during cooling. Note: In the image, the translation would be: metallic sphere

Hollow Sphere Saturated steam at 267°F is flowing inside a hollow sphere with an ID of 0.824 in. and an OD of 1.05 in. The pipe is insulated with 1.5 in. of insulation on the outside. The convective heat transfer coefficient inside and outside the pipe is hi = 1000 Btu/hr/ft2/°F and ho = 2 Btu/hr/ft2/°F, respectively. The mean thermal conductivity of the metal is 45 W/m/K or 26 Btu/hr/ft/°F, while that of the insulation material is 0.064 W/m/K or 0.037 Btu/hr/ft/°F. a. Calculate the heat loss for 1 ft of pipe using resistances if the surrounding air is at 80°F. b. Calculate the temperature profile developed for this system. c. Calculate the inside and outside overall heat transfer coefficients.