A stainless-steel rod (18% Cr, 8% Ni) 6.4 mm in diameter is initially at a uniform temperature of 25◦C and is suddenly immersed in a liquid at 150◦C with h= 120 W/m2 · ◦C. Using the lumped-capacity method of analysis, calculate the time necessary for the rod temperature to reach 120◦C.

2-2 A certain material 2.5 cm thick, with a cross-sectional area of 0.1 m², has one side maintained at 35°C and the other at 95°C. The temperature at the center plane of the material is 62°C, and the heat flow through the material is 1 kW. Obtain an expression for the thermal conductivity of the material as a function of temperature.

A cylindrical container is being designed to contain an exothermic chemical reaction. The container has an external diameter of 80 mm and is 0.2 m tall. The temperature of the cylinder must not exceed 500 °C. To improve cooling of the container, fins of thickness t=5 mm and length L= 40 mm are spaced at least 10 mm apart. Each fin has an efficiency of n= 40%. The ambient temperature is maintained at 22 °c and the heat transfer coefficient between the ambient air and the cylinder is 50 W/m2K. If the chemical reaction produces a maximum of 3.2 kW per kilogram of substance, the maximum mass of substance which can safely be processed in the container to 2 decimal places is kg. The effectiveness of each fin to 1 decimal place is You may neglect heat transfer from the tips of the fins and from the circular surfaces of the cylinder.

Given the following for a simple, cocurrent exchanger: tube outside diameter, Do = 0.75 inches tube inside diameter, Di = 0.62 inches inside heat transfer coefficient, hi = 569 btu/ft2-hr-F outside heat transfer coefficient, ho = 878 btu/ft2-hr-F outside fouling factor, hfo = 542 btu/ft2-hr-F tube wall thermal conductivity, 26 = btu/hr-ft-F What is the tube wall log mean diameter, Dlm in inches? What is the overall heat transfer coefficient, Uo in btu/ft2-hr-F?