The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. The properties of the junction are k = 35 W/m·K, r = 8500 kg/m3, and cp = 320 J/kg·K, and the heat transfer coefficient between the junction and the gas is h = 90 W/m2·K. Determine how long it will take for the thermocouple to read 99 percent of the initial temperature difference.

A cartridge electrical heater is shaped as a cylinder of length L = 300 mm and outer diameter D = 30 mm. Under normal operating conditions, the heater dissipates 2 kW while submerged in a water flow that is at 20°C and provides a convection heat transfer coefficient of h = 5000 W/m2 · K. Neglecting heat transfer from the ends of the heater, determine its surface temperature Ts and the thermal resistance due to convection. If the water flow is inadvertently terminated while the heater continues to operate, the heater surface is exposed to air that is also at 20°C but for which h = 50 W/m2 · K. What are the corresponding thermal resistance due to convection and surface temperature? What are the consequences of such an event?

Mechanical services

A small copper wire with a diameter of 0.792 mm and initially at 366.5 K is suddenly immersed in a liquid held constant at 311 K. The convection coefficient h = 85.2 W/m2 · K. The physical properties can be assumed constant and are k = 374 W/m · K, cp = 0.389 kJ/kg · K, and ρ = 8890 kg/m3. Determine the time in seconds for the average temperature of the wire to drop to 338.8 K (one-half the initial temperature difference). Do the same but for h=11.36W/m2·K. Forpart(b),calculate the total amount of heat removed for a wire 1.0 m long.