EML 3015C Thermal-Fluids I         Assignment 3                     fall 1999

Part 1: In an incandescent filament lamp, an electric current flows through a thin tungsten wire, which heats and excites the molecules of the filament and causes the filament to glow (see figure). The filament temperature is about 3000 K. The bulb must be filled with an inert gas to prevent the filament from burning out. Tungsten is used because it has a very high melting point of 3400° C. In this exercise, we are going to examine the operation of a household light bulb using heat transfer principles we just learned. First, the diameter of the tungsten filament of a 100W light bulb is about 0.04 mm. It is usually coiled to produce maximum heat available. We are going to assume the length of the filament is 0.5 m for our calculation. The total emissivity (e) of the tungsten can be assumed to be a constant of 0.3 in the temperature range of interest. We also assume 90% of the electric power is dissipated into the tungsten filament as the form of an increase of thermal energy. (a) First, model the filament as an elongated circular cylinder, estimate the temperature of the filament by assuming the wire is directly exposed to the outside (without outside glass shell). You can assume the room temperature is 27° C and the convective heat transfer coefficient is 10 W/m2 K. Hint: consider the energy balance between the filament and the surrounding. (b) However, directly exposing to air, the tungsten will oxidize rapidly and eventually shorten the life of light bulb. Therefore, a glass shell is added and inert gas such as argon or nitrogen is filled into the bulb to retard the evaporation. Now model the glass shell as a spherical glass ball of a diameter of 6 cm and has a transmissivity t=0.8 and reflectivity r=0 (What is then the absorptivity a=?; Assume a=e for simplicity; The surface area of a sphere is 4pR2). Estimate the surface temperature of the glass shell of the light bulb. Hint: Consider the energy balance between the light bulb and the room. (c) Is there any other heat loss also contributing to the overall energy balance? Identify at least one heat loss and discuss its influence on the final temperature of the filament.

 

Part 2: Hot water flows steadily into the water tank with a constant mass flow rate of 5 kg/s and a constant temperature of 90° C. Initially, the tank contains cold water of 20° C as shown. The tank has a constant cross-sectional area of 0.2 m2. (a) Use mass conservation concept, determine and plot the water level (h) as a function of time, up to 100 second. (b) Use energy balance concept, determine and plot the water temperature (T) inside the tank as a function of time. Assume the hot water mix instantaneously with the cold water inside the tank and no heat losses.  Energy of water (E) can be represented as E=mCpT, where Cp is the specific heat, and T is the temperature of the water.