UZB232E Heat Transfer

Fall 2013-2014

Assignment #1 (Due date: 26/10/2013, 23:30) Question #1: The wall of a drying oven is constructed by sandwiching an insulation material of thermal conductivity = 0.05 . between thin metal sheets. The oven air is at , =300, and the corresponding convection coefficient is = 30 . . The inner wall surface absorbs a radiant flux of = 100 from hotter objects within the oven. The room air is at , = 25, and the overall coefficient for convection and radiation from the outer surface is = 10 . . a) Draw the thermal circuit for the wall and label all temperatures, heat rates and thermal resistances. b) What insulation thickness L is required to maintain the outer wall surface at a safe to touch temperature of = 40 ?

Question #2: Starting with an energy balance on cylindrical and spherical shell volume elements, derive steady one-dimensional heat conduction equations for

a) a long cylinder with constant thermal conductivity and no heat generation, b) and a sphere with constant thermal conductivity in which heat is generated at a rate of

.

Note: Draw the shell volume elements and show lengths, area and the volumes for each derivation.

Question #3: Consider a long resistance wire that has a constant thermal conductivity and radius of r1=0.4 cm. Inside the wire, there is a uniform heat generation at a constant rate of = 5 W/cm3. The wire is covered with a 0.2 cm thick layer of plastic, whose thermal conductivity is also constant. The outer surface of the plastic cover loses heat by convection to the ambient air at T=25oC with an average combined heat transfer coefficient of h=15 W/m2.K. The temperature of the wire-plastic layer interface is measured to be 28oC. Determine the thermal conductivity of the plastic layer under steady one-dimensional heat transfer conditions.

Question #4: Figure 1 illustrates a spherical dewar containing saturated liquid oxygen that is kept at pressure p(Lox)=25psia; the saturation temperature of oxygen at this pressure is T(Lox) =95.6 K. The dewar consist of an inner and outer metal liner separated by polystyrene foam insulation. The inner metal liner has inner radius rmli,in =10.0 cm and thickness thm=2.5 mm. The conductivity of both metal liners is km=15 W/m.K. The heat transfer coefficient between the oxygen within the dewar and the inner surface of the dewar is hin=15 W/m2.K. The outer surface of the dewar is surrounded by air at T= 20oC. The emissivity of the outer surface of the dewar is =0.7. The heat transfer coefficient between the outer surface of the dewar and the surrounding air is hout=6 W/m2.K. The area-specific contact resistance that characterizes the interfaces between the insulation and the adjacent metal liners is Rc=3.0x10-3 K.m2/W. The thickness of the insulation between the two metal liners is thins = 1.0 cm and the conductivity of the polystyrene foam at cryogenic temperature is approximately kins=330 W/cm.K.

a) Draw a network that represents this situation using 1-D resistances and write down resistance expression for each element.

b) Estimate the rate of heat transfer to liquid oxygen c) Plot the rate of heat transfer to the liquid oxygen as a function of the insulation thickness

Question #5: A lens is used to focus the illumination energy (i.e. radiation) that is required to develop the resist in lithographic manufacturing process, as shown in the figure below. The lens can be modeled as a plane wall with thickness L=1.0 cm and thermal conductivity k=1.5 W/m.K . The lens is not perfectly transparent but rather absorbs some of the illumination energy that is passed through it. The absorption coefficient of the lens is =0.1 mm-1. The flux of radiant energy that is incident at the lens surface (x=0) is =0.1 W/cm2. The top and bottom surfaces of lens are exposed to air at T=20oC and the average heat transfer coefficient on the surfaces is h=20 W/m2.K.

a) Determine and plot the temperature distribution within the lens. b) Find locations inside the lens where the temperatures are the maximum and minimum.

Calculate the maximum and minimum values of the temperature inside lens.