EVERYDAY ENGINEERING EXAMPLES FOR SIMPLE CONCEPTS

Thermal Properties of Materials Engage: MSEIP Engineering Everyday Engineering Examples This module shows how different materials affect the amount of heat transferred. In order to conduct the experiment a box made from different materials needs to be assembled (Figure 1). Materials needed: Gorilla Epoxy For the sides of the box, i) Styrofoam square (1cm thick) ii) Aluminum metal square (1cm thick) iii) Wood square (1cm thick) iv) Polypropylene square (1cm thick) Ice cubes or hot water Issues to Address; 1. How do materials respond to the application of heat? 2. How do the thermal properties of ceramics, metals, and polymers differ? Figure 1. Box assembled from different materials Page 1

Explore: The thermal conductivity shows how well the material transfers heat. It can be defined as the quantity of heat transmitted through a unit thickness of a material due to a unit temperature gradient under steady state conditions. As preparation for the demonstration, place ice cubes (or hot water) into the box and allow about a minute for heat to transfer through the more insulating materials. Have a student feel the temperature of the ice water. Have them comment on if it is hot or cold. Point out that each side of the box has the same temperature on the outside and inside. Ask them if they think the different sides will feel different or if they will all feel the same. Have a student come up and feel the different sides of the box. Ask them which side felt coldest (or hottest) and which sides felt different. Rank the sides in order from coldest to hottest if using ice cubes and the opposite if using hot water. Point out that each of the sides has the same temperature outside and inside and about the same area and width. So, the only thing different between the materials is the thermal conductivity (k) value. Explain: The property that measures how well heat is transmitted through a material is called thermal conductivity (often denoted k). It is evaluated primarily in terms of Fourier's Law for heat conduction. Thermal conductivity units are W/ (m K) in the SI system and BTU/(hr ft F) in the Imperial system. Heat transfer occurs at a lower rate across materials of low thermal conductivity than across materials of high thermal conductivity. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications and materials of low thermal conductivity are used as thermal insulation. The thermal conductivity of a material may depend on temperature. The reciprocal of thermal conductivity is called thermal resistivity. Thermal conductivity of materials plays a significant role in the design of equipment. Thermal conduction is generated by the movement of electrons and the transfer of lattice vibrations. Metals with low electrical resistance and crystals in which lattice vibrations are transferred easily display high thermal Page 2

conductivity. For ceramics, factors such can affect this property. Higher or lower levels of thermal conductivity can be attained in ceramic materials by controlling internal porosity, grain boundaries and impurities. In the following equation, thermal conductivity is the proportionality factor k. The rate of heat transferred (q) through the material is proportional to the thermal conductivity and temperature difference, and inversely proportional to the distance. q k dt dx Elaborate: Thermal conductivity is the ability of a material to transport heat. This topic is of great importance because of the frequent need to either increase or decrease the rate at which heat flows between two locations. For instance, those who live in colder winter climates are in constant pursuit of methods of keeping their homes warm without spending too much money. Heat escapes from higher temperature homes to the lower temperature outdoors through walls, ceilings, windows and doors. People make efforts to reduce this heat loss by adding better insulation to walls and attics, caulking windows and doors, and buying high efficiency windows and doors. The following formula can be used to calculate the heat transfer (q); q= k A (Tout Tin)/x where k is the thermal conductivity, A is the surface area, and x is the thickness of material. As is apparent from the Table 1, heat is generally transferred by conduction at considerably higher rates through solids (s) in comparison to liquids (l) and gases (g). Heat transfer occurs at the highest rates for metals (first eight items in left-hand column) because the mechanism of conduction includes mobile electrons. Several of the solids in the right-hand column have very low thermal conductivity values and are considered insulators. The structure of these solids is characterized by pockets of trapped air interspersed between fibers of the solid. Since air is a great insulator, the pockets of air interspersed between these solid fibers give these solids low thermal conductivity values. One Page 3

of these solid insulators is expanded polystyrene, the material used in Styrofoam products. Table 1. Thermal Conductivity (k) Values for Materials Material k Material k Aluminum (s) 237 Sand (s) 0.06 Brass (s) 110 Cellulose (s) 0.039 Copper (s) 398 Glass wool (s) 0.040 Gold (s) 315 Cotton wool (s) 0.029 Cast Iron (s) 55 Sheep's wool (s) 0.038 Lead (s) 35.2 Cellulose (s) 0.039 Silver (s) 427 Expanded Polystyrene (s) 0.03 Zinc (s) 113 Wood (s) 0.13 Polyethylene (HDPE) (s) 0.5 Acetone (l) 0.16 Polyvinyl chloride (PVC) (s) 0.19 Water (l) 0.58 Dense Brick (s) 1.6 Air (g) 0.024 Concrete (Low Density) (s) 0.2 Argon (g) 0.016 Concrete (High Density) (s) 1.5 Helium (g) 0.142 Ice (s) 2.18 Oxygen (g) 0.024 Porcelain (s) 1.05 Nitrogen (g) 0.024 Explain students that different materials feel different because their k-values are different. The coldest material when using cold water and the hottest material when using hot water has the greatest k-value. Finish by asking some of the potential discussion question below. 1. Why does each side feel different? 2. Which side feels the coolest (or hottest)? Why is it the metal? 3. What are some things that affect us on a daily basis that are affected by k- values? What did you learn? The rate of heat transfer depends on the material through which heat is transferred. The effect of a material upon heat transfer rates is often expressed Page 4

in terms of a number known as the thermal conductivity. The higher that the value is for a particular material, the more rapidly that heat will be transferred through that material. The rate of heat transfer is inversely proportional to the thickness of the material. Evaluate: Invite students to attempt the following problem: Example 1: Calculate the heat transfer through an aluminum pot versus a stainless steel pot? Calculus: The conductive heat transfer through a pot wall can be calculated as q / A = k dt / x where q / A = heat transfer per unit area (W/m 2 ) k = thermal conductivity (W/mK) dt = temperature difference ( o C) x = wall thickness (m) Conductive Heat Transfer per square meter through an Aluminum Pot Wall with thickness 2 mm - temperature difference 80 o C Thermal conductivity for aluminum is 237 W/(m K) (from the Table 1). Conductive heat transfer per unit area can be calculated as q / A = (237 W/(m K)) (80 o C) / (2 x10-3 m) = 9480000 (W/m 2 ) = 94800 (kw/m 2 ) Page 5

Conductive Heat Transfer per square meter through a Stainless Steel Pot Wall with thickness 2 mm - temperature difference 80 o C Thermal conductivity for stainless steel is 17 W/(m K). Conductive heat transfer per unit area can be calculated as q / A = (17 W/(m K)) (80 o C) / (2x 10-3 m) = 680000 (W/m 2 ) = 680 (kw/m 2 ) Page 6