Heat Flow Meters

NOVEMBER 2017 ISSUE #107 TECHNICALTIDBITS MATERION PERFORMANCE ALLOYS

MEASURING THERMAL CONDUCTIVITY - PART 1 - HEAT FLOW METERS

Thermal conductivity is a measure of the rate of Real-world heat transfer problems have complicated heat flow through a material. It is not easy to quantify, geometries, with heat moving in all directions by all 3 Watt’s up! – How since it can’t be directly measured. However, there methods, and are rarely in a steady state condition. thermal conductivity are a number of other more or less easily measured The general equation for pure thermal conduction in uses specially designed parameters that depend on the conductivity. These a body without internal heat generation is: conductivity meters. parameters are measured and the conductivity is calculated from them. Note, however, that different ∙ c = + + methods do not necessarily produce the same results. ( ) ( ) ( ) ρ ∂T ∂ ∂T ∂ ∂T ∂ ∂T ρ κ κ κ Heat transfer is a complicated subject. Most engineers However,∂t we∂퓍 are talking∂퓍 about∂y thermal∂y conductivity∂z ∂z have taken multiple courses back in their university days as a material property, and not about general heat Thermal to cover the subject. To quickly summarize, thermal transfer, so we will ignore all that and look at an ideal Conductivity energy moves from areas of high concentration (hot case. Figure 1 shows 1-dimensional heat conduction Steady State areas) to areas of low concentration (cold areas), in through a simple geometry under steady state spontaneous search for thermal equilibrium. Steady conditions, with no heat transfer by convection or Heat Transfer state heat transfer occurs when thermal equilibrium radiation. (One dimensional implies that the heat is Transient is met and maintained. Transient heat transfer is only moving in one direction, with no perpendicular what happens while the system is on its way to thermal component. The temperature changes only along the Heat Transfer equilibrium. In both cases, thermal energy moves from length, and the entire cross section at any given point Heat Flow hot to cold by conduction (direct contact between along the length is at a uniform temperature.) different materials), convection (through the movement Heat Flux of adjacent fluids), and/or radiation. Heat Flow Meter Figure 1. Simple Representation of Thermal 1-Dimensional Heat Conduction through Conductivity a Cylindrical Specimen. At steady state, if the Meter ends are maintained at their respective tempera- tures, there is constant thermal gradient through the specimen, and a constant flow of heat from the hot side to the cold side.

Under such 1-dimenional steady state conditions, the Rearranging the equation, you get following equation describes heat conduction: ( Hot - Cold) = - . = . ( Hot - Cold) T LT q = - . A = . A A T T dT L κ κ dT d퓍 κ κ This puts the equation in terms of heat flux (q/A), where A is the crossd퓍 sectional area of the specimen, L is which is the amount of thermal energy passing through The next issue of Technical Tidbits the distance between the hot face and the cold face, the area within a given time. will discuss methods to determine is the thermal conductivity, and q is the heat flow. So, thermal conductivity by measuring with a given cross sectional area, conducting path length,κ the total heat transfer. and a temperature difference from end to end, the thermal conductivity determines the rate of heat flow.

To improve heat flow out of a hot zone in a device, transducers) on either side of the sample measure the Written by Mike Gedeon of Materion you can do one of four things: heat flow q( ). If you input the sample length (L) and Performance Alloys Marketing Department. Mr. Gedeon’s primary 1. Increase the cross sectional area (A) cross sectional area (A), then the thermal conductivity can then be easily calculated and reported by the meter. focus is on electronic strip for the 2. Decrease the distance between the heat source automotive, telecom, and computer and heat sink (L) q . L markets with emphasis on = 3. Reduce the temperature of the cold side ( Cold) A( Hot - Cold) application development. T κ T T 4. Increase the thermal conductivity of the heat trans- References: ferring material ( ) Alternatively, you can measure q by measuring the power consumed to electrically heat the hot side, since that Alan J. Chapman Fundamentals of Since the available spacesκ on most devices are limited, will be equal to the thermal energy produced. Of Heat Transfer © 1987 Macmillan Publishing Company and cooling is usually limited to ambient temperature, course, good insulation is required, since the latter options 2 and 4 are the only reasonable choices for method assumes that the overwhelming majority of ASTM C-518-15 Standard Test consumer environments. Number 2 is why heat the heat generated passes through the sample to the Method for Steady-State Thermal Transmission Properties by Means cold side and an insignificant amount is lost through spreaders are so thin, and why heat sinks are mounted of the Heat Flow Meter Apparatus directly on top of processors whenever possible. other paths. ©2015 ASTM International Number 4 is why thermal conductivity is becoming To achieve steady state conditions in a low thermal ASTM E-1225-13 Standard Test increasingly important in consumer electronics devices. conductivity (high thermal resistivity) material within Method for Thermal Conductivity a reasonable time frame, the ratio of the cross sectional of Solids Using the Guarded- Remember that heat must usually pass through Comparative-Longitudinal Heat multiple materials on its way to dissipation from the area to the length needs to be high. Therefore, Flow Technique ©2013 ASTM processors. The material with the lowest thermal disk-shaped samples are used. Higher conductivity International metals achieve steady state quickly no matter what conductivity usually dominates the overall thermal ASTM E-1952-11 Standard Test conductivity of the path, unless it is extremely thin. the sample size and shape are. However, a larger Method for Thermal Conductivity Therfore, it is important to know the thermal distance between the hot and cold faces is required and Thermal Diffusivity by conductivity of all the materials in the path. for adequate resolution of the heat flow and tempera- Modulated Temperature ture gradient. Therefore, relatively long cylindrical or Differential Scanning Calorimetry ©2011 ASTM International To measure thermal conductivity with a heat flow rectangular prisms are used for the test specimen. meter (also known as a thermal conductivity The next issue will discuss some specific measurement “Technical Tidbits” Issues 23, meter) you will need to replicate the 1-dimensional methods that use these principles. 104 & 106 steady state condition as closely as possible. This means that the specimen should be insulated around the Please contact your local sides, so no significant heat is lost through the sides by sales representative for conduction, convection, or radiation. The temperature further information or on the hot side and the cold side must be carefully questions pertaining to maintained. Thermocouples measure the temperature Materion or our products. difference, A( Hot - Cold) and sensors (thermal T T Health and Safety Handling copper beryllium in solid form poses no special health risk. Like many industrial materials, beryllium-containing materials may pose a health risk if recommended safe handling practices are not followed. Inhalation of airborne beryllium may cause a serious lung disorder in susceptible individuals. The Occupational Safety and Health Administration (OSHA) has set mandatory limits on occupational respiratory exposures. Read and follow the guidance in the Safety TECHNICALTIDBITS Data Sheet (SDS) before working Materion Performance Alloys Sales with this material. For additional 6070 Parkland Blvd. +1.216.383.6800 information on safe handling Mayfield Heights, OH 44124 800.321.2076 practices or technical data on [email protected] copper beryllium, contact Materion Performance Alloys Technical Service or your local representative. +1.216.692.3108 800.375.4205 [email protected]