METHODS OF MEASUREMENT OF THERMAL CONDUCTIVITY

Thermal conduction is the transfer of heat from one part of a body to another with which it is in contact.

Thermal conductivity ‘k’ is defined as ability of material to transmit heat and it is measured in watts per square meter of surface area for a temperature gradient of 1 K per unit thickness of 1m.

INTRODUCTION

k=(Q/A)÷(△T/△L)

Where, Q= amount of heat transferred; watt A= cross-sectional area; sq. meter △L= change in length of body; m △T= change in temperature of body; kelvin Q/A= heat flux

Therefore measurement of thermal conductivity involves:

1. The measurement of the heat flux

2. Temperature difference

the density of material

Density k

moisture of material and

Moisture k

ambient temperature

Temperature k

Factors affecting thermal coductivity(k)

Thermal conductivity of biological materials is usually measured using any of the following methods:

Steady state method constant temperature

Unsteady state method temperature varies with time

Methods of measurement

It takes long time (10-12 hrs) to attain the steady state conditions for agricultural materials like grains

Since the temperature difference is maintained for along time, the moisture available in the grain migrates from heat source towards outside due to which accuracy of measurement changes.

Steady state method

Four methods of measurement are followed in steady state condition:

1. Guarded hot plate method2. Concentric cylinder method3. Concentric sphere method4. Thermal diffusivity method

A solid sample of material is placed between two plates. One plate is heated and the other is cooled or heated to lesser extent. Temperature of the plates is monitored using thermo couple until they are constant.

The steady state temperatures, the thickness of the sample and the heat input to the hot plate are used to calculate thermal conductivity.

1. Guarded hot plate method

Simple method Suitable for agricultural materials specially

in the form of slabs like straw boards, bread-slice, meat slice etc.

The apparatus consists of two cylinders assembled co-axially. The sample is placed in the annular space between the cylinders.

The inner cylinder is heated by means of electrical network and cooled by flowing water.

The thermal conductivity k is measured by: Q= (2ΠkL .△T)/ln(R₂/R₁)Where, Q= rate of heat flow L=thickness material placed between cylinder △T= temperature difference across material R₂= radius of outer cylinder R₁= radius of inner cylinder

2. Concentric cylinder method

Temperatures along the height of the specimen is assumed uniform and little difference is neglected.

It is simple and economical method. Used for powder materials and variety of

grains. The sample material should be packed

properly to avoid any convection currents in between them.

The apparatus consists of two concentric thin spherical chambers with grain sample filled inside the annular space properly.

The inner sphere is heated electrically and the outer space is cooled in a water bath. The thermal conductivity ‘k’ will be:

Q=kA₂A₁(T₂-T₁/R₂-R₁)Where q= rate of heat flowA= areaT= temperature1,2 is suffix for outer and inner sphere

3.Concentric sphere method

It is indirect method of thermal conductivity measurement.

The thermal conductivity can be calculated by the knowledge of other properties of materials like specific heat, density and thermal diffusivity.

α=k/ρCWhere α= thermal diffusivity of materialk =thermal conductivityρ= density of materialC= sp. Heat at constant pressure

4.Thermal diffusivity method

This method can be used for wide variety of food materials.

This method is part of Laboratory lesson. This method belongs to the steady state

methods, guarded hot plate and is convenient for measuring of solid materials.

Hot plate is circular with the diameter 160 mm and is heated electrically. Hot plate is embedded by the compensation plate, which serves as insulation of the hot plate and has the same temperature as the hot plate.

Dr. Block’s appratus

Temperature in compensation and cooling plates is kept by water, running through two thermostats. For different materials is necessary to adjust proper intensity of heating to obtain steady state.

Thermal conductivity is calculated from:

Where, Q is thermal performance of hot plate [W]

d =mean thickness of the sample [m]A= hot plate area [m2]△t= thermal gradient between hot and cold

plate [K]o= correction of the thermal gradient about

heat looses in apparatus [K]

It is a quick method. Usually carried out by needle probes These method do not require the signal to

obtain a constant value. Instead, the signal is studied as a function of time.

The mathematical analysis of the data is in general more difficult.

Unsteady state method

There are four main types of instruments available to measure thermal conductivity:

1. transient plane source method 2. hot wire method 3. laser flash method 4. 3-ω method 5. time domain thermo reflectance method They differ in technique, sample size, testing time,

capability and methodologies of measurement.

It utilizes a plane sensor and a special mathematical model describing the heat conductivity, combined with electronics, enables the method to be used to measure k.

Range between at least 0.01-500 W/m/K The Transient Plane Source technique

typically employs two samples halves, in-between which the sensor is sandwiched.

1.Transient plane source method

The sensor is placed between two halves of the sample to be measured.

During the measurement a constant electrical effect is passes through the conducting spiral, increasing the sensor temperature.

The heat generated dissipates into the sample on both sides of the sensor, at a rate depending on the thermal transport properties of the material.

By recording temperature vs. time response in the sensor, the thermal conductivity, thermal diffusivity and specific heat capacity of the material can be calculated.

A heated wire is inserted into the material. The heat flows out radially from the wire into the sample and the temperature change in the wire is recorded.

The plot of the wire temperature versus the logarithm of time is used to calculate thermal conductivity, provided that density and capacity are known.

Since this is an intrusive measure, it cannot be used for solids; it works well for foams, fluids and melted plastics.

2. Hot wire method

This method is used to measure thermal diffusivity of a thin disc in the thickness direction.

This method is based upon the measurement of the temperature rise at the rear face of the thin-disc specimen produced by a short energy pulse on the front face.

With a reference sample specific heat can be achieved and with known density the thermal conductivity results as follows

α=k/ρC

3. Laser flash method

It is suitable for a multiplicity of different materials over a broad temperature range (−120°C to 2800°C).

In this method a thin metal strip evaporated on the sample acts as heat source and a thermometer.

The heater is driven with AC current at frequency ω, which causes heat source to oscillate at frequency 2ω.

By monitoring AC voltage as a function of the frequency of the applied AC current thermal conductivity can be determined.

4. 3-ω method

The measured voltage will contain both ω and 3ω components, because the Joule heating of the film causes small perturbation to its resistance with frequency 2ω as stated in the following equation

where C0 is constant. Thermal conductivity is determined by the linear slope of

ΔT vs. log(ω) curve. The main advantages of the 3ω-method are minimization of radiation effects and easier acquisition of the temperature dependence of the thermal conductivity than in the steady-state techniques.

Although some expertise in thin film patterning and microlithography is required, this technique is considered as the best pseudo-contact method available.

Time-domain thermo reflectance is a method by which the thermal properties of a material can be measured, most importantly thermal conductivity.

This method can be applied most notably to thin film materials, which have properties that vary greatly when compared to the same materials in bulk.

The idea behind this technique is that once a material is heated up, the change in the reflectance of the surface can be utilized to derive the thermal properties.

The change in reflectivity is measured with respect to time, and the data received can be matched to a model which contain coefficients that correspond to thermal properties

5. Time domain thermo reflectance method