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Non steady state thermal conductivity of ABS was estimated using an analytical approach in a Cold Climate Chamber at ?10?C and ?14?C. Two hollow cylinders of ABS of varying thickness were used to estimate the conductivity. The material was porous but the porosity was unknown. This paper is a case study to understand, if it is reasonable to estimate the thermal conductivity using the analytical varying thickness approach.

Energy exists in various forms. Thermal energy which is related with heat that can be transferred from one system to another as a result of temperature difference. Energy transfer mechanics can be principally of three types conduction (inside solid), convection (through a fluid) and radiation (electromagnetic emission). From the principle of conduction, thermal conductivity “k” is defined as the property of material to conduct heat flux due to a temperature variation between its ends. Mathematically,

where

There have been different methods and devices developed during the last few decades to experimentally determine the fundamental thermal conductivity of a material. The measurement of thermal conductivity in principle involves the measurement of heat flux and temperature difference across the boundary, nevertheless to determine heat flux is not trivial. Heat flux can however be estimated by an excitation e.g. electric power going into the heater (this is called an absolute measurement), whereas the flux measurement is done by comparison (this is called comparative) [

1. Steady State Technique

2. Non Steady State Techniques or Transient Techniques.

As name defines, in this technique the temperature change is allowed to stabilize such that

In this non steady state technique or transient technique the conductivity is measured as the process builds up its heating cycle. This measurement is common in practice as it measures the instantaneous conductivity and then if the techniques allows then they may be averaged. There are many non-steady state conductivity measurement technique, e.g.

a) Transient Plane Source Technique [

b) Modified Transient Plan Source Technique [

c) Transient Line Source Technique [

d) Laser Flash Technique [

e) 3w Technique [

f) Time Domain Thermoreflectance Method

Atmospheric icing research team at Narvik University College is developing an atmospheric icing sensor which is potentially capable to detect icing event, icing type, icing load, icing rate, melting rate. The final material of this icing sensor is aluminium, nevertheless to evaluate the option of using ABS (Acrylonitrile butadiene styrene) as one of the potential material, the thermal conductivity of ABS was important to estimate in freezing domain. The geometry of this model was a scaled down model of the rotating part of the actual sensor which was produced through rapid prototyping machine CubePro Duo (

The layer resolution for this model was “200 mm” and the print strength was “almost solid” whereas the print pattern was “diamonds”. These settings can be seen in

Narvik University College have three Cold Room Facilities for experimentation (see

The main idea of this work was to estimate non steady state or transient thermal conductivity of the material by analyzing heat transfer through two hollow cylinders of different thicknesses: 5 and 10 mm. The thermocouples were mounted on the geometries, as can be seen in

The experiment table was arranged as shown in

As shown in

1 - 2 Convection A (is the heat transfer from surrounding area to the outer surface of the model 1);

2 - 3 Conduction B (is the heat transfer from outer surface to inner surface of the model 1, in other words it is conduction through the wall);

3 - 4 Convection C (is the heat transfer from inner wall to the inner area of model 1)

1 - 5 Convection D (is the heat transfer from surrounding area to the outer surface of the model 2);

5 - 6 Conduction E (is the heat transfer from outer surface to inner surface of the model 2, in other words it is conduction through the wall)

6 - 7 Convection F (is the heat transfer from inner wall to the inner area of model 2)

Hence total heat transfer for the model 1 then is equal to:

q1 = Convection A + Conduction B + Convection C (2)

q2 = Convection D + Conduction E + Convection F (3)

where q1 is the heat transfer rate for model 1 and q2 is the heat transfer rate for model 2. Both of the models are located in the same surrounding conditions, hence it is reasonable to assume that the heat transfer rate can be equated q1 = q2. Therefore,

Convection A + Conduction B + Convection C = Convection D + Conduction E + Convection F (4)

Therefore from Equation 4 and

The inner and outer areas and all other dimensions of the two cylinders were found using the CAD package where these geometries were created (see

From each experiment, the instantaneous conductivity was measured for a period of 24 hours. The samples were then averaged. The results for each experiment are shown in

Model | Convection | Conduction | Convection |
---|---|---|---|

1 | |||

2 |

Model | Inner Area | Outer Areas | Thickness | h_{air } |
---|---|---|---|---|

1 | ||||

2 |

Experimental at −10˚C | Experimental at −14˚C | Actual ABS |
---|---|---|

k_{avg}=0.134 | k_{avg}=0.128 | k_{avg}=0.188 to 0.335 |

In this work, the thermal conductivity of ABS was estimated using an analytical approach by measuring the temperature distribution across the cylindrical geometries. The deviation between the analytically estimated and standardized limit values of ABS may be because of the following reasons,

1) This ABS used in this experiment was have porosity larger than 0 and it has the print pattern of diamonds therefore it has some air pockets (k_{air} = 0.021 W/mC).

2) There may be some chances of inadequate insulation of the both hollow cylinders which may have affected the results.

3) There may be chances of inadequate thermocouple attachments on the cylinders as the epoxy have less stickiness in freezing domains.

4) Also the exact limit values of ABS from 0.188 till 0.335 W/mC are based upon the composition of ABS as can be seen in Honeycutt [

The results of Experiment 2 at −14˚C have less non steady state thermal conductivity fluctuations than the results of Experiment 1 at −10˚C because of the reason that in second experiment there were low variations in cold chamber temperature as mentioned in Section 3. Nevertheless it is found that this approach to estimate thermal conductivity of a material by varying thickness of two geometries and testing it in cold chamber facility is sufficiently adequate and can be utilized for future experimentations at least to estimate the thermal conductivity of any material with unknown properties and composition. The results of this analysis can also be improved by introducing interface heat transfer principle in this thickness variation principle.

The work reported in this research paper was carried out by Atmospheric Icing Research Team at Industrial Engineering Department of Narvik University College and was funded by Research Council of Norway, project no. 195153 (ColdTech RT3 and RT5) and Norwegian Centre for International Cooperation in Education, project number- HNP-2014/10023.

Umair N. Mughal,Marina Makarova,Muhammad Shakeel Virk,Geanette Polanco, (2015) A Case Study to Estimate Thermal Conductivity of ABS in Cold Climate Chamber. World Journal of Engineering and Technology,03,309-315. doi: 10.4236/wjet.2015.33C046