FIELD OF THE INVENTION
The present invention generally relates to the measurement of thermal diffusivity and thickness of
the heat resistant resin coating on a metal substrate based on a continuous constant heat flux on
the metal surface. More particularly, the invention relates to a method of measuring thermal
diffusivity of coating destined for high temperature heat resistance applications.
BACKGROUND OF THE INVENTION
In high temperature applications for example coal fired power plants, gas turbines, aerospace
applications, an insulation is provided to protect the components from the harsh environment.
Conventional power plants operating using fossil fuel generates a huge amount of heat and hot
flue gases. The hot flue gas causes corrosion and erosion on the outer surface of the boiler tubes.
For protecting from the harsh conditions and extending the life of the component, a high
refractory coatings are applied on the boiler tubes. Thus, the coating increases the life of the
component and also bolsters the efficiency of the boiler. Similarly, in land and gas turbine
applications, the turbine blades are to be protected from thermal shock. Therefore, a thermal
shock resistant, heat resistant, adhesive and tenacious coating is applied on the blades. In both
the applications, a proper estimation of the insulation properties of the coating is essential.
Generally, the thermal insulation of a coating is qualified, in the form of thermal diffusivity value.
Hence, measurement of the thermal diffusivity is an important parameter for the above
conditions. Several methods are known in the art to measure the thermal diffusivity values for
example, flash method and laser heating method.
US Patent 7976215 issued to Kim, Seog Kwang, teaches "Apparatus and method for measuring
thermal diffusivity using flash method". According to this invention thermal diffusivity of a
specimen is measured using half time calculations wherein, the half time represents the
occurrence of half of the temperature rise for the measurement sample to reach thermal
equilibrium.
US Patent 7364354 issued to Lakestani describes et al, "Method and system for measuring
thermal diffusivity", in which the thermal diffusivity is calculated by determining the phase
difference or phase shift between the Modulated beam signal and Modulated temperature signal.
US6595685 to Baba et al, describes "Method and apparatus for measuring the thermo physical
properties", in which thermal diffusivity value is determined from reflected probe laser beam.
According to prior art, for any high temperature heat resistance applications, it is necessary to
determine the thermal diffusivity of the material. Especially, in evaluating a coating on high
temperature components, thickness of coating also plays an important role. For a particular heat
resistant application, thermal barrier coating thickness and thermal diffusivity should be known.
OBJECT OF THE INVENTION
It is therefore an object of the present invention to propose a method of measuring thermal
diffusivity of coating destined for high temperature heat resistance applications.
SUMMARY OF THE INVENTION
According to the present invention, a method is provided a method of measuring thermal
diffusivity of coating destined for high temperature heat resistance applications, in which a
constant heat flux on a substrate is used to measure thermal diffusivity or coating thickness. The
method is based on analytical solution of transient heat transfer of a composite slab. According to
the method a constant heat flux is provided on a metal substrate and the thermal profile of the
outer surface of coating is measured. The change in outer surface temperature of the coating
with respect to time, provides an empirical co-relation between the thermal diffusivity and coating
thickness. Hence, if a thermal diffusivity value is known, coating thickness can be measured
precisely. Therefore, this relationship is useful in designing the high temperature components.
This inventive method can easily predict the values of thermal diffusivity or coating thickness
within a short span of time. If one of the variables for example, thermal diffusivity or coating
thickness is known, the other variable can be obtained from the above experimental and
analytical solution.
According to the inventive measurement method, three samples of heat resistant resin coating of
thickness 225um, 630µm and 1010µm are applied on an Aluminium metal substrate of 2mm
thick. The samples are provided with identification tag, say Sample 1, Sample 2 and Sample 3.
Sample 1 is exposed to constant heat fluxes of 0.4KW and 0.5KW
Sample 2 is exposed to constant heat fluxes of 0.2KW and 0.3KW
Sample 3 is exposed to constant heat fluxes of 0.25KW and 0.3KW
Temperature of outer surfaces of the coating is measured with respect of frames in all above six
cases. Temperature difference of the outer surface coating for two different heat fluxes are
plotted against number of frames. The slope and intercept gives an empirical relationship
between the thermal diffusivity and coating thickness.
The slope/intercept is co-related to the equations obtained from solving the heat transfer problem
as shown in hereinafter.
The thermal diffusivity can be measured using above experimental procedure and the composite
slab heat transfer analytical solution.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
Figure 1 : Shows the heat transfer across a substrate and coating for a constant heat flux on
metal substrate
Figure 2 : Shows a test device of the constant heat flux method of the invention
Figure 3 : Shows a group of Temperature on coating surface with respect to frames on sample
1 with heat fluxes of 0.4 KW
Figure 4 : Shows a graph of Temperature on coating surface with respect to frames on sample
1 with heat fluxes of 0.5 KW
Figures 5 : Shows a graph of Temperature on coating surface with respect to frames on sample
2 with heat fluxes of 0.2 KW
Figure 6 : Shows a graph of Temperature on coating surface with respect to frames on sample
2 with heat fluxes of 0.3 KW
Figure 7 : Shows a graph of Temperature on coating surface with respect to frames on sample
3 with heat fluxes of 0.25 KW
Figure 8 : Shows a graph of Temperature on coating surface with respect to frames on sample
3 with heat fluxes of 0.3 KW
Figure 9 : Shows a graph of AT Vs number of frames for sample 1 for two different heat fluxes
Figure 10 : Shows a graph of AT Vs number of frames for sample 3 for two different heat
fluxes.
DETAIL DESCRIPTION OF THE PREFERRED EMBODIMENTS
The thermal diffusivity of the heat resistant coating on aluminium substrate is measured using an
Infrared camera, and with an application of a constant heat flux. For experimental purpose, an
aluminium substrate of dimensions, 75mm *75mm*2mm with coating thickness of 225µm, 630µm
and 1010µm was taken. Samples with thickness 225µm, 630µm and 1010µm are asigned as
Sample 1, Sample 2, and Sample 3, respectively for reference purpose. A bond coat of Strontium
chromate is applied as primer over the Aluminium substrate for better adherence of coating on
the metal substrate.
A constant heat flux is provided on the metal substrate using neon lamps as shown in Figure 1.
The temperature profile of the outer surface of coating is obtained using an IR camera as shown
in Figure 2. The following is a conductive heat transfer problem and is worked out with a constant
heat flux boundary condition:-
Solution for the above equations
FINAL SOLUTION FOR THE ANALYTICAL APPROACH
a1, a2 =Thermal Diffusivity values of Metal and Coating respectively
T1,T2 = Temperature of Metal and Coating respectively
L1,L2 = Thickness of Metal and Coating respectively
X = Space Co-ordinate of Metal and Coating
t = time
K1,K2 = Thermal Conductivity values of Metal and Coating respectively
Q = Constant Heat - flux given to Metal
?n = Eigen values
a1, a2,b1,b2,C1,C2,D1,D2,E1,E2 = Constants
Therefore, the governing equations 1 and 2, gives the temperature profile of the substrate and
coating. Equations 3 and 4 are the initial conditions representing the composite slab under room
temperature condition. The constant heat flux boundary condition and adiabatic boundary
condition are given in equations 5 and 6 for substrate boundary and coating boundary,
respectively. The equations 1 and 2 with initial conditions as in equations 3 and 4 and boundary
condition equations 5-8 are solved using separation of the variables as shown hereinafter.
Final solution is obtained as shown in equations 13 - 16. The outer coating surface temperature is
a function of the thermal properties of the material, heat flux and time. Evaluation of the function
f (a1, a2,K1,K2,L1,L2,t) is a very difficult process. The function is independent of heat flux.
Therefore, for two different heat fluxes at the same time, the function is nullified and temperature
difference of the outer surface gives a linear relationship with the time. Hence, the slope and
intercept of the linear graph between AT and time gives an empirical relationship between the
thermal diffusivity and coating thickness value. Experiments carried out on samples 1,2,3 and
observations are made as follows:
Two set of experiments with constant heat fluxes 0.4KW and 0.5KW on sample 1 with a coating
thickness of 225um were carried out. Constant heat flux was given for a time of 110 seconds at
a-frequency of 50Hz. The outer temperature of coating surface is measured using an IR camera
and plotted with respect to number of frames as in Figure 3 and 4. The temperature difference of
two heat fluxes is plotted against the number of frames as shown in Figure 9. The slope and
intercept values can be obtained using a linear regression on the obtained data as sown in Figure
8. The slope/intercept as shown in equation gives an empirical relationship between the thermal
diffusivity and coating thickness. The thermal diffusivity value obtained from this process is given
is given in Table 1.
Similar experiment was made on the sample 2 with a coating thickness of 630um. This is exposed
to two heat fluxes of 0.2KW and 0.3KW. The heat flux is given for a time of 110 Seconds with a
frame frequency of 50HZ. The outer temperature of coating surface is measured using an IR
camera and plotted with respect to number of frames as in Figure 5 and 6. The temperature
difference of two heat fluxes is plotted against the number of frames as shown in Figure 10. The
slope and intercept values can be obtained using a linear regression on the obtained data as
shown in Figure 9. The slope/intercept as shown in equation gives an empirical relationship
between the thermal diffusivity and coating thickness. The thermal diffusivity value obtained from
this process is given in Table 1.
The sample 3 with a coating thickness of l1010µm is exposed to two heat fluxes of 0.25KW and
0.3KW. The heat flux is given for a time of 110 Seconds with a frequency of 50HZ. The outer
temperature of coating surface is measured using an IR camera and plotted with respect to
number of frames as in figure 7 and 8. The temperature difference of two heat fluxes is plotted
against the number of frames as shown in Figure 11. The slope and intercept values can be
obtained using a linear regression on the obtained data as shown in Figure 10. The
slope/intercept as shown in equation gives an empirical relationship between the thermal
diffusivity and coating thickness. The thermal diffusivity value obtained from this process is given
in Table 1.
In all three samples of different coating thickness, the thermal diffusivity value was evaluated to
be in the order of 2* 10-9 m2/s.
LITERATURE REFERENCES
(1) "Measurement of thermal diffusivity of solids using Infrared Thermography", J.M.Laskar,
S.Bagavathiappan, M.Sardar, TJayakumar, John Phillip, Baldev Raj, Materials Letters 62,
2740-2742 (2008).
(2) "Quantitative Thermography for NDE", C.Spiessberger, V.Carl, A.Dillenz.
(3) "Heat flow in composite slab cylinder and sphere", Walter P.Reid, 351-357, (1962).
(4) "Transient analytical solution to heat conduction in composite circular cylinder", X.Lu,
P.Tervola, M.Viljanen, International journal of heat and mass transfer, 49, 341-348,
(2006).
(5) "Thermal Conduction in a composite circular cylinder: A new technique for thermal
conductivity measurements of lunar core samples", K.Horaj, J.L. Winkler jr, S.J. Keihm,
M.G. Langseth, J.A. Fountain, E.A.West, Royal Society Publishing, 293, 571-598, (1979).
(6) "Theory and practice of Infrared technology for Non destructive testing",
Xavier.P.V.Maldague, A Wiley-Interscience publication, (2001).
WE CLAIM
1. A non-destructive method of measuring thermal diffusivity of a coating on at least three
metal substrate samples with the application of a constant heat flux on the metal substrate
samples, the method comprising:
providing a first constant heat flux on metal substrate;
measuring the thermal profile with respect to time on an outer surface of the coating;
providing a second constant heat flux on the metal substrate and determining temperature
of the outer surface of the coating with respect to time; and
generating an empirical relation between the thermal diffusivity of coating and coating
thickness based on a difference of the outer temperatures with respect to time.
2. The method as claimed in claim 1, wherein the second constant heat flux value is more
than the first constant heat flux value.
3. The method as claimed in claim 1, wherein the thermal barrier coating is heat resistant
resin and the metal substrate is aluminium.
4. The method as claimed in claim 3, wherein the thickness of metal substrate for all the
three samples is constant and equal to 2mm.
5. The method as claimed in claim 3, wherein the thickness of thermal barrier coating of
sample 1, 2 and 3 are measured as 255um, and 1010µm, respectively.
6. The method as claimed in claim 5, wherein a bond coat is applied at the interface between
the metal substrate and coating, which comprises of Strontium oxide.
7. The method as claimed in claim 1, wherein the substrate is exposed to constant heat flux
for a time of 110 Seconds.
8. The method as claimed in claim 1, wherein the temperature of outer surface of the coating
is obtained using in Infrared (IR) camera for 110 seconds for two different heat fluxes.
9. The method as claimed in claim 8, wherein the infrared signals from the samples are
measured by Thermography.
10. The method as claimed in claim 8, wherein a frame frequency for 110 seconds time interval
is 50HZ.
11.The method as claimed in claim 8, wherein a total number of 5500 frames are used for the
measurement.
12. The method as claimed in claim 1, wherein the temperature difference (AT) with respect to
time show a linear relationship.

ABSTRACT

The invention relates to a non-destructive method of measuring thermal diffusivity of a coating on
at least three metal substrate samples with the application of a constant heat flux on the metal
substrate samples, the method comprising providing a first constant heat flux on metal substrate;
measuring the thermal profile with respect to time on an outer surface of the coating; providing a
second constant heat flux on the metal substrate and determining temperature of the outer
surface of the coating with respect to time; and generating an empirical relation between the
thermal diffusivity of coating and coating thickness based on a difference of the outer
temperatures with respect to time.