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M. Parikh et al.
[2, 3]. The main limitation of experiment analysis is that it is very difficult to put
probe at interface, and hence, interface conductance is estimated by extrapolation of
temperature field.
Inverse heat transfer (IHT) techniques are used when the unknown quantity is practically not accessible, the quantity is estimated by using temperature data through
some accessible distance, and the data is converged by minimizing the least squarebased objective function. These techniques are most widely used in the estimation of
boundary heat flux, heat transfer coefficient, thermo-physical properties of materials,
contact conductance between two contacting surfaces, etc. [4]. The IHT techniques
are classified in two categories: deterministic methods and stochastic methods. Deterministic methods use gradient of objective function for convergence while stochastic
methods are search based methods which pick the best fitting solutions from randomly
generated solution set. Conjugate gradient method (CGM) with an adjoin problem
is the most widely used deterministic method [5]. CGM method is fast, but its main
limitation is that it may converge up to local minima, and it is very sensitive to
measurement of errors. Jaya is a stochastic algorithm developed by Rao [6]. It is
simple in structure and does not require any other tuning parameters. The experimental solutions achieved by using Jaya algorithm proved to be superior over results
obtained by using the MOGA, NPGA, GEM, TLBO, LFOPC, and RSM algorithms
in terms of the results, computational effort, and function evaluations [7].
The current work includes estimation of contact conductance between two metal
rods for one-dimensional transient heat conduction problem using Jaya as an inverse
algorithm. Aluminum (K a = 205 W/mK) and brass (K b = 109 W/mK) are chosen
as rod materials, and several cases like different population size, different profiles of
contact conductance, and altered errors in temperature measurements are considered.
2 Methodology
The methodology includes: (1) Obtaining the temperature field profile by solving
direct problem using known value of contact conductance. (2) Formulation of inverse
heat transfer problem by using Jaya algorithm to estimate the contact conductance
using the temperature field obtained from direct problem.
2.1 Direct Problem
Figure 1 shows computational domain for one-dimensional transient heat conduction
between two contacting surface. Aluminum is used in region-1, while brass is used
in region-2. The left boundary (x = 0) is subjected to transient heat flux q(t), and
constant temperature is applied on right boundary (x = L 2 ). The interface is located
at x = L 1 where contact conductance h(t) is present [5, 8].
M. Parikh et al.
[2, 3]. The main limitation of experiment analysis is that it is very difficult to put
probe at interface, and hence, interface conductance is estimated by extrapolation of
temperature field.
Inverse heat transfer (IHT) techniques are used when the unknown quantity is practically not accessible, the quantity is estimated by using temperature data through
some accessible distance, and the data is converged by minimizing the least squarebased objective function. These techniques are most widely used in the estimation of
boundary heat flux, heat transfer coefficient, thermo-physical properties of materials,
contact conductance between two contacting surfaces, etc. [4]. The IHT techniques
are classified in two categories: deterministic methods and stochastic methods. Deterministic methods use gradient of objective function for convergence while stochastic
methods are search based methods which pick the best fitting solutions from randomly
generated solution set. Conjugate gradient method (CGM) with an adjoin problem
is the most widely used deterministic method [5]. CGM method is fast, but its main
limitation is that it may converge up to local minima, and it is very sensitive to
measurement of errors. Jaya is a stochastic algorithm developed by Rao [6]. It is
simple in structure and does not require any other tuning parameters. The experimental solutions achieved by using Jaya algorithm proved to be superior over results
obtained by using the MOGA, NPGA, GEM, TLBO, LFOPC, and RSM algorithms
in terms of the results, computational effort, and function evaluations [7].
The current work includes estimation of contact conductance between two metal
rods for one-dimensional transient heat conduction problem using Jaya as an inverse
algorithm. Aluminum (K a = 205 W/mK) and brass (K b = 109 W/mK) are chosen
as rod materials, and several cases like different population size, different profiles of
contact conductance, and altered errors in temperature measurements are considered.
2 Methodology
The methodology includes: (1) Obtaining the temperature field profile by solving
direct problem using known value of contact conductance. (2) Formulation of inverse
heat transfer problem by using Jaya algorithm to estimate the contact conductance
using the temperature field obtained from direct problem.
2.1 Direct Problem
Figure 1 shows computational domain for one-dimensional transient heat conduction
between two contacting surface. Aluminum is used in region-1, while brass is used
in region-2. The left boundary (x = 0) is subjected to transient heat flux q(t), and
constant temperature is applied on right boundary (x = L 2 ). The interface is located
at x = L 1 where contact conductance h(t) is present [5, 8].