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R. Prajapati et al.
heat flux, convection coefficient, thermo-physical properties, initial condition and
intensity of source term [1].
IHTP uses least square-based objective function for minimization, and hence,
they are ill posed problems. There are two type of approaches used for IHTP:
gradient-based approach and stochastic (population-based) approach. Gradientbased approach uses gradient of an objective function for solution. Among all
gradient-based method, conjugated gradient method (CGM) with an adjoint problem
is the most popular gradient-based approach. Liu and Ozisik [2] estimated the transient wall heat flux for hydrodynamically developed and thermally developing turbulent forced convection flow in a parallel plate channel and concluded that the accuracy
of CGM deteriorates with measurement error and step heat flux profile is difficult
to estimate than triangular heat flux profile. Huang and Chen [3] estimated transient
boundary heat flux for three-dimensional forced convection flow by using CGM.
They used commercial software CFX4.2 for the CGM algorithm and considered
the effect of duct height, inlet velocity and measurement errors on flux estimation.
The main limitation of CGM is that it is very sensitive to measurement error and
sometimes it converges up to local minima. The stochastic methods are more accurate than deterministic methods, and they obtain global solution. Cuckoo search,
genetic algorithm (GA), differential evolution (DE) and JAYA algorithm are some
examples of stochastic methods. Parwani et al. [4] used the DE approach for estimation of the position and strength of time-varying source in participating medium in
a two-dimensional enclosure. They considered conduction and radiation boundary
conditions and found that DE is quite reasonable for estimation. Li and Yang [5]
used GA for estimation of radiation parameters of the gray participating medium.
Above researchers used different stochastic (population-based) approach to estimate the required properties and found that these approaches are quite reasonable
for the estimation. For current case, a new stochastic algorithm—JAYA is used for
IHTP. JAYA is developed by Rao [6] and successfully implemented for solving benchmark problems. It has simple structure and does not require any tuning parameters.
Rao et al. [7] used a multi-objective JAYA algorithm (MO-JAYA) for optimization of modern machining process which includes plasma arc machining (PAM),
electro-discharge machining (EDM) and micro electro-discharge machining (μEDM) process. Rao and Saroj [8] used the elitist-JAYA algorithm for constrained
economic optimization of shell and tube heat exchanger at different combinations of
populations, iterations and elite size. They found that the elitist-JAYA algorithm is
better than other optimization methods used for the same problems.
As per authors’ knowledge, JAYA never used for IHTP. and due to its simple structure and versatility, it is used for solving IHTP of estimating transient boundary heat
flux for the laminar flow through 2D duct. The flow is considered as thermally developing and hydrodynamically developed. After JAYA, modified JAYA algorithm is
used to estimate the heat flux where JAYA algorithm is coupled with multi-population
JAYA algorithm. In multi-population JAYA algorithm, total population is divided into
groups. These groups are used to estimate the required quantity. Solution of simple
JAYA algorithm will be the input parameters for multi-population JAYA algorithm.
Different types of heat flux profiles like step heat flux profile, smooth heat flux profile,
R. Prajapati et al.
heat flux, convection coefficient, thermo-physical properties, initial condition and
intensity of source term [1].
IHTP uses least square-based objective function for minimization, and hence,
they are ill posed problems. There are two type of approaches used for IHTP:
gradient-based approach and stochastic (population-based) approach. Gradientbased approach uses gradient of an objective function for solution. Among all
gradient-based method, conjugated gradient method (CGM) with an adjoint problem
is the most popular gradient-based approach. Liu and Ozisik [2] estimated the transient wall heat flux for hydrodynamically developed and thermally developing turbulent forced convection flow in a parallel plate channel and concluded that the accuracy
of CGM deteriorates with measurement error and step heat flux profile is difficult
to estimate than triangular heat flux profile. Huang and Chen [3] estimated transient
boundary heat flux for three-dimensional forced convection flow by using CGM.
They used commercial software CFX4.2 for the CGM algorithm and considered
the effect of duct height, inlet velocity and measurement errors on flux estimation.
The main limitation of CGM is that it is very sensitive to measurement error and
sometimes it converges up to local minima. The stochastic methods are more accurate than deterministic methods, and they obtain global solution. Cuckoo search,
genetic algorithm (GA), differential evolution (DE) and JAYA algorithm are some
examples of stochastic methods. Parwani et al. [4] used the DE approach for estimation of the position and strength of time-varying source in participating medium in
a two-dimensional enclosure. They considered conduction and radiation boundary
conditions and found that DE is quite reasonable for estimation. Li and Yang [5]
used GA for estimation of radiation parameters of the gray participating medium.
Above researchers used different stochastic (population-based) approach to estimate the required properties and found that these approaches are quite reasonable
for the estimation. For current case, a new stochastic algorithm—JAYA is used for
IHTP. JAYA is developed by Rao [6] and successfully implemented for solving benchmark problems. It has simple structure and does not require any tuning parameters.
Rao et al. [7] used a multi-objective JAYA algorithm (MO-JAYA) for optimization of modern machining process which includes plasma arc machining (PAM),
electro-discharge machining (EDM) and micro electro-discharge machining (μEDM) process. Rao and Saroj [8] used the elitist-JAYA algorithm for constrained
economic optimization of shell and tube heat exchanger at different combinations of
populations, iterations and elite size. They found that the elitist-JAYA algorithm is
better than other optimization methods used for the same problems.
As per authors’ knowledge, JAYA never used for IHTP. and due to its simple structure and versatility, it is used for solving IHTP of estimating transient boundary heat
flux for the laminar flow through 2D duct. The flow is considered as thermally developing and hydrodynamically developed. After JAYA, modified JAYA algorithm is
used to estimate the heat flux where JAYA algorithm is coupled with multi-population
JAYA algorithm. In multi-population JAYA algorithm, total population is divided into
groups. These groups are used to estimate the required quantity. Solution of simple
JAYA algorithm will be the input parameters for multi-population JAYA algorithm.
Different types of heat flux profiles like step heat flux profile, smooth heat flux profile,