Estimation of Transient Boundary Heat Flux Using Modified JAYA …
333
triangular heat flux profile and linearly increasing heat flux profile are considered and
performance of JAYA and modified JAYA considered. Results show that modified
JAYA algorithm is found to be more accurate than JAYA.
2 Methodology
The methodology includes: (1) Find the temperature field profile in duct using known
value of heat flux by solving direct problem. (2) Estimate the boundary heat flux by
JAYA algorithm.
2.1 Direct Problem
Hydrodynamically and thermally fully developed transient laminar flow is considered
in 2D duct as shown in Fig. 1. Heat flux is applied on the upper surface of duct. Heat
flux is varying with respect to time. Length of duct is 1 m. Height of duct is 0.1 m.
Air flowing inside duct has mean velocity u m = 0.033 m/s. Corresponding Reynolds
number Re = 429 (Fig. 2).
Parabolic velocity profile has been assumed and is as below:
u(y) = 6u m
y
H
1 −
y
H
(2.1)
The governing equations for energy for the present case with boundary conditions
are given by
ρC pu
∂ T
∂ x
+ ρC p
∂ T
∂t
=
∂
∂ y
k
∂ T
∂ y
(2.2)
Fig. 1 2D duct