316
M. Parikh et al.
Fig. 2 Validation of direct problem with ANSYS software
where
For region 1 (Aluminum rod):
For region 2 (Brass rod):
T ai = Temperature of aluminum rod
T bj = Temperature of brass rod
T 1 = Temperature of aluminum rod at x = 0
T 2 = Temperature of brass rod at x = L2
T i = Temperature of aluminum rod at x = L1
T j = Temperature of brass rod at x = L1
ρ a = 2710 kg/m 3 , C pa = 921.096 J/kg-K
ρ b = 8587 kg/m 3 , C pb = 401.93 J/kg K
K a = 205 W/mK
K b = 109 W/m
System is discretized using above-shown governing equations for individual
regions with the help of finite volume method (FVM). The direct problem is solved
by MATLAB 2016b environment, and it is validated using ANSYS 17.2 academic
software as shown in Fig. 2.
2.2 Inverse Problem
Solutions of direct problem are taken as input parameters for the inverse heat transfer
methodology. Jaya algorithm which is selected as the evaluation algorithm approximate temperatures which are evaluated from direct problem for the given heat flux
and constant temperature boundary condition.
Evaluation was carried out considering four measurement locations (two locations
on each rods).
The algorithm converges by minimizing the following objective function:
J (h(t)) =
tn
1
n
1
[T a (t) − T e (t)]
2 dt
(3)
M. Parikh et al.
Fig. 2 Validation of direct problem with ANSYS software
where
For region 1 (Aluminum rod):
For region 2 (Brass rod):
T ai = Temperature of aluminum rod
T bj = Temperature of brass rod
T 1 = Temperature of aluminum rod at x = 0
T 2 = Temperature of brass rod at x = L2
T i = Temperature of aluminum rod at x = L1
T j = Temperature of brass rod at x = L1
ρ a = 2710 kg/m 3 , C pa = 921.096 J/kg-K
ρ b = 8587 kg/m 3 , C pb = 401.93 J/kg K
K a = 205 W/mK
K b = 109 W/m
System is discretized using above-shown governing equations for individual
regions with the help of finite volume method (FVM). The direct problem is solved
by MATLAB 2016b environment, and it is validated using ANSYS 17.2 academic
software as shown in Fig. 2.
2.2 Inverse Problem
Solutions of direct problem are taken as input parameters for the inverse heat transfer
methodology. Jaya algorithm which is selected as the evaluation algorithm approximate temperatures which are evaluated from direct problem for the given heat flux
and constant temperature boundary condition.
Evaluation was carried out considering four measurement locations (two locations
on each rods).
The algorithm converges by minimizing the following objective function:
J (h(t)) =
tn
1
n
1
[T a (t) − T e (t)]
2 dt
(3)