Identification of materials in a hyperbolic annular fin for a given temperature requirement

Figures & data

Figure 1. Geometry of the hyperbolic fin.

Figure 2. Flowchart of the inverse method.

Table 1. Different values of parameters considered to be fixed during the inverse analysis.

Parameters	Values
Reference temperature, Tref	460 K
Base temperature, Tb (only for no measurement error, i.e. er = 0)	460 K
Ambient temperature, Ta	300 K
Tip radius, r0	0.10 m
Base radius, rb	0.025 m
Semi fin thickness, yb	0.0085 m

Figure 3. Validation of the forward method for different non-dimensional thermo-physical parameters.

Table 2. Estimated values of various unknowns for temperature field without measurement error, e_r = 0. (Forward non-dimensional parameters: m = 0.7, ε = 0.1 and $r_{\text{b}}^{*}$ = 0.25.)

Run	Heat transfer coefficient, h (W[m^2K]^−1)	Thermal conductivity, ka (W [m K]^−1)	Coefficient of variable thermal conductivity, β (K^−1)	Non-dimensional thermal conductivity parameter, ε (estimated)	Non-dimensional fin parameter, m (estimated)	CPU time (s)	Feasible materials[49]
1	24.157	79.365	−1.764 × 10^−3	−0.2822	0.5984	1509	Iron
2	18.740	53.251	−5.870 × 10^−4	−0.0939	0.6434	1511	Carbon steel
3	79.530	204.000	7.211 × 10^−4	0.1154	0.6772	1509	Aluminium
4	6.431	16.545	7.131 × 10^−4	0.1141	0.6762	1512	Stainless steel
5	154.194	400.264	−3.780 × 10^−5	−0.0060	0.6732	1510	Copper

Figure 4. Variation of the objective function, F and unknown parameters (h, k, β) with number of iterations of hybrid algorithm; e_r = 0.

Figure 5. Comparison of the exact and measured temperature fields along with measurement error; m = 0.7, e = 0.1 and $r_{\text{b}}^{*}$ = 0.25.

Table 3. Estimated values of various unknowns for temperature field with measurement error, e_r≠ 0. (Forward non-dimensional parameters: m = 0.7, e = 0.1 and $r_{\text{b}}^{*}$ = 0.25.)

Run	Heat transfer coefficient, h (W [m^2K]^−1)	Thermal conductivity, ka (W [m K]^−1)	Coefficient of variable thermal conductivity, β (K^−1)	Non-dimensional thermal conductivity parameter, ε (estimated)	Non-dimensional fin parameter, m (estimated)	CPU time (s)	Feasible materials [49,50]
1a (max)	47.419	114.971	−3.356 × 10^−4	−0.0537	0.6966	1510	Zinc
1b (min)	43.991	115.409	−4.207 × 10^−4	−0.0673	0.6697	1509	Zinc
2	27.716	68.401	−6.162 × 10^−4	−0.0986	0.6904	1511	Tin
3	31.537	70.852	1.516 × 10^−4	0.0243	0.7236	1510	Platinum
4	11.681	37.926	−9.000 × 10^−4	−0.1444	0.6020	1508	Alumina
5	20.923	53.748	−5.245 × 10^−4	−0.0839	0.6767	1512	Carbon steel

Figure 6. Variation of the objective function, F and unknown parameters (h, k, β) with number of iterations of hybrid algorithm; e_r≠ 0.

Figure 7. Comparison of the exact and reconstructed temperature fields, (a) without involving measurement error, e_r = 0, (b) and (c) involving measurement error, e_r≠ 0.

Figure 8. Comparison of the residuals between the exact and the reconstructed temperature fields, (a) without involving measurement error, e_r= 0 and (b) involving measurement error, e_r≠ 0.

Figure 9. Comparison of the exact and the reconstructed temperature fields for different measurement points.

Thermal conductivity of some common materials and gases. Available from: www.engineeringtoolbox.com/thermal-conductivity-d_429.html.

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