Modeling Thermal Conductivity of Iranian Flat Bread Using Artificial Neural Networks

Figures & data

Figure 1 Data acquisition system for measuring bread temperature variations (color figure available online).[28]

Figure 2 Modified Fitch apparatus developed to measure thermal conductivity (color figure available online).

Table 1 Range of different operating variables used in the simulation model

Variables	Symbol	Unit	Range
Wheat flour cultivars:			Pishtaz Marvdasht Chamran
Baking temperature	T	°C	232, 249, 260
Measuring times	t	minutes	0, 5, 8, 10,12, 14
Inputs:
Bread's top temperature	Tt	°C	0–100
Bread's bottom temperature	Tb	°C	0–100
Moisture content	M	%w.b.	32–39
Apparent density	ρ	kg / m ^3	200–900
Output: thermal conductivity	K	W/m K	0.32–0.40

Table 2 Thermo-physical properties of Iranian flat breads made from different cultivars

		Moisture content (%w.b.)			Apparent density (kg / m ^3)			Thermal conductivity (W/m K)
		Baking temperature (°C)			Baking temperature (°C)			Baking temperature (°C)
Cultivar	Measuring times (min)	232	249	260	232	249	260	232	249	260
Pishtaz	0	0.385	0.3845	0.384	880	881	882	0.361	0.3612	0.3622
	5	0.375	0.3725	0.37	778	753	743	0.3635	0.3645	0.3658
	8	0.367	0.365	0.3615	540	527	491	0.357	0.3562	0.353
	10	0.355	0.3525	0.35	371	356	334	0.343	0.341	0.34
	12	0.3425	0.3365	0.3315	262	237	232	0.333	0.33	0.327
	14	0.3316	0.327	0.323	234	225	224	0.328	0.324	0.322
Marvdasht	0	0.3551	0.355	0.3551	830	831	832	0.39	0.3901	0.3902
	5	0.3516	0.349	0.346	747	732	735	0.396	0.3955	0.397
	8	0.343	0.3405	0.336	684	649	620	0.388	0.387	0.3844
	10	0.337	0.331	0.3275	581	543	500	0.381	0.379	0.377
	12	0.3285	0.3215	0.318	483	440	376	0.375	0.3727	0.3701
	14	0.3205	0.3135	0.3075	383	310	263	0.3692	0.3649	0.363
Chamran	0	0.3605	0.3601	0.36	980	981	982	0.37	0.3701	0.3702
	5	0.3545	0.3536	0.352	851	840	815	0.374	0.373	0.3745
	8	0.3495	0.3465	0.3445	635	600	573	0.372	0.3696	0.371
	10	0.3444	0.341	0.338	452	411	384	0.368	0.365	0.3641
	12	0.34	0.3365	0.333	328	301	281	0.3634	0.359	0.3571
	14	0.3355	0.332	0.328	283	245	228	0.3561	0.352	0.349

Figure 3 Neural network architecture.

Table 3 Prediction errors in the thermal conductivity with different ANN configurations

	Hidden layers ^1			Performance measures^2
Model #	N	NH1	NH2	MAE	MRE	SE	R^2
1	1	4	–	2.72E-03	0.6303	1.35E-03	0.950
2	1	7	–	2.65E-03	0.6261	1.40E-03	0.958
3	1	9	–	2.85E-03	0.6262	1.43E-03	0.955
4	1	14	–	2.77E-03	0.6279	1.50E-03	0.952
5	2	3	4	3.71E-03	0.6208	1.87E-03	0.971
6	2	3	5	1.66E-03	0.6323	8.56E-04	0.988
7	2	3	4	3.71E-03	0.6208	1.87E-03	0.971
8	2	3	7	3.40E-03	0.6221	1.86E-03	0.961
9	2	3	8	1.77E-03	0.6314	9.51E-04	0.979
10	2	3	9	2.20E-03	0.6271	1.28E-03	0.966
11	2	3	10	1.79E-03	0.6288	1.04E-03	0.975
12	2	3	11	3.23E-03	0.6381	1.70E-03	0.963
13	2	3	13	1.77E-03	0.6342	9.36E-04	0.987
14	2	3	14	3.65E-03	0.6205	1.92E-03	0.969
15	2	3	15	1.99E-03	0.6282	1.05E-03	0.975
16	2	3	16	2.27E-03	0.6299	1.15E-03	0.970
^1N, NH1 and NH2 are the number of hidden layers, neurons in the first hidden layer and neurons in the second hidden layer, respectively. ^2MAE, MRE (%), SE and R^2 are the mean absolute error, the mean relative error, the standard error and the coefficient of determination of thermal conductivity, respectively.

Figure 4 Predicted vs. actual values of K for the optimum ANN configuration (color figure available online).

Akram , A. , Omid , M. , Golmohammadi , A. and Ghasemi-Varnamkhasti , M. 2009 . Effects of wheat flour and baking temperature on the quality of Iranian flat bread-Part I: Physico-chemical Properties . Asian Journal of Chemistry , 21 ( 5 ) : 3910 – 3920 .

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