Determination and Modeling of Thermal Properties of Tofu

Figures & data

Figure 1. Schematic of the measurement system for thermal conductivity and thermal diffusivity.

Figure 2. Comparison between experimental and calculated specific heats.

Figure 3. Specific heat calculated from an empirical model [Eq. 9] as a function of moisture content and temperature of the tofu.

Table 1a. Specific heat (kJ kg⁻¹ K⁻¹) data of the tofu at different moisture contents and temperatures

	Temperature, °C
m (wb), %	10	30	50	70	90	105
0.677	3.450–3.583	3.479–3.610	3.519–3.649	3.541–3.669	3.544–3.679	3.556–3.689
0.604	3.160–3.311	3.283–3.333	3.310–3.363	3.321–3.378	3.325–3.384	3.329–3.391
0.510	2.980–3.198	2.987–3.188	3.026–3.197	3.115–3.216	3.160–3.268	3.197–3.282
0.428	2.661–2.998	2.701–2.907	2.732–2.924	2.770–2.931	2.779–2.951	2.851–2.884
0.333	2.530–2.649	2.626–2.666	2.648–2.690	2.657–2.722	2.660–2.707	2.663–2.713

Table 1b. Thermal conductivity and thermal diffusivity data of the tofu at different moisture contents and temperatures

m (wb), %	T, °C	ρ, kg m ^−3	k, W m^−1 K^−1	α × 10^7, m^2 s^−1
0.702	7.5–12.8	1,078	0.35–0.38	1.00–1.01
0.704	20.8–21.2	1,054	0.37–0.40	1.06–1.07
0.732	49.4–53.2	1,059	0.39–0.42	1.10–1.15
0.724	48.1–65.4	1,053	0.40–0.42	1.12–1.13
0.712	62.7–74.2	1,059	0.39–0.43	1.11–1.12
0.616	6.4–11.3	1,112	0.33–0.34	0.90–0.95
0.594	20.9–21.4	1,118	0.33–0.36	0.96–1.01
0.617	46.6–54.6	1,112	0.34–0.37	0.95–1.00
0.626	48.4–56.9	1,113	0.35–0.38	1.00–1.01
0.623	64.5–73.4	1,082	0.36–0.37	1.02–1.03
0.512	7.1–11.8	1,134	0.28–0.30	0.82–0.85
0.510	21.6–21.7	1,180	0.29–0.31	0.82–0.84
0.506	44.4–48.1	1,133	0.32	0.90–0.91
0.539	50.3–63.9	1,157	0.32–0.33	0.89–0.91
0.524	65.2–73.1	1,157	0.31–0.33	0.89–0.90
0.420	6.04–12.7	1,203	0.24–0.28	0.78–0.79
0.406	22.0–22.2	1,207	0.25–0.27	0.77–0.78
0.418	42.9–43.9	1,187	0.27–0.29	0.82
0.423	52.8–63.0	1,211	0.28–0.30	0.81–0.83
0.434	64.8–73.6	1,206	0.28–0.31	0.83–0.84
0.344	7.8–12.4	1,225	0.23–0.27	0.76–0.78
0.342	21.5–21.7	1,251	0.26–0.28	0.78–0.81
0.358	45.3–48.9	1,215	0.27–0.28	0.82
0.365	37.4–54.2	1,215	0.24–0.28	0.78–0.79
0.366	64.6–72.7	1,235	0.26–0.28	0.78–0.80

Table 2. Thermal property models and root mean square errors in comparison to experimental data

References	Equation	RMS
[15]		0.0987
[16]		0.1030
Present study		0.0684
[15]		0.0118
		0.0118
Present study		0.0113
[14]		3.01 × 10^−8
Present study		2.224 × 10^−9

Table 3. Summary of the stepwise selection of variables in the empirical model of specific heat of the tofu

Input variables	Variables selected	Estimate	SEE ^a	Pr > F
m, T, m × T, m ^2,	m ^2	1.596	0.3228	< 0.0001
T ^2, m × T ^2,	T	1.06 × 10^−3	1.38 × 10^−4	< 0.0001
m ^2 × T, m ^2 × T ^2	m	1.064	0.328	0.0013
	Intercept	2.055	0.08	< 0.0001

a: Standard error of estimate.

Note: Model R ² = 0.959, degree of freedom of error = 296.

Figure 4. Comparison between experimental and calculated thermal conductivity from structural models and empirical model.

Figure 5. Thermal conductivity calculated from an empirical model [ Eq.13] as a function of moisture content and temperature of the tofu.

Table 4. Summary of the stepwise selection of variables in the empirical model of thermal conductivity of the tofu

Input variables	Variables selected	Estimate	SEE	Pr > F
m, T, m × T, m ^2,	m ^2	0.3077	0.0119	< 0.0001
T ^2, m × T ^2,	m × T	8.943 × 10^−4	1.207 × 10^−4	< 0.0001
m ^2 × T, m ^2 × T ^2	Intercept	0.2112	0.00357	< 0.0001

Note: Model R ² = 0.944, degree of freedom of error = 69.

Figure 6. Comparison between experimental and calculated thermal diffusivity from Martens' and empirical model.

Figure 7. Thermal diffusivity calculated from an empirical model [Eq. 15] as a function of moisture content and temperature of the tofu.

Table 5. Summary of the stepwise selection of variables in the empirical model of thermal diffusivity of the tofu

Input variables	Variables selected	Estimate	SEE	Pr > F
m, T, m × T, m ^2,	m ^2	1.164 × 10^−7	2.056 × 10^−8	< 0.0001
T ^2, m × T ^2,	m ^2 × T	6.866 × 10^−10	1.87 × 10^−10	0.0005
m ^2 × T, m ^2 × T ^2	m	−5.682 × 10^−8	2.157 × 10^−8	0.0105
	m ^2 × T ^2	−5.17 × 10^−12	2.35 × 10^−12	0.0315
	Intercept	8.16 × 10^−8	5.51 × 10^−9	< 0.0001

Note: Model R ² = 0.965, degree of freedom of error = 67.

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