Induction heating of sugarcane juice: thermo-enviro-economic analyses

Abstract

Heating of sugarcane juice gives concentrated sugarcane juice (CSJ) which becomes raw material for the production of a variety of value added products. Conventional ways of CSJ production are environment polluting and indulge in huge amount of energy losses. In this study, an attempt is made to obtain final CSJ (98°B) by induction heating (IH) which is environment friendly and causes minimum energy losses. The experiments are performed at constant heat flux (9947.5 W m⁻²) on samples of sugarcane juice having 14.2°B, 18.8°B, 23.9°B, and 27.4°B values of initial brix contents. Thermo-enviro-economic analyses are carried out for the experiments conducted on given samples. The results concluded that time required for obtaining final CSJ decreases and evaporation rate increases with increase in initial brix value of sugarcane juice. The energy required for obtaining final CSJ from sugarcane juice of 27.4°B is 683.43 kJ which is 154.3% less as compared to that of fresh sugarcane juice heating with 14.2°B. The environmental parameters have no discernible effects of initial brix value while economic factors were improved. IH is observed thermally and environmentally beneficial with lower costs of CSJ production from the juice of higher initial brix contents.

Appendices

Appendices

Appendix 1: Parameters used in thermal model for sensible heating

The various parameters used in thermal model for sensible heating are calculated by the below equations [8, 11].

$$P\left( {T_{{\text{j}}} } \right) = \exp \left[ {25.317 - \frac{5144}{{\left( {T_{{\text{j}}} + 273.15} \right)}}} \right]$$

(27)

$$P\left( {T_{{\text{v}}} } \right) = \exp \left[ {25.317 - \frac{5144}{{\left( {T_{{\text{v}}} + 273.15} \right)}}} \right]$$

(28)

$${\text{Gr}}\Pr = \frac{{g \cdot \beta \cdot X_{{\text{c}}}^{3} \cdot \rho^{2} \cdot \Delta T \cdot C_{{\text{v}}} }}{{\mu \cdot K_{{\text{v}}} }}$$

(29)

$$\beta = \frac{1}{{T_{{\text{v }}} + 273.15}}$$

(30)

$$\rho = \frac{353.44}{{T_{{\text{v}}} + 273.15}}$$

(31)

$$\Delta T = T_{{\text{j}}} - T_{{\text{v}}}$$

(32)

$$C_{{\text{v}}} = 999.2 + 0.1434T_{{\text{v}}} + 1.101 \times 10^{ - 4} T_{{\text{v}}}^{2} - 6.7581 \times 10^{ - 8} T_{{\text{v}}}^{3}$$

(33)

$$\mu = 1.718 \times 10^{ - 5} + 4.62 \times 10^{ - 8} T_{{\text{v}}}$$

(34)

$$K_{{\text{v}}} = 0.0244 + 0.7673 \times 10^{ - 4} T_{{\text{v}}}$$

(35)

$$\lambda = 2.4935 \times 10^{6} \times \left[ {1 - 9.4779 \times 10^{ - 4} T_{{\text{v}}} + 1.3132 \times 10^{ - 7} T_{{\text{v}}}^{2} - 4.7974 \times 10^{ - 9} T_{{\text{v}}}^{3} } \right];\;\;{\text{for}}\;\;T_{{\text{v}}} < 70\,^{^\circ } {\text{C}}$$

(36)

$$\lambda = 3.1615 \times 10^{6} \times \left[ {1 - \left( {7.616 \times 10^{ - 4} \times T_{{\text{v}}} } \right)} \right];\;\;{\text{for}}\;\;T_{{\text{v}}} > 70\,^{^\circ } {\text{C}}$$

(37)

Appendix 2: Parameters used in thermal model of heat transfer during pool boiling

The various parameters used in thermal model of heat transfer during pool boiling are evaluated by the below equations [8, 9, 11, 17].

$$\rho_{{\text{l}}} = 1043 + 4.854B - 1.07T_{{\text{j}}}$$

(38)

$\rho_{{\text{l}}}$ is density of juice at $T_{{\text{j}}}$ and B is the brix content.

$$\rho_{{\text{v}}} = \frac{353.44}{{\left( {T_{{\text{i}}} + 273.15} \right)}}$$

(39)

where, $\rho_{{\text{v}}}$ is density of vapor at $T_{{\text{i}}} = \frac{{T_{{\text{j}}} + T_{{\text{v}}} }}{2}$

$$h_{{{\text{fg}}}} = c_{{\text{p}}} X_{{\text{w}}}$$

(40)

$h_{{{\text{fg}}}}$ is enthalpy of vaporization, $c_{{\text{p}}}$ is specific heat capacity of vapor and $X_{{\text{w}}}$ is mass of evaporated water content.

Thermal conductivity ($k_{{\text{l}}}$), specific heat ($c_{{{\text{pl}}}}$), viscosity ($\mu_{{\text{l}}}$) of sugarcane juice are evaluated as

$$k_{{\text{l}}} = 0.3815 - 0.0051B + 0.001866T_{{\text{j}}}$$

(41)

$$c_{{{\text{pl}}}} = 2.38 - 0.006T_{{\text{j}}}$$

(42)

$$\mu_{{\text{l}}} = e^{{\left( {11.229 + \frac{3257.5}{{T_{{\text{j}}} }} + 0.07572B} \right)}}$$

(43)

Appendix 3: Environmental analysis of the system [31, 32, 37,38,39,40,41].

$$E_{{\text{m}}} = C_{{\text{Eem }}} M_{{\text{x}}}$$

(44)

where M_x is mass of the material in kg and C_Eem is embodied energy coefficient in kWh kg⁻¹

$${\text{Daily thermal output}}\; \left( {{\text{TO}}_{{{\text{day}}}} } \right) = \frac{{ m_{{\text{t}}} \lambda }}{{3.6 \times 10^{6} }}$$

(45)

where, $\lambda$ is the latent heat of vapourization (i.e., $\lambda$ = 2.43 × 10⁶ J kg⁻¹).

$${\text{Annual energy output}}\;(E_{{\text{a}}} ) = {\text{TO}}_{{{\text{day}}}} S_{{{\text{days}}}}$$

(46)

$S_{{{\text{days}}}}$ are the operating days for system which is taken as 290 days

$${\text{EPBT}} = \frac{{E_{{\text{m}}} }}{{E_{{\text{a}}} }}$$

(47)

$${\text{CO}}_{2} {\text{ emission/year}} = \frac{{ 0.98 \times E_{{\text{m}}} }}{a}$$

(48)

where $a$ is the lifespan of the designed system taken as 30 years.

$${\text{CO}}_{2} \;{\text{mitigation}} \;\left( {{\text{CO}}_{{\text{m}}} } \right) = 2.042 \times \left( { aE_{{\text{a}}} {-} E_{{\text{m}}} } \right)$$

(49)

$${\text{CCE}} = {\text{C}}_{{{\text{CCE}}}} \times {\text{CO}}_{{\text{m}}}$$

(50)

In Eq. (50), the cost of carbon credit (${\text{C}}_{{{\text{CCE}}}}$) is taken as $15.