Difference between revisions of "Team:Jilin China/Model/For Practices"

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<p>u=u(t,x) represents temperature, which is a function of time variable and space variable. ∂u/∂t is the rate of temperature change with time. k, c,ρ represent the thermal conductivity, specific heat and density respectively. x is the space variable. m, n is boundary condition, while m<sub>0</sub> is the initial condition. </p>
 
<p>u=u(t,x) represents temperature, which is a function of time variable and space variable. ∂u/∂t is the rate of temperature change with time. k, c,ρ represent the thermal conductivity, specific heat and density respectively. x is the space variable. m, n is boundary condition, while m<sub>0</sub> is the initial condition. </p>
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<p>As an instance, we used classical difference method to get the temperature distribution of 304 stainless steel board at different heat transfer time(Figure 2).</p>
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<p>As an instance, we used classical difference method to get the temperature distribution of a board at different heat transfer time(Figure 2).</p>
  
 
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       <img src="https://static.igem.org/mediawiki/2018/5/53/T--Jilin_China--amount_of_energy_saving_8.svg" width="100%" />
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       <img src="https://static.igem.org/mediawiki/2018/3/3b/T--Jilin_China--amount_of_energy_saving_max.svg" width="100%" />
 
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<p class="figure">
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     Figure 2. Temperature distribution of 304 stainless steel board at different heat transfer time. Boundary condition: m=42℃, n=25℃. Initial condition: m<sub>0</sub>=25℃.
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     Figure 2. Temperature distribution of a board at different heat transfer time. Boundary condition: m, n. Initial condition: m<sub>0</sub>=m.
 
     </p>
 
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Revision as of 19:58, 17 October 2018

For Practices
Energy Conservation

Model

  • Background

    For the potential use of decreasing fermentation temperature and saving energy, we developed RNA-based thermosensors which can theoretically sense the energy conservation during fermentation. Hence, we modeled the energy saving process based on the data from Ground Diary.

    The schematic of fermenter is shown in Figure 1. Mixing system helps raw material contact sufficiently with oxygen. And the heating jacket with flow inside is the stable heat source of fermenter. The heat transfer with air is considered as the main energy consumption process. As a result, estimating the heat dissipated power is the first step to get the amount of energy saving.

    Figure 1. Fermenter

  • Methodology

    1. The Features

    Here are the features of the fermenters in Ground Diary from HP(Table.1)

    material 304 stainless steel
    Radiating area 20.4 m2
    Capacity 6t
    Thermal conductivity 16W·m-1·K-1
    Board thickness 50 mm

    Here are the features of parameters in yogurt fermentation(Table.2)

    Real fermentation temperature 42℃
    Ideal fermentation temperature 39℃
    Fermentation duration 4h
    Environment temperature 25℃

    2. The simplifed radiating system

    Heat equation represents temperature history in a certain area:

    $$\left\{ \begin{array}{}{\partial{u}\over{\partial{t}}}={k\over{c\rho}}{{\partial^2u}\over{\partial^2}{x^2}}\\ u(0,t)=m\\ u(x,0)=n\\ u(\delta,t)=m_0 \end{array} \right. $$

    u=u(t,x) represents temperature, which is a function of time variable and space variable. ∂u/∂t is the rate of temperature change with time. k, c,ρ represent the thermal conductivity, specific heat and density respectively. x is the space variable. m, n is boundary condition, while m0 is the initial condition.

    As an instance, we used classical difference method to get the temperature distribution of a board at different heat transfer time(Figure 2).

    Figure 2. Temperature distribution of a board at different heat transfer time. Boundary condition: m, n. Initial condition: m0=m.

    According to this, the curve is close to a straight line. To simply the system, we assumed that the heat transfer process is relatively stable, which follows Newton’s law of cooling(Figure. 3).

    Figure 3. the Radiating System

    3. ThermodynamicS

    Heat flux: A flow of energy per unit of area per unit of time. $$Φ_{q}=-k{{dT(x)}\over{dx}}$$ k means thermal conductivity, which is the property of a material to conduct heat. T(x) is a function of correlation with temperature distribution. Here, x represents the distance between one certain point and interior surface (Figure 4).

    Figure 4. x represents the distance between one certain point and interior surface.

    Heat dissipated power: $$P=Φ_{q}A$$ A is the radiating area.

  • Results

    Figure 5. A) and B) show the temperature distribution on the fermenter board under different fermentation temperature(Tf). C) shows the heat flux(Φ) changing under different fermentation temperature.

    According to graph C), we calculated the energy saving while the fermentation temperature decreased.

    Figure 6. shows the change of power to overcome heat dissipation during fermentation with temperature rising. ΔE represents the energy saving by 1 ℃ decline of fermentation temperature.

  • Conclusions

    From the figures above, we got the amount of energy saving with fermentation temperature decrease. According to Enterprise energy saving calculation method (GB/T13234-91), the energy cost was expressed by using standard coal (see Table. 3).

    Real energy cost 21kg coal/t
    1℃ saving 0.20kg coal/t
    Energy saving ratio 0.95%