Solar Air Heating For Preserving Waste Food

Solar Air Heating For Preserving Waste Food

B. Tudu, A. Tripathy, H. Chattopadhyay, P. C. Roy, S. Simlandi, and N. Barman

Department of Mechanical Engineering, Jadavpur University, Kolkata, India

Abstract – Preserving waste food using direct solar irradiation is a challenge in this decade. The present study thus employs numerical analysis to provide preliminary insights into transport phenomena during solar air heating in an inclined rectangular duct, intending to preserve waste food. The process is modelled by solving the mass, momentum, and energy equations along with the necessary boundary conditions. The absorption of solar irradiation is incorporated in the boundary condition using a simple model. The use of such a simple model is a novelty of this study. The set of governing equations is discretised using the finite volume method and solved numerically by developing a FORTRAN code using the SIMPLER and TDM algorithms.

The bottom surface temperature increases with time due to greater absorption of solar irradiation, resulting in a high air outlet temperature ( 98 °C) during midday and a subsequent decrease thereafter, following the pattern of solar irradiation and decreasing with the inlet air flow. It reduces to 87 C when the inlet airflow is set to 0.02 m/s. The present predictions agree well with the existing experiments.

Keywords: Solar irradiation, air heating, modelling, finite volume method, transport phenomena

cp Specific heat

k Thermal conductivity P Pressure

Greek symbols

Density

ref Reference density

NOMENCLATURE

1. INTRODUCTION

   The literature shows that about 30-40% [1] of the cultivated foods are being wasted due to a lack of preservation and timely transportation. In contrast, there is an additional demand for food that increases day-to-day due to an increase in the population [2]. Preserving food waste is one suitable option for supplying the additional food required. Several preservation methods are reported in the literature [3,4]. Use of heated air is one of the best methods to preserve waste foods using direct solar irradiation [3]. Such an air heating process involves the absorption of solar irradiation and the transport of mass, momentum, and energy. Research on understanding transport phenomena during solar air heating is in progress and is essential for designing an efficient air heater. This study considers a numerical investigation to predict transport phenomena during air heating in a duct enclosure of rectangular cross-section using solar irradiation. A simple model to represent the solar air heating is considered, which is the novelty of this study.

2. PROBLEM DESCRIPTION

   This study considers a duct enclosure as shown in Fig. 1, with a rectangular cross-section that makes an angle () of 30 to the horizontal plane. The top surface of the enclosure is considered glass, transmitting solar irradiation into it. The air enters the enclosure at an inlet velocity of Uin and is heated by solar irradiation. The heated air is removed from the other end of the enclosure for subsequent drying of the waste food. Other surfaces of the enclosure are assumed to be adiabatic, absorbing incident solar irradiation at the maximum rate. It is noted that only the solar air-heating part is presented in this study, undertaking a numerical investigation. Assuming a large enclosure width, a 2-D computational domain, as per Fig. 1, of 2 m length (L) and 6 cm height (H) is considered for the present analysis. The respective thermo-physical properties used in the simulation are presented in Table 1.

   Fig. 1: Schematic of the present problem Table 1: Thermo-physical properties [5, 6]

   Description	Values
   Air density (, kg/m3)	1.2
   Air specific heat (Cp, J/kg.C)	1005
   Air thermal conductivity (k, W/m.C )	0.026
   Air viscosity (, Pa.s)	0.0018
   Air thermal expansion coefficient (T, 1/C)	1/(T+273)

3. MATHEMATICAL MODELLING

   This study considers air heating in a rectangular cross-sectional enclosure under direct solar irradiation to use the hot air to dry waste food for respective preservation. There is a negligible temperature rise at the upper glass surface of the enclosure, as it allows transmission of about 95-98% of the solar irradiation; in contrast, the absorption of the transmitted solar irradiation at the bottom surface raises its temperature to a high value. Under such differential temperature conditions, air is heated. The air flows at a low magnitude, and hence the flow is laminar. Respective transport phenomena are represented by the conservative mass, momentum, and energy equations as [7, 8]:

   = 0 (1)

   where is the velocity vector.

    

   () = + ( ) +

   (2)

   where is density, is the pressure field, is the viscosity of air, and is body force represented as

   = ( )(sin + cos ) (2a)

   where is the thermal expansion coefficient and is the initial temperature.

   () = () (3)

   In Eq. (3), represents the temperature field, k is the thermal conductivity, and is the specific heat of air.

   1. Boundary conditions

      The present study considers an airflow through a 2-D duct, with a transparent glass sheet of low thermal conductivity placed at its top and a black surface at its bottom. Accordingly, the necessary boundary conditions are modelled assuming a high emissivity for the bottom surface.

      where is emissivity (0.95), is density (500 kg/m3), is specific heat (2400 J/kg.C), and is the thickness (1.2 cm) of the

      bottom surface. is the transmissivity (0.95) of the glass, and is the Stefan-Boltzmann constant (5.67×10-8 W/m2.K4). I is the solar irradiation (W/m2) that varies throughout the day [4] as shown in Fig. 2. The simplicity of the model exists in this consideration.

      Fig. 2: Variation of solar irradiation in a day (0 indicates sunrise.)

4. NUMERICAL MODELLING

   The governing equations, Eqs. (1-3), with the boundary conditions discretized using the finite volume method (FVM) and the power-law scheme. The SIMPLER and TDM algorithms are used to solve the obtained linear simultaneous equations by developing a FORTRAN-based numerical code, where the convergence is declared when the following relation is satisfied.

   where is the value of a variable at the present iteration, is its value at the previous iteration, and is the maximum value of the variable in the entire domain of the present iteration. A grid-independent study is subsequently carried out, and a suitable grid size of 8232 is considered with a time step of 0.001 s to improve convergence in the present simulation. The simulation solves Eq. (4) simultaneously using the Euler formula to predict the time-dependent temperature of th duct bottom surface.

5. RESULTS AND DISCUSSION

   Fig. 3 shows the temperature evolution within the domain at three different times of the day. It is observed that the bottom surface temperature increases with time due to absorption of solar irradiation, reaching a higher value during midday and then decreasing thereafter. Air is heated accordingly.

   1. t = 2.77 hr
   2. t = 6.93 hr
   3. t = 8.84 hr

   Fig. 3: Temperature distribution at different times of the day

   The average air temperature at the duct outlet is also calculated during the daytime and presented in Fig. 4 under different air inlet conditions. A grid-independent study is also presented in Fig. 4 with two grid sizes (82×32 and 102×42) and concluded that the 82×32 grid is suitable for the present study. It is found that the outlet air temperature increases with time until midday, then decreases in line with the nature of irradiation. Further, the maximum air outlet temperature decreases as the inlet air flow increases. Using the maximum temperature rise of the inlet air, the heating efficiency of the duct is defined by comparing it to the inlet temperature. It varies between 2.4 and 2.8.

   The maximum air outlet temperature also depends on the length of the heating duct. Fig. 5 shows the variation in the maximum outlet air temperature with the length of the air heating duct. It is observed that the maximum outlet temperature increases with duct length. The present prediction is then compared with similar experimental works [9, 10]. A good agreement is observed with differences occurring from the lack of application of exact experimental conditions.

   Fig. 4: Outlet air temperature during the day

   Fig. 5: Maximum temperature with duct length

6. CONCLUSIONS

   This study presents a numerical analysis of transport phenomena during solar air heating in an inclined rectangular duct to use the heated air in preserving waste food. The heating process is modelled using conservative equations of mass, momentum, and energy, including proper boundary conditions. The absorption of solar irradiation and subsequent heating are incorporated, with a suitable boundary at the bottom wall. The set of model equations is discretized using the finite volume method (FVM) and solved numerically with a FORTRAN code that incorporates the SIMPLER and TDM algorithms.

   It is found that the bottom surface temperature increases with time due to an increase in absorption of solar irradiation, resulting in an increase in the air outlet temperature to a high value during midday and decreases thereafter, following the nature of the solar irradiation. It is also found that the air outlet temperature decreases as the inlet air flow increases. In conclusion, the present prediction shows a good agreement with existing experiments. Hence, such a model helps in providing necessary preliminary information and applying it to reduce food waste.

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