Zero Energy Cooling Chamber

Welcome to Zero Energy Cooling Chamber

Food waste is one of the leading causes of worldwide hunger. Agricultural output becomes unusable if there is little capacity to store food. “Much of the food being collected is either not consumed or never makes it to the market.” (NPR) Not only is the potential profit lost, but so are the lives of those suffering from food shortages.

The Zero Energy Cool Chamber (ZECC) is an eco-friendly storage system developed to preserve food in a hot, arid climate, where access to electricity is sparse. It is often used by small-scale farmers to reduce postharvest loss in developing countries.

The ZECC functions similar to a conventional refrigerator in the sense that the chamber 'pushes' heat out. However, it is cheaper and has a higher energy efficiency than your typical fridge. It requires no electrical energy whatsoever, just water to maintain function.

The design consists of an inner chamber, a surrounding layer of wet sand, and another wall encasing it. The center storage space is made cool by the principle of passive evaporative cooling: the liquid water molecules in the sand layer travel through the outer layer and evaporate due to the source of heat coming from the produce being stored, as well as the humidity difference between the sand layer and the outer air. This cooling process is similar to sweating.

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Setting up the experiment

Assumptions:

One metric ton of potatoes is being stored in the center of the inner chamber
Sand remains saturated throughout the process
Potatoes respirate, giving off a source of heat that drives the heat and mass transfer out of the system
Water travels from the wet sand out through the brick, evaporating off of the surface of the outer brick wall, creating a cooling effect at each layer of the chamber (similar to sweat evaporating off skin to cool you down)

Independent Variables (User Input):

Inner Chamber Temperature

The desired inner temperature will dictate how much heat you need to be pushed out.
The inner temperature will also dictate how much fruit you could sell and how useful the ZECC could be.

Outer Air Temperature

The ambient temperature (based on location) will decide whether or not the ZECC can function properly, and for what times of the year.

Outer Air Relative Humidity

The humidity affects the evaporation rate, and whether or not the water will evaporate at all.
The humidity will decide whether or not the dewpoint temperature will cause condensation, and if the chamber can work.

Size of Inner Chamber (length and width varied, fixed height)

The dimensions will change how much heat is conducted to the water, how much food can be stored, and how much the initial cost will be.
The amount of food stored increases your profit, the operating budget.

Size of Wet Sand Layer (thickness)

Dependent Variables (Calculated by the Model):

Temperatures at each medium interface (HT)
Dew Point Temperature at outer brick wall (HT)
Diffusion of Water through the layers to the outer brick wall (MT)
Evaporation of Water at outer brick surface (MT)
Liters of Water needed to be added daily to replace lost water via MT
Annual cost of design (both fixed and variable expenses)

The choice of materials affects the initial cost of the ZECC and the amount of heat that can be pushed out through conduction.

With this given information, optimize the ZECC as much as possible and create a self sufficient system.

Equations

General Balance:

IN + GENERATION = OUT
IN = water is added into the system to force heat transfer outward
GENERATION = heat is generated by the potatoes in the center of the storage container
OUT = heat conducted out, water evaporated out at brick surface

Heat Transfer:

Composite wall heat balance to find temperatures at each interface

$q = \frac{(T_{c} - T_{4})}{\frac{1}{h_{c} \times A_{c}}} = \frac{(T_{4} - T_{3})}{\frac{L_{inner brick}}{k_{brick} \times A_{inner brick}}} = \frac{(T_{3} - T_{2})}{\frac{L_{wet sand}}{k_{wet sand} \times A_{wet sand}}} = \frac{(T_{2} - T_{1})}{\frac{L_{outer brick}}{k_{brick} \times A_{outer brick}}} = \frac{(T_{1} - T_{bulk})}{\frac{1}{h_{bulk} \times A_{bulk}}}$

$q = Heat produced by potato respiration$

$h_{c} = Heat transfer coefficient inside the chamber$

$A_{c} = Area of inner chamber$

$L_{inner brick} = Length of the inner brick layer$

$k_{brick} = Thermal conductivity of brick$

$A_{bulk} = Area outside of chamber$

$h_{bulk} = Heat transfer coefficient of outdoor air$

$A_{inner brick} = Area of inner brick layer$

$L_{wet sand} = Length of wet sand layer$

$k_{wet sand} = Thermal conductivity of wet sand$

$A_{wet sand} = Area of wet sand layer$

$L_{outer brick} = Length of outer brick layer$

$A_{outer brick} = Area of outer brick layer$

$T_{c} = Inner Chamber Temperature$

$T_{4} = Inner Chamber/Inner Brick Interface Temperature$

$T_{3} = Inner Brick/Wet Sand Interface Temperature$

$T_{2} = Wet Sand/Outer Brick Interface Temperature$

$T_{1} = Outer Brick/Bulk Air Interface Temperature$

$T_{bulk} = Temperature of outdoor air$

Magnus Formula to find dew point temperature based on input value of bulk air temperature and relative humidity.

$T_{dew point} = \frac{b [\frac{a \times T_{bulk}}{b + T_{bulk}} + ln(RH)]}{a - [\frac{a \times T_{bulk}}{b + T_{bulk}} + ln(RH)]}, where ‎ a = 17.27, ‎ b = 237.7, ‎ RH = 0 \to 1$

Dew Point temperature is critically dependent on both the design of the chamber and inputted values. If the outer brick wall temperature becomes too low, water will begin to condense on the surface of the brick, and no evaporation will occur, halting the cooling of the inner chamber.

The heat transfer that occurs in the zero energy cooling chamber is a combination of all three of the above heat transfer methods. The radiation from solar energy heats the chamber and the surrounding area. The ground also radiates heat. The fluid flow and the conduction of the water is what helps to cool the chamber down.

Mass Transfer:

Antoine equation to calculate pressure at a certain temperature

$ln(P^{*}) = A - \frac{B}{C + T}, where ‎ A = 18.3036, ‎ B = 3816.44, ‎ C = −46.13$

Mass balance to calculate the outer mass transfer coefficient, $k_{bulk}$

$q + h_{bulk} \times A_{outer brick} \times (T_{bulk} - T_{1}) = λ \times k_{bulk} \times A_{bulk} [P^{*} (T_{1}) - P_{bulk}],$

$where ‎ λ = latent heat of evaporation, ‎ q = heat of respiration$

Finding the concentration of water moving from the sand through the outer brick

$\frac{ε_{brick} \times \ D_{wb} \times A_{outer brick} (C_{sand} \times C_{outer brick})}{L_{outer brick}} = k_{bulk} \times A_{bulk} [P^{*} (T_{1}) - P_{bulk}]$

When one mole of a substance at atmospheric pressure goes from the liquid phase to the gaseous phase, there is energy required to bring the substance to a boil and make the phase change occur. Bringing a substance to its boiling point is not enough since there is still energy required to make phase change occur. This energy required is the latent heat of vaporization. Temperature changes cannot occur without phase changes.

Guiding Questions

Consider the region and time of year this would be implemented. How does that change the outer air temperature and relative humidity values you will be inputting?
What is a normal refrigerator temperature? Do potatoes need to be stored at this temperature?
How much is one metric ton of potatoes in kg? What kind of space might that many potatoes occupy? Will this affect your initial guesses?
How will changing each variable affect your overall design? Which is the most costly to manipulate and why?
Is this design useful? Does it make sense to build a ZECC here at Lehigh, or would it be better suited elsewhere? Can this be used year-round?