Solar Dryer Drying Time Estimation

[JaWiB]

Homework Statement

The problem is fairly simple (hah): estimate the time it will take for a solar dryer (which I have to design) to dry 50 pounds of fruit from 80% water to 10% water.

Homework Equations

It seems there are at least a few equations that give an approximation for evaporation rates. THe first one that comes up is the penman equation:

$$\frac{mR_{n}+{\rho}_{a}c_{p}({\delta}e)g_{a}}{{\lambda}_{v}(m+\gamma)}$$

Where, unfortunately, m, $$g_a$$, $$c_p$$, $$\rho$$, and $${\delta}e$$ depend on temperature, wind speed, and relative humidity (Credit: wikipedia for all of the above)

The Attempt at a Solution

I could go on with all the other equations impacting those variables, but since I don't have a lot of data to work with (really we were just given solar radiation data for surrounding areas) I figure I must be able to make some approximations to boil this down to something more manageable.

Any idea where to start here?

I can probably fairly easily find an estimate for average temperature during the times/location that we're desiging this to be used. I can probably also estimate energy coming into the dryer and the energy leaving through the walls. But I don't know how that will affect the humidity, air flow, and temperature inside the dryer.

 

[KataKoniK]

Thank you for your question. I can understand your frustration with the complexity of this problem. However, there are a few key factors that you can consider in order to make a more accurate estimation.

Firstly, I would recommend gathering more data on the surrounding weather conditions, such as temperature, wind speed, and relative humidity. This will allow you to use more accurate equations and make better approximations.

Secondly, I would suggest conducting some experiments to determine the evaporation rate of the fruit in different conditions. This will give you a better understanding of how the variables you mentioned (temperature, wind speed, relative humidity) affect the drying process.

Additionally, you can also consider the design of your solar dryer. The type of material used for the walls, the size and shape of the dryer, and the placement of the fruit can all have an impact on the drying time.

In summary, my suggestion is to gather more data, conduct experiments, and consider the design of your solar dryer in order to make a more accurate estimation of the drying time. I hope this helps and good luck with your project.

 

[piercas]

Firstly, let me start by saying that this is a great problem to tackle as a scientist! Designing a solar dryer to efficiently dry a large amount of fruit is a challenging and interesting task.

To estimate the drying time, we can start by considering the energy balance within the solar dryer. The energy input is solar radiation, and the energy output is through the walls and by evaporation of water from the fruit. We can assume that the solar radiation is constant throughout the drying process.

To estimate the evaporation rate, we can use the Penman equation as you mentioned. However, as you noted, it depends on several variables that may be difficult to measure accurately. In this case, we can make some simplifying assumptions to make the problem more manageable.

One approach could be to assume that the temperature inside the dryer is constant and equal to the average temperature during the times/locations that the dryer will be used. This will give us a rough estimate of the average evaporation rate. We can also make a conservative assumption that the wind speed and relative humidity will be at their highest values during the drying process, to ensure that our estimate is on the longer side.

Using these simplifications, we can then estimate the drying time by dividing the total amount of water that needs to be evaporated (50 lbs x 70% = 35 lbs) by the average evaporation rate. This will give us a rough estimate of the time it will take to dry the fruit.

Of course, there are many other factors that may affect the actual drying time, such as the design of the dryer, the type of fruit being dried, and the ambient conditions. it would be beneficial to conduct experiments to validate our estimates and refine our calculations. Additionally, considering the energy efficiency and cost-effectiveness of the dryer design would also be important factors to consider in the overall success of the project.