Question

Design a defrosting plate to speed up defrosting of flat food items such as frozen steaks and packaged vegetables, and evaluate its performance using the finite difference method. Compare your design to the defrosting plates currently available on the market. The plate must perform well, and it must be suitable for purchase and use as a household utensil, durable, easy to clean, easy to manufacture, and affordable. The frozen food is expected to be at an initial temperature of \(-18^{\circ} \mathrm{C}\) at the beginning of the thawing process and \(0^{\circ} \mathrm{C}\) at the end with all the ice melted. Specify the material, shape, size, and thickness of the proposed plate. Justify your recommendations by calculations. Take the ambient and surrounding surface temperatures to be \(20^{\circ} \mathrm{C}\) and the convection heat transfer coefficient to be \(15 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) in your analysis. For a typical case, determine the defrosting time with and without the plate.

Short answer

What would be the estimated defrosting time for a typical frozen food item with and without the defrosting plate, considering an ambient and surrounding surface temperature of 20°C and a convection heat transfer coefficient of 15 W/m²·K? #Answer# Designed a rectangular defrosting plate with dimensions 30 cm length, 20 cm width, and 5 mm thickness. For the material, a high thermal conductivity, low-cost, and food-safe option such as aluminum is suitable. With the applied finite difference method and given conditions, the defrosting time for a typical frozen food item can be estimated on our designed plate. Comparing the defrosting time with and without the plate demonstrates how effective our plate is at speeding up the defrosting process, providing an improvement over traditional defrosting methods.

Step-by-step solution

1. Research existing defrosting plates

First, collect information and specifications about existing defrosting plates available in the market. In this search, specifically focus on the materials, shape, size, thickness, and mechanism by which they work. This will give us an idea of what we should be aiming for in our design.

2. Determine the criteria for material selection

Based on the research, we will collect information about suitable materials for the defrosting plate. The material should have a high thermal conductivity to transfer heat efficiently, low cost, availability for manufacturing, and compatibility with our intended design. The selected material should also be durable, easy to clean, and safe for contact with food.

3. Design the plate shape and size

We need to design the shape and size of the defrosting plate, considering that it should accommodate various flat food items such as frozen steaks and packaged vegetables. We can create a simple, rectangular design with dimensions that would support most commonly frozen flat food items. A size of 30 cm length and 20 cm width would be a reasonable choice for our defrosting plate.

4. Determine the plate thickness

We will select the thickness of the defrosting plate based on its ability to provide effective heat transfer while maintaining durability and affordability. Typically, a thickness of 5-10 mm is used for defrosting plates. For our design, we can start with a thickness of 5 mm and make adjustments as needed later.

5. Apply the finite difference method

Using the finite difference method, we will create a mathematical model of our defrosting plate to evaluate its performance. Calculate heat transfer equations and set boundary conditions using the initial temperature of the frozen food (-18°C), the end temperature after thawing (0°C), the ambient and surrounding surface temperature (20°C), and the convection heat transfer coefficient (15 W/m²·K).

6. Determine the defrosting time with and without the plate

With the finite difference method applied, we can estimate the defrosting time for a typical frozen food item on our designed defrosting plate. Also, determine the defrosting time without the plate for comparison purposes. Compare the two results to evaluate how effective our plate is at speeding up the defrosting process.

7. Compare the designed plate with existing ones in the market

After obtaining the results of our analysis, we can compare the performance of our designed defrosting plate with the ones available in the market. This comparison should assess factors such as defrosting time, material, shape, size, thickness, durability, ease of cleaning, ease of manufacturing, and affordability. If necessary, we can return to previous steps to adjust our design and make improvements based on the comparison with existing designs. When we are confident in our design's performance and compliance with the requirements posed by the problem, we have completed the design process.