Write a computer program to evaluate the variation of temperature with time of thin square metal plates that are removed from an oven at a specified temperature and placed vertically in a large room. The thickness, the size, the initial temperature, the emissivity, and the thermophysical properties of the plate as well as the room temperature are to be specified by the user. The program should evaluate the temperature of the plate at specified intervals and tabulate the results against time. The computer should list the assumptions made during calculations before printing the results. For each step or time interval, assume the surface temperature to be constant and evaluate the heat loss during that time interval and the temperature drop of the plate as a result of this heat loss. This gives the temperature of the plate at the end of a time interval, which is to serve as the initial temperature of the plate for the beginning of the next time interval. Try your program for \(0.2\)-cm-thick vertical copper plates of \(40 \mathrm{~cm} \times 40 \mathrm{~cm}\) in size initially at \(300^{\circ} \mathrm{C}\) cooled in a room

Step by step solution

01

Obtain input values from the user

The user should provide the following inputs: - Plate thickness (in meters) - Plate size (in meters) - Initial plate temperature (in Celsius) - Emissivity - Thermophysical properties (thermal conductivity, specific heat, and density) - Room temperature (in Celsius) For the given example: - Thickness: \(0.002\) m - Size: \(0.4\) m x \(0.4\) m - Initial temperature: \(300^{\circ} \mathrm{C}\) - Emissivity: Constant (find the emissivity value for copper) - Thermophysical properties: Copper (thermal conductivity, specific heat, and density) - Room temperature: \(22^{\circ} \mathrm{C}\)

02

Calculate the heat transfer coefficient

Determine the heat transfer coefficient (h) by finding the natural convection heat transfer coefficient, which depends on the temperature difference between the plate and the air, as well as the plate's dimensions and material properties.

03

Calculate the heat loss

For each time interval, calculate the heat loss using the following equation: \(Q = h * A * (T_{plate} - T_{room})\) where: - \(Q\) is the heat loss - \(h\) is the heat transfer coefficient - \(A\) is the plate surface area - \(T_{plate}\) is the initial temperature of the plate - \(T_{room}\) is the room temperature

04

Calculate the temperature drop

Find the temperature drop during the time interval using the following equation: \(\Delta T = \frac{Q * dt}{m * C_p}\) Where: - \(\Delta T\) is the temperature drop - \(Q\) is the heat loss - \(dt\) is the time interval (in seconds) - \(m\) is the mass of the plate - \(C_p\) is the specific heat capacity

05

Update the plate temperature

Subtract the temperature drop from the initial plate temperature to get the updated plate temperature for the next time interval. \(T_{plate\_new} = T_{plate} - \Delta T\)

06

Tabulate and output the results

Create a table with columns for time, heat loss, temperature drop, and updated plate temperature. Repeat Steps 3-5 for each desired time interval and add the results to the table. Display the table as the output. After analyzing the problem, it can now be converted into a computer program using the above steps. The program will need to ask the user for input values, perform the necessary calculations, and then display the results in a tabular format.

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