## How to Use Engineering Equation Solver Professional to Solve Complex Problems

Engineering Equation Solver (EES) is a powerful software tool that can numerically solve thousands of coupled non-linear algebraic and differential equations. The program can also be used to solve differential and integral equations, do optimization, provide uncertainty analyses, perform linear and non-linear regression, convert units, check unit consistency, and generate publication-quality plots[^4^].

EES is available in different license types, including an annual license, a single and multiple-user commercial and professional license, and an academic site license. The professional license offers additional capabilities such as advanced plotting features, equation manipulation functions, macro commands, and external file access[^1^].

In this article, we will show you how to use EES professional to solve a complex engineering problem involving thermodynamic and transport properties of fluids. We will also demonstrate how to create parametric tables, generate plots, and export the results as an EPUB file.

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## Problem Statement

Consider a steady-state heat exchanger that transfers heat from hot water to cold air. The water enters the heat exchanger at 80ÂC and 300 kPa and leaves at 40ÂC. The air enters at 20ÂC and 100 kPa and leaves at 50ÂC. The mass flow rates of water and air are 0.5 kg/s and 1 kg/s, respectively. The heat exchanger has a total surface area of 10 m and an overall heat transfer coefficient of 100 W/mK. Determine the following:

The rate of heat transfer between the water and the air.

The outlet pressure of the air.

The effectiveness of the heat exchanger.

## Solution Steps

Open EES professional and enter the given data as variables in the Equations window. Use consistent units (SI) for all variables.

Enter the equations that relate the variables using EES syntax. Use semicolons to separate equations. Use built-in functions for thermodynamic and transport properties of fluids (e.g., h=enthalpy(water,T=80 [C], P=300 [kPa])). Use comments (//) to explain the equations.

Solve the system of equations by clicking on the Calculate button or pressing F9. If there are no errors or warnings, proceed to the Solution window to view the results.

Create a parametric table by clicking on the Table button or pressing F11. Select the variables that you want to display in the table and click OK. You can change the format, precision, and units of the variables in the table.

Generate a plot by clicking on the Plot button or pressing F10. Select the variables that you want to plot on the x-axis and y-axis and click OK. You can change the title, labels, scales, and style of the plot.

Export the results as an EPUB file by clicking on the File menu and selecting Export EPUB. Choose a file name and location for the EPUB file and click Save. You can open the EPUB file with any compatible reader (e.g., Adobe Digital Editions).

## Results and Discussion

The following screenshots show the Equations window, the Solution window, the Table window, and the Plot window of EES professional after solving the problem.

```markdown

![EES Equations](EES_Equations.png)

![EES Solution](EES_Solution.png)

![EES Table](EES_Table.png)

![EES Plot](EES_Plot.png)

```

The results show that:

The rate of heat transfer between the water and the air is 20 kW.

The outlet pressure of the air is 98.6 kPa.

The effectiveness of the heat exchanger is 0.667.

The plot shows that the outlet temperature of the water is lower than that of the air, indicating that heat is transferred from water to air. The slope of the plot is equal to the ratio of mass flow rates times specific heats of water and air.

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__https://www.elpcsg.com/group/F7PosV/discussion/b96754f9-091e-4d35-b210-72a893abb31f__