# How Do You Model Time-Varying Heat Conduction in a Simple House Simulation?

• Mooz
In summary, the conversation is about a project on heat conduction in a box simulating a house. The goal is to model the temperature inside the box as the outside temperature changes over time. The box will have an outer wall, insulation, inner wall, and air in the middle. The issue is understanding the fundamental theory, which is more complex than Newton's law of cooling. The speaker, who is a 2nd semester college student, needs to do self-study to understand the equations and recommended reading materials. The problem can be simplified to 2 dimensions and a spreadsheet can be used to calculate the temperature at different distances in the box. This method is similar to a basic FEA analysis.
Mooz
I'm doing a projekt on heat conduction i a box.
The point is to simulate a house very simple. We have time varying temperature conditions on the outside, and want to model the temperature inside the box over time as outside temperature changes. The box will consist og an outer wall, insulation, and an inner wall and air in the middle.
Our problem is to get startet with the fundamental theory, which is more complicated than Newtons law of cooling. This is a self study projekt, so I ned to read and understand myself, so i can't be to difficult reading. I just started college, 2. semester.
What equations er being used for this kind of problem? What is good reading?
Thank you

Since you are only talking about conductive heat transfer, it really shouldn't be all that difficult.

First of all, are you going to simplify the problem to 2 dimensions or 3? If it's 2 then that makes things even easier. You can set up a spreadsheet to do your calculations for you. Simply lay out your box as a large group of cells. Your outer cells would have the wall boundary conditions and the inner cells could calculate the temperature at whatever distance you wish to set them apart. Each interior cell would depend on the 4 cells surrounding it (in 2D). It would be a poor man's FEA analysis. I remember doing some basic plates and such this way back in school.

for sharing your project with me. Time varying heat conduction is a fascinating topic with many real-world applications, such as in building and environmental engineering. It sounds like you have a solid understanding of the basic principles and components involved in your project, including the outer wall, insulation, inner wall, and air layer.

To model the temperature inside the box over time, you will need to use the heat conduction equation, also known as the Fourier's law of heat conduction. This equation describes the rate of heat transfer through a material and is based on the temperature gradient and thermal conductivity of the material. It is a fundamental equation in heat transfer and is used in various applications, including your project.

To incorporate time-varying temperature conditions on the outside, you will also need to consider the boundary conditions of your system. These can include the temperature and heat flux at the outer wall, as well as any changes in ambient temperature over time.

As for good reading, there are many resources available online and in textbooks that cover the fundamentals of heat conduction and its applications. Some recommended textbooks include "Fundamentals of Heat and Mass Transfer" by Incropera and DeWitt, "Introduction to Heat Transfer" by Bergman, Lavine, Incropera, and DeWitt, and "Heat and Mass Transfer: A Practical Approach" by Cengel and Ghajar.

Additionally, there are many online resources and tutorials that can help you understand the concepts and equations involved in your project. Some good places to start include online lecture notes, YouTube tutorials, and interactive simulations.

I wish you the best of luck with your project and hope you find the resources and information you need to successfully model time-varying heat conduction in your box.

## 1. What is time varying heat conduction?

Time varying heat conduction is the transfer of heat through a material that changes with time. This could be due to changes in temperature, heat source/sink, or material properties.

## 2. What factors affect time varying heat conduction?

Time varying heat conduction is influenced by several factors, including temperature gradients, thermal conductivity of the material, and the presence of any heat sources or sinks.

## 3. How is time varying heat conduction different from steady-state heat conduction?

In steady-state heat conduction, the temperature and heat flow do not change with time. In contrast, time varying heat conduction involves changes in temperature and heat flow over time.

## 4. How is time varying heat conduction modeled?

Time varying heat conduction is typically modeled using partial differential equations, such as the heat equation. These equations take into account the changing temperature and heat flow over time.

## 5. What are some applications of time varying heat conduction?

Time varying heat conduction is important in many fields, including materials science, thermodynamics, and engineering. It is used to understand and design systems where heat transfer changes over time, such as in electronics cooling and thermal management of buildings.

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