Breadcrumbs

Steady-State Heat Conduction JavaScript Simulation Applet HTML5

 

 

 

Download ModelDownload SourceembedLaunch Website ES WebEJS

About

Description

Multi-layered wall
The goal of this virtual lab is to illustrate the computation of the steady-state heat conduction in a three-layered wall. The steady-state heat conduction is assumed to be one-dimensional.

The wall is composed of three layers of different materials and thickness LA, L B an LC . The temperature of the inner surface of the wall is T1 and the outside temperature T4 (see figure 1).
The heat flow per unit area (qx )and the temperature at the interfaces of the diferent layers (T 2, T3 ) are calculated.
Thermal conductivities of the layer's materials (kA , kB , kC ) are assumed to be independent of others model variables. The thickness of the layer that compose the walls are model parameters. The wall surface (S) is assumed to be constant. The S parameter is not used in the model equations, because qx doesn't depend on this parameter.

The mathematical model is described by the following equations:
T1 - T2 = (La/ka)  *  qx T2 - T3 = (Lb/kb)  *  qx T3 - T4 = (Lc/kc)  *  qx
Authors Carla Martín
Dpto. de Informática y Automática
E.T.S. de Ingeniería Informática, UNED
Juan del Rosal 16, 28040 Madrid, Spain  

Translations

Code Language Translator Run

Credits

Carla Martn; Tan Wei Chiong; Loo Kang Wee

1. Overview:

This document reviews the "Steady-State Heat Conduction JavaScript Simulation Applet HTML5" resource, which is an interactive virtual laboratory tool designed to illustrate the principles of steady-state heat conduction through a multi-layered wall. The applet is part of the Open Educational Resources / Open Source Physics @ Singapore initiative.

2. Main Theme:

The central theme of this resource is to provide a visual and interactive way for students (and potentially educators) to understand the concept of steady-state heat conduction through a composite material. It focuses on how heat flows through different layers with varying thermal conductivities and thicknesses when a constant temperature difference is maintained across the wall.

3. Key Concepts and Ideas:

  • Steady-State Heat Conduction: The simulation models a scenario where the temperature at any point within the system does not change over time. This is explicitly stated: "We call this a steady-state conduction if the temperature difference driving the heat transfer is constant."
  • Multi-layered Wall: The model specifically focuses on a wall composed of three distinct layers, each potentially having different materials and thicknesses (LA, LB, LC) and thermal conductivities (kA, kB, kC). The description notes: "Multi-layered wall The goal of this virtual lab is to illustrate the computation of the steady-state heat conduction in a three-layered wall."
  • One-Dimensional Heat Flow: The simulation simplifies the scenario by assuming that heat transfer occurs in only one direction, perpendicular to the layers of the wall. The description states: "The steady-state heat conduction is assumed to be one-dimensional."
  • Temperature Gradient and Interface Temperatures: The simulation calculates and visualizes the temperature at the inner surface (T1), the outer surface (T4), and the interfaces between the different layers (T2, T3).
  • Heat Flow per Unit Area (qx): The applet calculates the rate of heat transfer per unit area through the composite wall. Notably, the description points out: "The S parameter is not used in the model equations, because qx doesn't depend on this parameter," indicating that the total surface area of the wall does not affect the heat flow per unit area.
  • Thermal Conductivity and Thickness: The resource highlights the dependence of heat conduction on the material properties (thermal conductivity) and the physical dimensions (thickness) of each layer. The "For Teachers" section explicitly states: "Heat conducts through solids at different rates, and is dependent on the thickness of the solid and the heat conductivity of the solid."
  • Mathematical Model: The underlying physics is represented by a set of linear equations relating the temperature differences across each layer to the heat flow per unit area and the thermal resistance of each layer (thickness divided by thermal conductivity):
  • "T1 - T2 = (La/ka) * qx"
  • "T2 - T3 = (Lb/kb) * qx"
  • "T3 - T4 = (Lc/kc) * qx"
  • Interactive Exploration: The simulation provides users with six sliders to adjust the thickness and thermal conductivity of each of the three layers. This allows for interactive investigation of how these parameters affect the temperature profile and heat flow.
  • Visual Representation: The applet includes a graphical representation of the three-layered wall and a temperature-thickness graph. The graph is "color-coded to represent the solid the heat travels through at that point," providing a clear visual understanding of the temperature distribution within the composite wall.
  • Closed System Assumption: The simulation operates under the assumption of a closed system where there is "no loss of heat from the system."
  • Constant Boundary Temperatures: The simulation sets fixed temperatures at the left side (inner surface, T1, assumed to be 25°C in the teacher's notes) and the right side (outer surface, T4, assumed to be 0°C in the teacher's notes) to drive the heat transfer.

4. Target Audience and Learning Goals:

The resource appears to be designed primarily for students learning about thermal physics and the thermal properties of matter. The "Sample Learning Goals" (although the actual text is "[text]") would likely focus on understanding the relationship between thermal conductivity, thickness, temperature difference, and heat flow in composite materials under steady-state conditions. The "For Teachers" section indicates its utility in demonstrating these concepts in a virtual environment.

5. Technical Aspects:

  • The simulation is developed using JavaScript and is embedded as an HTML5 applet, making it accessible through web browsers without the need for additional plugins.
  • The embedding code (<iframe...>) is provided, facilitating easy integration of the simulation into other web pages or learning management systems.
  • The authors are identified as Carla Martín, Tan Wei Chiong, and Loo Kang Wee.

6. Strengths:

  • Interactive Learning: The sliders allow for direct manipulation of parameters and observation of the resulting changes in temperature distribution and heat flow, fostering a deeper understanding of the underlying principles.
  • Visual Representation: The graphical display of the wall and the temperature profile provides a clear and intuitive way to grasp the abstract concept of heat conduction.
  • Mathematical Foundation: The explicit statement of the mathematical model provides a link between the visual simulation and the underlying physical laws.
  • Accessibility: Being an HTML5 applet, it is likely cross-platform compatible and easily accessible through standard web browsers.
  • Educational Resource: The resource is explicitly presented as an Open Educational Resource, promoting its free use and adaptation for educational purposes.

7. Potential Areas for Consideration (Based on the Provided Excerpts):

  • The "Sample Learning Goals," "Research," and "Video" sections contain "[text]," indicating that further information might be available in the full resource.
  • While the mathematical equations are provided, a more detailed explanation of their derivation or the concept of thermal resistance might be beneficial for some learners.
  • The simulation focuses on a three-layered wall. Expanding to a variable number of layers or different geometries could enhance its versatility.

8. Conclusion:

The "Steady-State Heat Conduction JavaScript Simulation Applet HTML5" is a valuable interactive tool for teaching and learning about heat transfer through composite materials under steady-state conditions. Its visual nature, interactive elements, and underlying mathematical model provide a comprehensive approach to understanding this important concept in thermal physics. The accessibility of the HTML5 format and its availability as an open educational resource further enhance its potential for widespread use in educational settings.

 

Steady-State Heat Conduction Study Guide

Quiz

  1. What is the primary goal of the Steady-State Heat Conduction JavaScript Simulation Applet HTML5?
  2. What key assumption is made about the nature of heat conduction in this simulation?
  3. Describe the physical setup modeled by the simulation, including the number of layers and the temperature conditions.
  4. Identify the parameters that can be adjusted in the simulation using the provided sliders.
  5. Explain what the graph on the right side of the simulation represents and how it is color-coded.
  6. What does it mean for heat conduction to be in a "steady-state"?
  7. According to the provided text, what two properties of a solid influence the rate of heat conduction through it?
  8. Why is the surface area (S) of the wall not a direct factor in the model equations for heat flow per unit area (qx)?
  9. What are the roles of T2 and T3 in the context of the three-layered wall?
  10. Briefly outline the mathematical relationships presented for the temperature differences across each layer.

Quiz Answer Key

  1. The primary goal of the simulation is to illustrate the computation of steady-state heat conduction in a three-layered wall composed of different materials and thicknesses. It allows users to visualize how heat flows through these layers under constant temperature differences.
  2. The key assumption made in this simulation is that the steady-state heat conduction is one-dimensional, meaning heat flows only in one direction, perpendicular to the layers of the wall. This simplifies the analysis by neglecting heat transfer in other directions.
  3. The simulation models a wall composed of three distinct layers, each with its own material and thickness (LA, LB, LC). The inner surface of the wall is maintained at a constant temperature T1, while the outer surface is held at a different constant temperature T4.
  4. There are six sliders in the simulation that allow users to adjust the thickness (LA, LB, LC) and thermal conductivity (kA, kB, kC) of each of the three layers that make up the wall.
  5. The graph on the right plots the temperature as a function of the thickness through the three solids. It visually represents how the temperature changes as heat travels through each layer, with different colors indicating which solid the heat is currently passing through.
  6. Steady-state conduction refers to a condition where the temperature at any point within the system does not change over time. This occurs when the rate of heat entering a system equals the rate of heat leaving, resulting in a constant temperature distribution.
  7. According to the text, the rate at which heat conducts through a solid is dependent on the thickness of the solid and the heat conductivity (thermal conductivity) of the material.
  8. The surface area (S) is not directly used in the equations for heat flow per unit area (qx) because qx is defined as the heat flow per unit area. Therefore, the area has already been factored into the definition of qx, making it independent of the overall surface area.
  9. T2 and T3 represent the temperatures at the interfaces between the different layers of the wall. T2 is the temperature at the boundary between layer A and layer B, while T3 is the temperature at the boundary between layer B and layer C.
  10. The mathematical relationships show that the temperature difference across each layer is directly proportional to the thickness of that layer and the heat flow per unit area (qx), and inversely proportional to the thermal conductivity of the layer's material. Specifically: T1 - T2 = (La/ka) * qx, T2 - T3 = (Lb/kb) * qx, and T3 - T4 = (Lc/kc) * qx.

Essay Format Questions

  1. Discuss the concept of steady-state heat conduction and explain why it is a useful simplification in many engineering and physics problems. How does the JavaScript simulation illustrate this concept?
  2. Explain the role of thermal conductivity and thickness in determining the rate of heat transfer through a multi-layered wall. Using the provided simulation as a model, describe how changing these parameters for individual layers affects the overall temperature profile.
  3. The simulation assumes a closed system with no heat loss. In real-world scenarios, heat loss is often significant. Discuss the implications of neglecting heat loss and how the results from the simulation might differ from real-world measurements.
  4. Describe how the provided mathematical model (T1 - T2 = (La/ka) * qx, etc.) relates the temperature differences, layer properties, and heat flow in the three-layered wall. Explain the physical meaning of each term in the equations.
  5. The Open Educational Resources platform provides a variety of physics simulations. Discuss the benefits of using such interactive tools for learning about abstract concepts like heat transfer, and suggest other physics topics where similar simulations could be particularly effective.

Glossary of Key Terms

  • Steady-State Heat Conduction: A condition where the temperature at every point within a system remains constant over time, indicating a balance between the rate of heat flow into and out of any given point.
  • Thermal Conductivity (k): A measure of a material's ability to conduct heat. A higher thermal conductivity indicates that the material transfers heat more readily. In the simulation, it is represented by kA, kB, and kC for each layer.
  • Thickness (L): The physical dimension of each layer of the wall in the direction of heat flow. In the simulation, it is represented by LA, LB, and LC for each layer.
  • Heat Flow per Unit Area (qx): The rate of heat energy transfer through a unit cross-sectional area perpendicular to the direction of heat flow. It is assumed to be constant through all layers in steady-state.
  • Interface Temperature (T2, T3): The temperature at the boundary between two adjacent layers of the multi-layered wall. These temperatures are intermediate values between the initial and final temperatures.
  • Multi-layered Wall: A composite structure consisting of two or more layers of different materials, each potentially having different thermal properties and thicknesses, through which heat is conducted.
  • One-Dimensional Heat Conduction: Heat transfer that occurs predominantly in a single direction, simplifying the analysis by neglecting heat flow in other directions. This is the assumption made in the simulation.
  • Closed System: A system that does not exchange matter with its surroundings. The simulation assumes no loss of heat to the environment, making it a closed system in terms of energy transfer (though it's specifically about heat transfer, not matter).
 

Sample Learning Goals

[text]

For Teachers

Heat conducts through solids at different rates, and is dependent on the thickness of the solid and the heat conductivity of the solid.

We call this a steady-state conduction if the temperature difference driving the heat transfer is constant. In this simulation, it is assumed that the left side of a three-layered solid is set at a constant 25°C and the right side is set at a constant 0°C.

This simulation assumes that there is no loss of heat from the system (i.e.: this is a closed system). There are 3 walls in the graph on the left, representing 3 different solids that the heat conducts through. The graph on the right plots the temperature-thickness graph, showing how the temperature changes through the solids, and color-coded to represent the solid the heat travels through at that point.

There are 6 sliders to adjust the thickness and conductivity of each wall at the top of the simulation.

Research

[text]

Video

[text]

 Version:

  1. http://weelookang.blogspot.com/2018/05/steady-state-heat-conduction-javascript.html
  2. http://www.euclides.dia.uned.es/simulab-pfp/curso_online/cap7_caseStudies/sec_heatWall.htm by Alfonso Urquia and Carla Martin-Villalba

Other Resources

[text]

Frequently Asked Questions: Steady-State Heat Conduction Simulation

What is steady-state heat conduction?

Steady-state heat conduction occurs when the temperature difference driving heat transfer across a material is constant over time. This means the temperature at any point within the material does not change with time, and the rate of heat flow is constant.

What does this simulation illustrate?

This virtual lab demonstrates the calculation of steady-state heat conduction through a composite wall made of three distinct layers. It focuses on a one-dimensional heat flow scenario.

What parameters can be adjusted in the simulation?

Users can modify the thickness (LA, LB, LC) and thermal conductivity (kA, kB, kC) of each of the three layers composing the wall using interactive sliders.

What values are calculated by the simulation?

The simulation calculates the heat flow per unit area (qx) passing through the wall and the temperatures at the interfaces between the different layers (T2 and T3), given the temperatures of the inner (T1) and outer (T4) surfaces.

How does the simulation model the temperature profile through the wall?

The simulation includes a graph that visually represents how the temperature changes as heat travels through the different layers of the wall. This temperature-thickness graph is color-coded to correspond to each specific layer.

What are the underlying mathematical equations used in the model?

The steady-state heat conduction through each layer is modeled by the following equations:

  • T1 - T2 = (La/ka) * qx
  • T2 - T3 = (Lb/kb) * qx
  • T3 - T4 = (Lc/kc) * qx These equations relate the temperature difference across each layer to its thickness, thermal conductivity, and the heat flow per unit area.

Does the surface area of the wall affect the heat flow per unit area in this model?

No, the surface area (S) of the wall is assumed to be constant and is not used in the model equations for heat flow per unit area (qx). This is because qx represents the heat flow rate divided by the cross-sectional area, thus making it independent of the total surface area in one-dimensional conduction.

What are some of the learning goals associated with this simulation?

This simulation helps users understand that heat conducts through different solid materials at varying rates. These rates are dependent on both the material's thermal conductivity and its thickness. It also reinforces the concept of steady-state conduction, where the temperature difference driving the heat transfer remains constant.

1 1 1 1 1 1 1 1 1 1 Rating 0.00 (0 Votes)
Details
Parent Category: 13 Thermodynamic Systems
Category: 04 Thermal Properties of Matter
Hits: 6131