Learn Finite Volume Analysis from Daily Life Examples

Examples of a heat pan and my lunch box

Created byL'imagist Studio

Last updated 5/2019

English

What you'll learn

Conduct finite volume analysis through visualization,key concept and math manipulation
Discretize 1D and 2D domain from two real-life examples
Apply boundary conditions to governing equation

Course content

2 sections • 16 lectures • 32m total length

Introduction0:47
Explore how finite volume analysis models temperature change along a heated pan handle, revealing whether the temperature decays linearly or exponentially and comparing results with the analytical solution.
Visualization2:08
Visualize this problem as a fin, define 50 C base, 25 C room, and grid the fin into control volumes with delta x.
Key Concept1:31
Derive the one-dimensional steady-state governing equation, integrate over the control volume, relate the integrated form to interior and boundary nodes, and rearrange for clarity.
Interior Nodes 2, 3 and 41:25
Explain the finite-volume equation for interior nodes 2, 3, and 4 using a central control volume, east and west face temperatures, and a source term.
Boundary Node 11:12
Demonstrate boundary node 1 in finite volume analysis using a control volume at node 1 with delta x and a west boundary temperature, eliminating TE terms and including source term.
Boundary Node 51:11
Analyze boundary node 5 with a control volume, use delta x on the east-west faces, insulating at eight drops the west term, yielding the east-face equation with a source term.
Math Manipulation1:04
Replace T.P., T.W., and T with corresponding temperatures in the nodal equations, compute coefficients from known values, form a matrix, and solve with Matlab to obtain the temperature distribution.

Introduction1:16
Apply the finite volume method in Matlab to model temperature distribution inside a lunchbox, using visualization and dimensions to compare ice cream, sandwich, and water temperatures.
Grid Generation1:20
Grid generation splits the lunchbox into six by six nodes with delta x and delta y, defining node temperatures and north, south, east, and west faces for a volume setup.
Key Concept2:17
Explore the two-dimensional heat diffusion equation without heat generation in steady state, and derive a finite-volume balance by integrating over a control volume in x and y.
Interior Nodes1:37
Learn finite volume analysis for interior nodes by deriving the coefficient form from east, west, north, and south faces and isolating a source term.
Left and Right Boundary Nodes3:03
Apply finite-volume analysis to left and right boundary nodes, excluding corners; form volumes and replace west/east terms with Ta and Tb, using delta x over two to derive coefficient form.
Top and Bottom Boundary Nodes2:19
Learn how top and bottom boundary nodes are treated in finite volume analysis, using insulated north and south faces with no heat flux, and rewriting the equation in coefficient form.
Interior Insulation2:34
Explore interior insulation in finite volume analysis by forming control-volume equations for horizontal and vertical insulation using east, west, north, and south faces, with zero heat flux simplifying terms.
Corner Nodes7:05
Learn how to label corner nodes in finite volume analysis and construct control volumes with east, west, north, and south faces. Apply insulated boundary conditions to simplify the coefficients form.
Math Manipulation1:40
Apply math manipulation to solve temperature using interior, boundary, and corner node relations in MATLAB with for loops, noting how 6 by 6 vs 50 by 50 meshes affect resolution.

Requirements

Basic calculus background would be useful, such as integration and differentiation

Description

Hi everyone,

I know sometimes finite volume analysis might sound intimidating. However, I found that it is easier to understand when we associate the abstract knowledge with examples that are tangible to us. In this course, you will learn how to use Finite Volume Analysis to determine the temperature profile of a handle of a pan as well as what the temperature distribution look like in my lunch box! I hope you can join me on this fun journey!

Who this course is for:

Potential Engineers
Potential Mathematicians
Someone that is interested in getting to know how Finite Volume Analysis works
Someone that need help in Finite Volume Analysis for homework, project, career advancement, etc
Someone that is interested in relating abstract math equations to meaningful real-world challenges
Someone hops to use Finite Volume Analysis to build predictive models for various projects

Learn Finite Volume Analysis from Daily Life Examples

What you'll learn

Explore related topics

Course content

The handle of a pan: Too hot to hold?7 lectures • 9min

What's in my lunch box?9 lectures • 23min

Requirements

Description

Who this course is for: