Finite Volume model of 1D fully-developed pipe flow. This page has links to MATLAB code and documentation for the finite volume solution to the one-dimensional equation for fully-developed flow in a round pipe. Μ r ∂ ∂ r ( r ∂ u ∂ r) − ∂ p ∂ x = 0. Where u is the axial velocity, p is the pressure, μ is the viscosity and r is the. Object detection is a computer vision technique for locating instances of objects in images or videos. We can recognize and locate objects of interest within a matter of moments. The goal of object detection is to replicate this intelligence using a computer. By default, the detector is configured to detect faces. 4: Face detection Fig. 5: Eyes detection Fig. 6: Upper body detection Download Source Code for the face detection using MATLAB project: click here. Call the step method with input image I, cascade object detector, points PTS and any other optional properties. This tutorial presents MATLAB code that implements the explicit finite difference method for option pricing as discussed in the The Explicit Finite Difference Method tutorial. The code may be used to price vanilla European Put or Call options. Note that the primary purpose of the code is to show how to implement the explicit method.
Description
The power consumption and sensitivity of the sensor should be predicted in order to ensure that it will perform acceptably in the micropump system. The placement of the sensor in the middle of the flow channel is ideal for maximum sensitivity, but the exact size and shape of the sensor may also be adjusted to maximize the sensitivity and reduce the power loss. Theoretical analysis of the sensor can be performed by programming governing equations, sensor geometries, and material properties into MATLAB. Trends are extracted and optimum design features can be determined. The typical sensor layout is shown in Figure 1.
Thermal anemometer diagram for electrical and thermal analysis
The process of configuring and running this massive set of simulations is facilitated using MATLAB. A MATLAB script is written that will go through the different area, ratio, and flow rate values, and create an input file read by ANSYS. When one simulation is completed, the temperature data of the heating element is written to a text file, and ANSYS will continue on to the next simulation. Only the temperature of the heating element must be recorded, since this represents the overheat temperature of the sensor. The heat generation divided by the overheat temperature is used to calculate the thermal conductance. Another MATLAB script is written to read all of the text files produced by ANSYS, and to analyze the results. All of the MATLAB scripts written to aid in the ANSYS simulation and data analysis can be found in this project.
This page contains links to MATLAB codes used to demonstrate the finitedifference and finite volume methods for solving PDEs. This page also containslinks to a series of tutorials for using MATLAB with the PDE codes.
The finite volume codes can handle non-uniform meshes and non-uniformmaterial properties. Therefore, these codes could be used or adapted topractical problems, and have been done so by me and others.
Contents
Here are direct links the web pages in this sereis. Short descriptions ofthe pages, with links, are given below.
Beware! I have tested the codes on a variety of demonstration problems.The codes are qualitatively correct for the test cases, and in several of thosecases I show that the code exhibit the correct asymptotic truncation error. Aswith any tool, however, these codes can be applied incorrectly or to asituation they were not designed to handle. Although the codes are designed tobe flexible, and have been tested fairly extensively, I do not guaranteethat they will be useful to you. Please let meknow if you find any bugs.
Finite-Difference Models of the Heat Equation
This page has links MATLAB code and documentation for finite-difference solutions theone-dimensional heat equation
where is the dependent variable, and are the spatial and time dimensions,respectively, and is the diffusion coefficient.
Finite Volume model of 1D convection
This page has links to MATLAB code and documentation for the finite volumemethod solution to the one-dimensional convection equation
where is the -direction velocity, is a convective passive scalar, is the diffusion coefficient for , and is the spatial coordinate.
Finite Volume model of 1D fully-developed pipe flow
This page has links to MATLAB code and documentation for the finite volume solution to the one-dimensional equation for fully-developed flow in a round pipe
where is the axial velocity, is the pressure, is the viscosity and is the radial coordinate.This is a simple and well-known flow with the exact solution
where is the pipe radius.
Finite Volume model in 2D Poisson Equation
This page has links to MATLAB code and documentation for the finite volumesolution to the two-dimensional Poisson equation
where is the scalar field variable, is a volumetric source term,and and are the Cartesian coordinates.This equation is a model of fully-developed flow in a rectangular duct, heat conductionin rectangle, and the pressure Poisson equation for finite volume models of fluid flow.
Set up MATLAB for working with the course codes
This page gives recommendations for setting up MATLAB to use the finite-differenceand finite-volume codes for the course. The main goals are to create a library folderfor storing the codes after downloading them, and setting up MATLAB so thatcode library is always included in the search path.
This page is part of a series of MATLAB tutorials for ME 448/548:
- Set up MATLAB for working with the course codes – This page
Basic MATLAB Practice
This page walks you through some practice exercises to help develop your MATLAB skills.It's part of a series of MATLAB tutorials for ME 448/548:
- Basic MATLAB Practice – This page
Practice with PDE codes in MATLAB
This page demonstrates some basic MATLAB features of the finite-difference codesfor the one-dimensional heat equation. This is a MATLAB tutorial without muchinterpretation of the PDE solution itself. Consult another web pagefor links to documentation on the finite-difference solution to the heat equation.
This page is part of a series of MATLAB tutorials for ME 448/548:
- Practice with PDE codes in MATLAB – This page
Debugging MATLAB Code
This page walks you through some practice exercises to help develop your MATLAB skills.
Introduction to debugging
This page builds on the previous examples to introduce debugging. Any substantialprogramming effort involves a lot of debugging. Using the built-in debugger willmake that effort more productive.
In addition to the examples on the rest of the page, or maybe even before youwork through those examples, I recommend the following YouTube videos that introducethe debugger
- MATLAB Debugging Tutorial (11 minutes) by Ilya Mikhelson
- Lesson 4.5: Debugging (25 minutes) from the 2015 version of theCoursera course, Introduction to programming with MATLAB.
Both of those videos give a good introduction to the debugger. You probably only needto watch one. The second one provides a bigger perspectiveon MATLAB programming, and I got a lot out of it while watching at 1.5x speed. :-)