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Views
Date
Relevance
Modeling Scenario
251
views
246
downloads
0
comments
7-020-ThermometerInVaryingTempStream-ModelingScenario
We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.
temperature
steady state
thermometer
heat exchange
transfer function
phase lag
Invers Laplace Transform
Technique Narrative
393
views
202
downloads
0
comments
9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
Maternal-Fetal interface
heat equation
Conservation of Energyt
heat flux
Euler's forward method
central difference
skin burn
hyperthermia
thermal conductivity
layers
Potential Scenario
113
views
43
downloads
0
comments
1981-Geoffrey_Berresford-Differential Equations and Root Cellars
This is a classic module from UMAP in which the heat equation in one dimension is fully developed by using the standard technique of measuring the heat flow in and out of a small element of mass and equating them at equilibrium.
temperature
thermal conductivity
heat flow
thermal diffusivity
root cellar
Modeling Scenario
233
views
552
downloads
0
comments
9-020-HeatDiffusion-ModelingScenario
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
laboratory
Diffusion
heat
Modeling Scenario
185
views
164
downloads
0
comments
3-150-ItsABlastFurnace-ModelingScenario
This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.
steady state
heat equation
inverse problem
furnace
Potential Scenario
238
views
79
downloads
0
comments
2012-Bech-EtAl-Resources For Engineering Applications Of Math
Illustrations of applied mathematics including statics, truss, heat equation, column analysis, coupled oscillators, feedback control, AC circuit, chemical reactions, kinetics.
kinetics
heat equation
column analysis
coupled oscillators
feedback control
AC circuit
chemical reactions
Modeling Scenario
255
views
251
downloads
0
comments
1-079-HomeHeating-ModelingScenario
This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
Optimal Control Theory
temperature
heat
furnace
Newton's Law of Cooling
home heating
specific heat
Modeling Scenario
218
views
230
downloads
0
comments
3-069-HeatInBar-ModelingScenario
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
heat transfer
experiment
conduction
convection
boundary conditions
finite volume method
Potential Scenario
122
views
35
downloads
0
comments
1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange
A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.
mechanical ventilation
ventilation
carbon dioxide exchange
tracheal gas insufflation
alveolar ventilation
shunt
two-compartment model
Potential Scenario
140
views
59
downloads
0
comments
2016-Spayd-Puckett- A Three-Fold Approach to the Heat Equation - Data Modeling Numerics
This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course.
separation of variables
experiment
heat equation
Lab Equipment
collect data
Modeling Scenario
772
views
2028
downloads
0
comments
9-014-TurkeyCook-ModelingScenario
The goal of this project is to investigate several models for the cooking time for a turkey based on weight, test these models with data obtained from heating curves for turkeys of various weights, and develop a new model to fit this data.
sphere
heat equation
turkey
Panofsky
radial symmetry
Potential Scenario
110
views
36
downloads
0
comments
2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
ice
ice spike
bulk heat transfer
mass conservation
Potential Scenario
158
views
45
downloads
0
comments
1989-EY_Rodin-S_Jaques-Countercurrent Oxygen Exchange in the Swim Bladders of Deep-Sea Fish
Oxygen diffuses from lungs into blood, nutrients diffuse from intestinal tracts into blood and from blood into various cells, and waste products diffuse from cells back into blood.
fish
Cell Membrane
flow
blood
bladder
countercurrent
Modeling Scenario
439
views
845
downloads
0
comments
9-002-GroundWaterFlow-ModelingScenario
The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
s
groundwater flow
Darcy's Law
heat equation
aquifer
hydraulic head
Fourier's Law
sand tank
Free Online Textbook
233
views
118
downloads
0
comments
2021-G_Nagy-Ordinary_Differential_Equations
This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations.
differential equations
textbook
Potential Scenario
153
views
62
downloads
0
comments
2007-Mogen_Steffensen-Differential Equations in Finance and Life Insurance
The mathematics of finance and the mathematics of life insurance were always intersecting. Life insurance contracts specify an exchange of streams of payments between the insurance company and the contract holder.
finance
disability
life insurance
mortality
insurane
Thiele’s equation
Black-Scholes equation
Modeling Scenario
233
views
95
downloads
0
comments
4-065-GasInjection-ModelingScenario
Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary...
Prandtl-Blasius equations
boundary layer
gas injection
esponential box scheme
uniform convergence
FORTRAN
Technique Narrative
539
views
312
downloads
0
comments
1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.
carbon dioxide
Surface Atmosphere Exchange
bifurcation
fold bifurcation
saddle node
Free Online Textbook
152
views
59
downloads
0
comments
2016-Langtangen-Pedersen - Scaling of Differential Equations
Nowadays, the greatest practical benefit of scaling is related to running numerical simulations, since scaling greatly simplifies the choice of values for the input data and makes the simulations results more widely applicable.
scaling
dimensionless
continuum mechanics
Modeling Scenario
474
views
191
downloads
0
comments
5-012-LipoproteinModeling-ModelingScenario
Data from a study on the amounts of low-density-lipoprotein (LDL), form of cholesterol, in blood plasma is presented. Students build, validate, and use a compartment model of the kinetic exchange of the LDL between body tissue and blood plasma.
wildlife
low-density-lipoprotein
tracer
compartment model
cholesterol
blood plasma
body tissue
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