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    Modeling Scenario
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    1-110-TidePoolSnails-ModelingScenario
    Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the sun heats the water. Students model the tide pool's...
    datasnailstemperatureNewton's Law of CoolingcoolingNewtonwarmingtital pooltide pool
    Potential Scenario
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    2018-Chris McCarthy-Newtons Law of Cooling
    You have hot water (initial temperature ) in a container, say a cup or glass. The temperature in the room is cooler, say a constant degrees Celsius. Come up with a differential equation that models the water's temperature.
    datawaterNewton's Law of Coolingcooling
    Modeling Scenario
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    1-031-CoolIt-ModelingScenario
    We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...
    SpanishNewton's Law of Coolingcooling
    Modeling Scenario
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    1-045-TimeOfDeath-ModelingScenario
    Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.
    body masstemperaturedeathNewton's Law of Coolingbody temperature
    Modeling Scenario
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    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.
    temperaturesteady statethermometerheat exchangetransfer functionphase lagInvers Laplace Transform
    Modeling Scenario
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    1-088-RoomTemperature-ModelingScenario
    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
    environmentclimatetemperatureNewton's Law of Coolingcoolingperiodic function
    Modeling Scenario
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    1-114-EarthClimate-ModelingScenario
    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
    climateenergytemperaturelinearizationphase linesenergy balance modelroot finding
    Modeling Scenario
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    230

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    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 transferexperimentconductionconvectionboundary conditionsfinite volume method
    Potential Scenario
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    43

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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Modeling Scenario
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    1-061-PotatoCooling-ModelingScenario
    We model the cooling of a baked potato and compare it to student-collected data.
    least sum of square errorsNewton's Law of Coolingcoolingpotato
    Modeling Scenario
    175

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    70

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    1-144-HeatCool-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
    temperatureNewton's Law of Coolingcooling
    Potential Scenario
    125

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    2013-Murray_Bourne-Modeling fish stocks
    It is possible to have a sustainable fishing industry with proper planning and strictly enforced quotas.
    logisticFishingfishing industryfish managementfood availabilityreeding ratewater temperature
    Potential Scenario
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    30

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    2004-Denny-Yackel-Temperature Models for Ware Hall
    This paper offers some very nice extended models for cooling off a new office area for a mathematics department.
    Newton's Law of Coolingcoolingoffice building
    Modeling Scenario
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    1-076-ClimateBifurcation-ModelingScenario
    We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
    energy balanceclimateenergyalbedoHysteresisbifurcationice-agegreenhousebalanceStefan Boltzmann Law
    Modeling Scenario
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    1-033-SouthernBarbeque-ModelingScenario
    We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat.
    nonlinear regressionlogisticNewton's Law of Cooling-Warmingbarbecue
    Modeling Scenario
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    215

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    1-043-CoolingUpAndDown-ModelingScenario
    We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.
    temperatureoscillationNewton's Law of Coolingcoolingthermostatair conditioner
    Modeling Scenario
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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
    bNewton's Law of Coolingwater bottleautonomousbottle
    Potential Scenario
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    43

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    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.
    temperaturethermal conductivityheat flowthermal diffusivityroot cellar
    Modeling Scenario
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    2017

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    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.
    sphereheat equationturkeyPanofskyradial symmetry
    Modeling Scenario
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    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.
    laboratoryDiffusionheat