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    Modeling Scenario
    223

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    256

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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
    Modeling Scenario
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    246

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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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    596

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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
    Modeling Scenario
    190

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    166

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    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 stateheat equationinverse problemfurnace
    Modeling Scenario
    260

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    265

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    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 TheorytemperatureheatfurnaceNewton's Law of Coolinghome heatingspecific heat
    Modeling Scenario
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    2068

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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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    907

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    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.
    sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank
    Modeling Scenario
    444

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    264

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    7-011-CoupledSystemLaplace-ModelingScenario
    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
    transfer functionpolycarbonatebaby heatercoupled systemheating
    Modeling Scenario
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    103

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    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 equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN
    Modeling Scenario
    432

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    263

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    3-092-WirelessPower-ModelingScenario
    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.
    DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law