Heat Transfer: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=197
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 22 Oct 2019 09:16:53 GMTTue, 22 Oct 2019 09:16:53 GMTNew applications in the Heat Transfer categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgHeat Transfer: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=197
Analysis of a Refrigeration Cycle with CoolProp
https://www.maplesoft.com/applications/view.aspx?SID=153490&ref=Feed
<p>This application analyzes a vapor compression refrigeration cycle for the refrigerant R134a. The application calculates heat changes over the compressor, condenser, throttle and evaporator, together with the coefficient of performance. Additionally, a P-h-T chart illustrating the refrigeration cycle is plotted.</p>
<p>Thermophysical properties are provided by the open source C++ CoolProp library (<a href="http://coolprop.org/">http://coolprop.org</a>). Once compiled and linked to Maple, CoolProp lets you access the properties of pure fluids, pseudo-pure fluids, and humid air with a function call. This application comes with a CoolProp DLL for 64-bit Windows. You may need to compile CoolProp for your own environment for a compatible library. </p><img src="https://www.maplesoft.com/view.aspx?si=153490/PT_Chart.png" alt="Analysis of a Refrigeration Cycle with CoolProp" style="max-width: 25%;" align="left"/><p>This application analyzes a vapor compression refrigeration cycle for the refrigerant R134a. The application calculates heat changes over the compressor, condenser, throttle and evaporator, together with the coefficient of performance. Additionally, a P-h-T chart illustrating the refrigeration cycle is plotted.</p>
<p>Thermophysical properties are provided by the open source C++ CoolProp library (<a href="http://coolprop.org/">http://coolprop.org</a>). Once compiled and linked to Maple, CoolProp lets you access the properties of pure fluids, pseudo-pure fluids, and humid air with a function call. This application comes with a CoolProp DLL for 64-bit Windows. You may need to compile CoolProp for your own environment for a compatible library. </p>https://www.maplesoft.com/applications/view.aspx?SID=153490&ref=FeedFri, 17 Jan 2014 05:00:00 ZSamir KhanSamir KhanClassroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package
https://www.maplesoft.com/applications/view.aspx?SID=134198&ref=Feed
The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion.<img src="https://www.maplesoft.com/view.aspx?si=134198/thumb.jpg" alt="Classroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package" style="max-width: 25%;" align="left"/>The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion.https://www.maplesoft.com/applications/view.aspx?SID=134198&ref=FeedMon, 14 May 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezCountercurrent Double Pipe Heat Exchanger
https://www.maplesoft.com/applications/view.aspx?SID=119402&ref=Feed
This application models the temperature dynamics of a countercurrent double pipe heat exchanger. Three partial differential equations are derived from heat balances across the tube- and shell-side liquids, and the tube wall (accounting for heat flow from the shell- and tube-side liquids, and conduction along the length of the tube).
The equations are solved numerically, and the temperature profiles are plotted. The heat exchanger is assumed to be perfectly insulated. Densities, specific heat capacities, heat transfer coefficients, and thermal conductivities are assumed to be constant.<img src="https://www.maplesoft.com/view.aspx?si=119402/381585\tube.png" alt="Countercurrent Double Pipe Heat Exchanger" style="max-width: 25%;" align="left"/>This application models the temperature dynamics of a countercurrent double pipe heat exchanger. Three partial differential equations are derived from heat balances across the tube- and shell-side liquids, and the tube wall (accounting for heat flow from the shell- and tube-side liquids, and conduction along the length of the tube).
The equations are solved numerically, and the temperature profiles are plotted. The heat exchanger is assumed to be perfectly insulated. Densities, specific heat capacities, heat transfer coefficients, and thermal conductivities are assumed to be constant.https://www.maplesoft.com/applications/view.aspx?SID=119402&ref=FeedThu, 28 Apr 2011 04:00:00 ZMaplesoftMaplesoftDouble Pipe Countercurrent Heat Exchanger
https://www.maplesoft.com/applications/view.aspx?SID=100377&ref=Feed
In this model, water on the shell-side heats milk on the tube-side in a countercurrent double-pipe heat exchanger. The heat exchanger is modeled via a heat balance on a discretized control volume, with the system equations implemented in a custom component. A full derivation of the system equations is given in an attached document (look under Project>Attachments>Documents). Heat transfer coefficients are given by the Dittus-Boelter correlation, and the temperature variation of the milk viscosity is accounted for.<img src="https://www.maplesoft.com/view.aspx?si=100377/sim_icon.jpg" alt="Double Pipe Countercurrent Heat Exchanger" style="max-width: 25%;" align="left"/>In this model, water on the shell-side heats milk on the tube-side in a countercurrent double-pipe heat exchanger. The heat exchanger is modeled via a heat balance on a discretized control volume, with the system equations implemented in a custom component. A full derivation of the system equations is given in an attached document (look under Project>Attachments>Documents). Heat transfer coefficients are given by the Dittus-Boelter correlation, and the temperature variation of the milk viscosity is accounted for.https://www.maplesoft.com/applications/view.aspx?SID=100377&ref=FeedWed, 22 Dec 2010 05:00:00 ZMaplesoftMaplesoftClassroom Tips and Techniques: Diffusion with a Generalized Robin Condition
https://www.maplesoft.com/applications/view.aspx?SID=96958&ref=Feed
<p>The one-dimensonal heat equation with a generalized Robin condition is solved on [0, 1] by a finite-difference scheme and by the Laplace transform, with the inversion implemented numerically. The left end is insulated and the initial temperature is zero. The Robin condition at the right end is driven by a function governed by an ODE, that is in turn, driven by the endpoint temperature.</p><img src="https://www.maplesoft.com/view.aspx?si=96958/thumb.jpg" alt="Classroom Tips and Techniques: Diffusion with a Generalized Robin Condition" style="max-width: 25%;" align="left"/><p>The one-dimensonal heat equation with a generalized Robin condition is solved on [0, 1] by a finite-difference scheme and by the Laplace transform, with the inversion implemented numerically. The left end is insulated and the initial temperature is zero. The Robin condition at the right end is driven by a function governed by an ODE, that is in turn, driven by the endpoint temperature.</p>https://www.maplesoft.com/applications/view.aspx?SID=96958&ref=FeedFri, 17 Sep 2010 04:00:00 ZRobert LopezRobert LopezHeat Exchanger Dynamics
https://www.maplesoft.com/applications/view.aspx?SID=35160&ref=Feed
<p>Simplified dynamic model of a heat exchanger, based upon a heat balance across the hot and cold streams, and a simplified temperature difference (temperature of hot stream at entrance – temperature of cold stream at entrance).</p><img src="https://www.maplesoft.com/applications/images/custom_component_sm.jpg" alt="Heat Exchanger Dynamics" style="max-width: 25%;" align="left"/><p>Simplified dynamic model of a heat exchanger, based upon a heat balance across the hot and cold streams, and a simplified temperature difference (temperature of hot stream at entrance – temperature of cold stream at entrance).</p>https://www.maplesoft.com/applications/view.aspx?SID=35160&ref=FeedTue, 09 Feb 2010 05:00:00 ZMaplesoftMaplesoftCooling a Solid with a Cold Air Stream with MapleSim and Maple
https://www.maplesoft.com/applications/view.aspx?SID=33210&ref=Feed
<p>This article looks at each of the components of cooling a solid with a cold air stream by convection.</p><img src="https://www.maplesoft.com/view.aspx?si=33210/thumb.png" alt="Cooling a Solid with a Cold Air Stream with MapleSim and Maple" style="max-width: 25%;" align="left"/><p>This article looks at each of the components of cooling a solid with a cold air stream by convection.</p>https://www.maplesoft.com/applications/view.aspx?SID=33210&ref=FeedFri, 10 Jul 2009 04:00:00 ZMaplesoftMaplesoftCylinder Heated by Induction
https://www.maplesoft.com/applications/view.aspx?SID=7240&ref=Feed
In this worksheet we consider a long metal cylinder that has a magnetic field applied parallel to the axis and a constraint on the current density at a particular depth. We demonstrate how the temperature depends on time and depth from the surface in a very long cylinder. This is calculated using the current density, the power density and the partial differential equation of heat conduction. In induction, the heating is caused by eddy currents, which themselves give rise to alternating magnetic fields. Because of the skin effect and depending on the frequency of the magnetic field, the highest current density exists directly under the surface of the heated work piece. It decreases rapidly with increasing depth. We calculate the effective magnetic field intensity on the surface required to reach a given temperature in a given time.<img src="https://www.maplesoft.com/view.aspx?si=7240/A_Cylinder_heated_by_Induction_2009_2.gif" alt="Cylinder Heated by Induction" style="max-width: 25%;" align="left"/>In this worksheet we consider a long metal cylinder that has a magnetic field applied parallel to the axis and a constraint on the current density at a particular depth. We demonstrate how the temperature depends on time and depth from the surface in a very long cylinder. This is calculated using the current density, the power density and the partial differential equation of heat conduction. In induction, the heating is caused by eddy currents, which themselves give rise to alternating magnetic fields. Because of the skin effect and depending on the frequency of the magnetic field, the highest current density exists directly under the surface of the heated work piece. It decreases rapidly with increasing depth. We calculate the effective magnetic field intensity on the surface required to reach a given temperature in a given time.https://www.maplesoft.com/applications/view.aspx?SID=7240&ref=FeedWed, 11 Feb 2009 00:00:00 ZMaplesoftMaplesoftPlotting Capabilities for Engineers
https://www.maplesoft.com/applications/view.aspx?SID=6979&ref=Feed
Maple contains an extensive set of visualization tools and options, including many plots and options commonly used by engineers. This Tips & Techniques document demonstrates how to create and customize your plots using interactive techniques and command options, with emphasis on options used in engineering contexts.<img src="https://www.maplesoft.com/view.aspx?si=6979/thumb.gif" alt="Plotting Capabilities for Engineers" style="max-width: 25%;" align="left"/>Maple contains an extensive set of visualization tools and options, including many plots and options commonly used by engineers. This Tips & Techniques document demonstrates how to create and customize your plots using interactive techniques and command options, with emphasis on options used in engineering contexts.https://www.maplesoft.com/applications/view.aspx?SID=6979&ref=FeedThu, 04 Dec 2008 04:00:00 ZMaplesoftMaplesoftHeat Exchanger and Cooling Liquids
https://www.maplesoft.com/applications/view.aspx?SID=6684&ref=Feed
This worksheet considers a common design of heat exchanger consisting of a double walled cylinder. A cooling liquid in the outer cylinder flows in the opposite direction to the hot gas inside the inner pipe.<img src="https://www.maplesoft.com/view.aspx?si=6684/thumb.gif" alt="Heat Exchanger and Cooling Liquids" style="max-width: 25%;" align="left"/>This worksheet considers a common design of heat exchanger consisting of a double walled cylinder. A cooling liquid in the outer cylinder flows in the opposite direction to the hot gas inside the inner pipe.https://www.maplesoft.com/applications/view.aspx?SID=6684&ref=FeedMon, 22 Sep 2008 00:00:00 ZMaplesoftMaplesoftDesigning a More Effective Car Radiator
https://www.maplesoft.com/applications/view.aspx?SID=6403&ref=Feed
The demand for more powerful engines in smaller hood spaces has created a problem of insufficient rates of heat dissipation in automotive radiators. As a result, many radiators must be redesigned to be more compact while still having sufficient cooling power capabilities.
This application proposes a new design for a smaller radiator assembly, which is capable of dissipating the same heat as the original design, given a set of operating conditions.<img src="https://www.maplesoft.com/view.aspx?si=6403/thumb.jpg" alt="Designing a More Effective Car Radiator" style="max-width: 25%;" align="left"/>The demand for more powerful engines in smaller hood spaces has created a problem of insufficient rates of heat dissipation in automotive radiators. As a result, many radiators must be redesigned to be more compact while still having sufficient cooling power capabilities.
This application proposes a new design for a smaller radiator assembly, which is capable of dissipating the same heat as the original design, given a set of operating conditions.https://www.maplesoft.com/applications/view.aspx?SID=6403&ref=FeedWed, 02 Jul 2008 04:00:00 ZMaplesoftMaplesoftHeating an Oil Stream Through Three Steam-Heated Tanks
https://www.maplesoft.com/applications/view.aspx?SID=1400&ref=Feed
Cold oil is being heated by steam through a series of three tanks connected in series. The transient change in temperature is modeled by three coupled ordinary differential equations.<img src="https://www.maplesoft.com/view.aspx?si=1400/1405.jpg" alt="Heating an Oil Stream Through Three Steam-Heated Tanks" style="max-width: 25%;" align="left"/>Cold oil is being heated by steam through a series of three tanks connected in series. The transient change in temperature is modeled by three coupled ordinary differential equations.https://www.maplesoft.com/applications/view.aspx?SID=1400&ref=FeedMon, 01 Nov 2004 00:00:00 ZMaplesoftMaplesoftPDE Boundary Value Problems Solved Numerically with pdsolve
https://www.maplesoft.com/applications/view.aspx?SID=4259&ref=Feed
Maple 8 can now compute numerical solutions to linear PDE systems over rectangular regions. One application of this feature is the solution of classical boundary-value problems from physics, such as the heat conduction equation and the wave equation.<img src="https://www.maplesoft.com/view.aspx?si=4259/pdes.gif" alt="PDE Boundary Value Problems Solved Numerically with pdsolve" style="max-width: 25%;" align="left"/>Maple 8 can now compute numerical solutions to linear PDE systems over rectangular regions. One application of this feature is the solution of classical boundary-value problems from physics, such as the heat conduction equation and the wave equation.https://www.maplesoft.com/applications/view.aspx?SID=4259&ref=FeedMon, 15 Apr 2002 16:04:37 ZMaplesoftMaplesoftMultiple Steady States in a Catalyst Pellet
https://www.maplesoft.com/applications/view.aspx?SID=4245&ref=Feed
In this document we show multiple steady states in a catalyst pellet can be predicted using Maple.<img src="https://www.maplesoft.com/view.aspx?si=4245//applications/images/app_image_blank_lg.jpg" alt="Multiple Steady States in a Catalyst Pellet" style="max-width: 25%;" align="left"/>In this document we show multiple steady states in a catalyst pellet can be predicted using Maple.https://www.maplesoft.com/applications/view.aspx?SID=4245&ref=FeedFri, 22 Mar 2002 10:20:21 ZDr. Ralph WhiteDr. Ralph WhiteHeat exchange in a series of tanks
https://www.maplesoft.com/applications/view.aspx?SID=3722&ref=Feed
Finding temperatures during heat exchange among tanks<img src="https://www.maplesoft.com/view.aspx?si=3722//applications/images/app_image_blank_lg.jpg" alt="Heat exchange in a series of tanks" style="max-width: 25%;" align="left"/>Finding temperatures during heat exchange among tankshttps://www.maplesoft.com/applications/view.aspx?SID=3722&ref=FeedTue, 19 Jun 2001 00:00:00 ZMaplesoftMaplesoftTemperature sensor in a gas stream
https://www.maplesoft.com/applications/view.aspx?SID=3766&ref=Feed
This worksheet demonstrates the transient response of a temperature sensor in an air stream.<img src="https://www.maplesoft.com/view.aspx?si=3766//applications/images/app_image_blank_lg.jpg" alt="Temperature sensor in a gas stream" style="max-width: 25%;" align="left"/>This worksheet demonstrates the transient response of a temperature sensor in an air stream.https://www.maplesoft.com/applications/view.aspx?SID=3766&ref=FeedTue, 19 Jun 2001 00:00:00 ZMaplesoftMaplesoftHeat transfer through a multilayered wall
https://www.maplesoft.com/applications/view.aspx?SID=3763&ref=Feed
This worksheet demonstrates how Maple can be used in a problem of the heat transfer through a multilayer wall. The heat loss per unit area is found along with the layer temperatures. We plot the temperature distribution in the wall.
<img src="https://www.maplesoft.com/view.aspx?si=3763//applications/images/app_image_blank_lg.jpg" alt="Heat transfer through a multilayered wall" style="max-width: 25%;" align="left"/>This worksheet demonstrates how Maple can be used in a problem of the heat transfer through a multilayer wall. The heat loss per unit area is found along with the layer temperatures. We plot the temperature distribution in the wall.
https://www.maplesoft.com/applications/view.aspx?SID=3763&ref=FeedTue, 19 Jun 2001 00:00:00 ZMaplesoftMaplesoftModeling a Thermal System
https://www.maplesoft.com/applications/view.aspx?SID=3765&ref=Feed
This worksheet demonstrates a problem of heating a liquid. Producing chemicals almost always requires control of temperature of liquids contained in vessels. In a batch process a vessel would typically be filled with liquid, sealed and heated to a prescribed temperature. This Maple worksheet models and analyses such a system and calculates the time required for the liquid to reach the desired temperature<img src="https://www.maplesoft.com/view.aspx?si=3765/358.jpg" alt="Modeling a Thermal System" style="max-width: 25%;" align="left"/>This worksheet demonstrates a problem of heating a liquid. Producing chemicals almost always requires control of temperature of liquids contained in vessels. In a batch process a vessel would typically be filled with liquid, sealed and heated to a prescribed temperature. This Maple worksheet models and analyses such a system and calculates the time required for the liquid to reach the desired temperaturehttps://www.maplesoft.com/applications/view.aspx?SID=3765&ref=FeedTue, 19 Jun 2001 00:00:00 ZMaplesoftMaplesoftHeating a liquid with a time-dependent heat source
https://www.maplesoft.com/applications/view.aspx?SID=3764&ref=Feed
This worksheet analyses a thin-walled vessel containing water, which is heated by a time-dependent heat source. When the heater is turned off, the water temperature should reach no more than 40°C.
<img src="https://www.maplesoft.com/view.aspx?si=3764//applications/images/app_image_blank_lg.jpg" alt="Heating a liquid with a time-dependent heat source" style="max-width: 25%;" align="left"/>This worksheet analyses a thin-walled vessel containing water, which is heated by a time-dependent heat source. When the heater is turned off, the water temperature should reach no more than 40°C.
https://www.maplesoft.com/applications/view.aspx?SID=3764&ref=FeedTue, 19 Jun 2001 00:00:00 ZMaplesoftMaplesoftFourier Method for Heat Equation
https://www.maplesoft.com/applications/view.aspx?SID=3682&ref=Feed
In this session we find solutions of boundary value problems for heat equation using Fourier method.<img src="https://www.maplesoft.com/view.aspx?si=3682//applications/images/app_image_blank_lg.jpg" alt="Fourier Method for Heat Equation" style="max-width: 25%;" align="left"/>In this session we find solutions of boundary value problems for heat equation using Fourier method.https://www.maplesoft.com/applications/view.aspx?SID=3682&ref=FeedTue, 19 Jun 2001 00:00:00 ZAleksas DomarkasAleksas Domarkas