adding all files

CFMvsRPM.csv

@@ -0,0 +1,2 @@
+0.0, 0.0
+2500.0, 100.0

Chip_temperature_control.prj

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+<?xml version="1.0" encoding="UTF-8"?>
+<MATLABProject xmlns="http://www.mathworks.com/MATLABProjectFile" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" version="1.0"/>

README.md

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+# Modeling Systems Governed by PDEs in Simulink
+
+The system being modeled in this Simulink example is a variable-speed fan cooling a CPU which,
+depending on the model and the operating point, can generate variable amount of heat. Each component
+of the system is modeled using techniques that  easily incorporate empirical data and technical
+specifications, and all assumptions are stated in the following discussion regarding levels of
+modeling fidelity.
+
+The plant in this system is the thermal dynamics of the heat-generating CPU and the heat-dissipating heat
+sink. These dynamics are modeled by a finite element formulation of the heat equation on the 3D
+geometry. The geometry, meshing, and discretization in this example are done using MATLAB’s PDE
+Toolbox. The finite element matrices generated can then be solved using Simulink’s Descriptor State Space
+block. For more information on time-dependent finite-element formulations, please see the MathWorks
+documentation.
+The dominant mode of heat transfer in this scenario is due to convection. A convective boundary condition
+is constructed in Simulink for the ducted airflow where forced convection coefficients 
+would be applied on the internal fin surfaces, and free convection coefficients are applied on the
+external facing surfaces of the system.
+The heat generation of the CPU can be controlled by the user in this formulation as an input Wattage. This
+demonstration provides examples of different loadings of the processor that lead to different heat
+generation, thus lending itself useful for design decisions in determining if a certain heat sink is suitable
+for a specific CPU.
+
+# Running the Model
+
+This example is organized inside a Simulink Project. Once the project is opened, running “top_script” will
+load all the variables needed for the simulation and then execute a parameter sweep. Six scenarios are
+included in this example. The six simulations run varied levels of heat generation from the CPU as input
+to the plant subsystem.
+Upon completion of the parameter sweep, the Simulation Manager will launch. The socket temperature
+signal is logged using Simulink Data Inspector and can be visualized by selecting the simulations of
+interest and clicking the “Show Results” option. The Signal Editor block, data logging, and adding
+additional systems to the model can all provide opportunities to expand on physical system modeling
+and the engineering design decision process that goes along with it.
+Note, there is an included “debug” plant model that uses the same parameters, but a simpler geometry
+with fewer mesh nodes to reduce the number of degrees of freedom. This is useful for debugging the
+model and iterating on other parameters in the system outside of the plant. This feature can be utilized
+by commenting out “heat_sink_defs” in the “top_script” and replacing it with “heat_sink_defs_DEBUG”.
+
+
+Contents:
+
+Chip_temperature_control.prj: the Simulink project file
+
+CFMvsRPM.csv, RPMvsV.csv: data tables used to construct 1D lookup tables in Simulink model, can be digitized data from plots
+
+fan.slx, heat_sink.slx, sensor.slx: subsystem files referenced by the top level model
+
+fan_defs.m, heat_sink_defs.m, heat_sink_defs_DEBUG.m, sensor_defs.m: MATLAB scripts to initialize subsystem parameters
+
+top_system.slx: top level model of complete control systems
+
+HeatInput.mat: MAT file that defines Signal Editor scenarios
+
+top_script.m: MATLAB script that calls subsytem scripts, runs simulations with different input scenarios, and opens Simulation Manager
+
+Demo_description.pdf: Detailed write-up of model development and design decisions made

RPMvsV.csv

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+0.0, 0.0
+12.0, 2500.0

SECURITY.md

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+# Reporting Security Vulnerabilities 
+
+If you believe you have discovered a security vulnerability, please report it to 
+[[email protected]](mailto:[email protected]). Please see 
+[MathWorks Vulnerability Disclosure Policy for Security Researchers](https://www.mathworks.com/company/aboutus/policies_statements/vulnerability-disclosure-policy.html) 
+for additional information.  

fan_defs.m

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+%% cooling fan
+tauFan = 0.2192;
+%% load digitized data
+V2RPM = readmatrix('RPMvsV.csv');
+RPM2CFM = readmatrix('CFMvsRPM.csv');
+%% conversion constants
+CFM2CMS = 0.00047194745; % CFM to cubic meters per second

heat_sink_defs.m

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+%% heat sink
+heatsink = createpde('thermal','transient');
+%% heat sink+chip geometry
+W = 27*10^-3; % heat sink width
+H = 17.5*10^-3; % heat sink fin height
+t = 2*10^-3; % approximated fin thickness
+nFin = 8; % number of fins on heat sink
+dFin = (W - (nFin*t))/(nFin-1); % space between fins, calculated from approximations
+R1 = [3 4 0.0 W W 0.0 0.0 0.0 t t]'; % base plate
+R2 = [3 4 (0*(t+dFin)) (0*(t+dFin))+t (0*(t+dFin))+t (0*(t+dFin)) t t H-t H-t]'; % fin1
+R3 = [3 4 (1*(t+dFin)) (1*(t+dFin))+t (1*(t+dFin))+t (1*(t+dFin)) t t H-t H-t]'; % fin2
+R4 = [3 4 (2*(t+dFin)) (2*(t+dFin))+t (2*(t+dFin))+t (2*(t+dFin)) t t H-t H-t]'; % fin3
+R5 = [3 4 (3*(t+dFin)) (3*(t+dFin))+t (3*(t+dFin))+t (3*(t+dFin)) t t H-t H-t]'; % fin4
+R6 = [3 4 (4*(t+dFin)) (4*(t+dFin))+t (4*(t+dFin))+t (4*(t+dFin)) t t H-t H-t]'; % fin5
+R7 = [3 4 (5*(t+dFin)) (5*(t+dFin))+t (5*(t+dFin))+t (5*(t+dFin)) t t H-t H-t]'; % fin6
+R8 = [3 4 (6*(t+dFin)) (6*(t+dFin))+t (6*(t+dFin))+t (6*(t+dFin)) t t H-t H-t]'; % fin7
+R9 = [3 4 (7*(t+dFin)) (7*(t+dFin))+t (7*(t+dFin))+t (7*(t+dFin)) t t H-t H-t]'; % fin8
+R0 = [3 4 0.001 0.026 0.026 0.001 0.0 0.0 -t -t]'; % chip
+gd = [R1 R2 R3 R4 R5 R6 R7 R8 R9 R0]; % Geometry description matrix
+sf = 'R1+R2+R3+R4+R5+R6+R7+R8+R9+R0'; % Set formula for adding 2D shapes
+ns = (char('R1','R2','R3','R4','R5','R6','R7','R8','R9','R0'))'; % Name-space matrix
+g  = decsg(gd,sf,ns); % Decompose constructive solid 2-D geometry into minimal regions
+pg = geometryFromEdges(heatsink,g); % apply geometry to model
+gm = extrude(pg,W); % generate 3D geometry from 2D cross section
+heatsink.Geometry = gm; % replace model geometry with 3D
+m = generateMesh(heatsink,'Hmin',t,'Hgrad',1.9); % try to min(nDoF)
+%% visualize geometry to get i/o #s
+% figure; pdegplot(heatsink,'FaceLabels','on') % visualize geometry
+% figure; pdegplot(heatsink,'CellLabels','on')
+% figure; pdemesh(m); axis equal
+% figure; pdemesh(m,'NodeLabels','on') % visualize mesh
+CPUcell = 1;
+freeBCfaces = 1:20; % faces that do not see flow, using free convection
+forcedBCfaces = 21:heatsink.Geometry.NumFaces; % faces aligned with flow
+outID = findNodes(m,'nearest',[0.026 -t/2 W/2]'); % middle of yz side of casing
+%% internal properties
+k = 210; % W*m^-1*K^-1
+rho = 2710; % kg/m^3
+Cp = 900; % J*kg^-1*K^-1
+mtl = thermalProperties(heatsink,'ThermalConductivity',k, ...
+                                 'MassDensity',rho, ...
+                                 'SpecificHeat',Cp); % aluminum alloy 6060 T6
+chipHeat = 1; % Watts
+chipW = 25e-3; % m
+chipL = W; % m
+chipH = t; % m
+heatPerVol = chipHeat/(chipL*chipW*chipH); % W/m^3
+heatSource = internalHeatSource(heatsink,heatPerVol,'Cell',CPUcell);
+IC = 294; % Kelvin
+thermIC = thermalIC(heatsink,IC); % T = IC everywhere @T=0
+%% boundary conditions
+Tinf = IC; % ambient temperature, Kelvin
+xSectionA = (2*W)*(2*H); % duct cross-sectional area, m^2
+rho = 1.225; % kg/m^3
+h_free = 9.0;
+h_forced = [ ...
+0.0, h_free; ...
+3.0, 50.0; ...
+]; % [V_linear, convective heat transfer coeff]
+h_forced(:,1) = h_forced(:,1) * xSectionA * rho; % convert to h = f(mdot)
+freeBC = thermalBC(heatsink,'Face',freeBCfaces,'HeatFlux',1); % used as convective BC
+forcedBC = thermalBC(heatsink,'Face',forcedBCfaces,'HeatFlux',1); % used as convective BC
+%% FE formulation
+femat = assembleFEMatrices(heatsink);
+K = femat.K; % is the stiffness matrix, the integral of the c coefficient against the basis functions
+M = femat.M; % is the mass matrix, the integral of the m or d coefficient against the basis functions.
+A = femat.A; % is the integral of the a coefficient against the basis functions.
+F = femat.F; % is the integral of the f coefficient against the basis functions.
+Q = femat.Q; % is the integral of the q boundary condition against the basis functions.
+G = femat.G; % is the integral of the g boundary condition against the basis functions.
+H = femat.H; % The H and R matrices come directly from the Dirichlet conditions and the mesh.
+R = femat.R; % %
+%% construct SL vectors
+nDoF = size(K,1);
+freeBCnodes = findNodes(m,'Region','Face',freeBCfaces);
+unitFreeBC = zeros(nDoF,1);
+unitFreeBC(freeBCnodes) = 1;
+normalizedFreeBC = zeros(nDoF,1);
+normalizedFreeBC(freeBCnodes) = G(freeBCnodes);
+forcedBCnodes = findNodes(m,'Region','Face',forcedBCfaces);
+unitForcedBC = zeros(nDoF,1);
+unitForcedBC(forcedBCnodes) = 1;
+normalizedForcedBC = zeros(nDoF,1);
+normalizedForcedBC(forcedBCnodes) = G(forcedBCnodes);
+x0 = ones(nDoF,1)*IC;
+unitCPUHeat = full(F);

heat_sink_defs_DEBUG.m

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+%% heat sink
+heatsink = createpde('thermal','transient');
+%% heat sink+chip geometry
+L = 15e-3; % m
+R1 = [3 4 0.0 L L 0.0 0.0 0.0  L  L]'; % top cube
+R2 = [3 4 0.0 L L 0.0 0.0 0.0 -L -L]'; % bot cube
+gd = [R1 R2];
+sf = 'R1+R2';
+ns = (char('R1','R2'))';
+
+g  = decsg(gd,sf,ns); % Decompose constructive solid 2-D geometry into minimal regions
+pg = geometryFromEdges(heatsink,g); % apply geometry to model
+gm = extrude(pg,L); % generate 3D geometry from 2D cross section
+heatsink.Geometry = gm; % replace model geometry with 3D
+m = generateMesh(heatsink,'Hmin',5e-3); % try to min(nDoF)
+%% visualize geometry to get i/o #s
+% figure; pdegplot(heatsink,'FaceLabels','on') % visualize geometry
+% figure; pdegplot(heatsink,'CellLabels','on')
+% figure; pdemesh(m); axis equal
+% figure; pdemesh(m,'NodeLabels','on') % visualize mesh
+CPUcell = 1;
+freeBCfaces = [1 3 6 8 10]; % faces that do not see flow, using free convection
+forcedBCfaces = [2 4 5 9 11]; % faces aligned with flow
+outID = 7; % top right corner
+%% internal properties
+k = 210; % W*m^-1*K^-1
+rho = 2710; % kg/m^3
+Cp = 900; % J*kg^-1*K^-1
+mtl = thermalProperties(heatsink,'ThermalConductivity',k, ...
+                                 'MassDensity',rho, ...
+                                 'SpecificHeat',Cp); % aluminum alloy 6060 T6
+chipHeat = 1; % Watts
+chipW = L; % m
+chipL = L; % m
+chipH = L; % m
+heatPerVol = chipHeat/(chipL*chipW*chipH); % W/m^3
+heatSource = internalHeatSource(heatsink,heatPerVol,'Cell',CPUcell);
+IC = 294; % Kelvin
+thermIC = thermalIC(heatsink,IC); % T = IC everywhere @T=0
+%% boundary conditions
+Tinf = IC; % ambient temperature, Kelvin
+xSectionA = (2*L)^2; % duct cross-sectional area, m^2
+rho = 1.225; % kg/m^3
+h_free = 9.0;
+h_forced = [ ...
+0.0, h_free; ...
+3.0, 50.0; ...
+]; % [V_induced, convective heat transfer coeff]
+h_forced(:,1) = h_forced(:,1) * xSectionA * rho; % convert to h = f(mdot)
+freeBC = thermalBC(heatsink,'Face',freeBCfaces,'HeatFlux',1); % used as convective BC
+forcedBC = thermalBC(heatsink,'Face',forcedBCfaces,'HeatFlux',1); % used as convective BC
+%% FE formulation
+femat = assembleFEMatrices(heatsink);
+K = femat.K; % is the stiffness matrix, the integral of the c coefficient against the basis functions
+M = femat.M; % is the mass matrix, the integral of the m or d coefficient against the basis functions.
+A = femat.A; % is the integral of the a coefficient against the basis functions.
+F = femat.F; % is the integral of the f coefficient against the basis functions.
+Q = femat.Q; % is the integral of the q boundary condition against the basis functions.
+G = femat.G; % is the integral of the g boundary condition against the basis functions.
+H = femat.H; % The H and R matrices come directly from the Dirichlet conditions and the mesh.
+R = femat.R; % %
+%% construct SL vectors
+nDoF = size(K,1);
+freeBCnodes = findNodes(m,'Region','Face',freeBCfaces);
+unitFreeBC = zeros(nDoF,1);
+unitFreeBC(freeBCnodes) = 1;
+normalizedFreeBC = zeros(nDoF,1);
+normalizedFreeBC(freeBCnodes) = G(freeBCnodes);
+forcedBCnodes = findNodes(m,'Region','Face',forcedBCfaces);
+unitForcedBC = zeros(nDoF,1);
+unitForcedBC(forcedBCnodes) = 1;
+normalizedForcedBC = zeros(nDoF,1);
+normalizedForcedBC(forcedBCnodes) = G(forcedBCnodes);
+x0 = ones(nDoF,1)*IC;
+unitCPUHeat = full(F);

license.txt

@@ -0,0 +1,7 @@
+Copyright (c) 2020, The MathWorks, Inc.
+All rights reserved.
+Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
+3. In all cases, the software is, and all modifications and derivatives of the software shall be, licensed to you solely for use in conjunction with MathWorks products and service offerings. 
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

resources/project/KAXfQgCar2Yb8zOxgvf9hdmLP1E/Eif_Q8-eW8o4x10LdM3S54txieId.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<Info Type="Basic" Visible="1" Icon="" File="top_script.m" Name="Run simulations" />

resources/project/KAXfQgCar2Yb8zOxgvf9hdmLP1E/Eif_Q8-eW8o4x10LdM3S54txieIp.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4d.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/2kj09UetkV_lru3gvSPXnY6-nM4p.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/KKyDJtbdIBOlaeHmIZd5VX6vqx8d.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/KKyDJtbdIBOlaeHmIZd5VX6vqx8p.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/QWNDYJD5mGW1bWYvPx9DtKnxzw4d.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/QWNDYJD5mGW1bWYvPx9DtKnxzw4p.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/R1RggVhA72agIvELiuhWPRS8F0Id.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/R1RggVhA72agIvELiuhWPRS8F0Ip.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/aEHSZBIY-yve10yGis12Zr5DLZod.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/aEHSZBIY-yve10yGis12Zr5DLZop.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/j4xwF_j8iFTVayUMfxLgMnTbencd.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/j4xwF_j8iFTVayUMfxLgMnTbencp.xml

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resources/project/NjSPEMsIuLUyIpr2u1Js5bVPsOs/r8LR4nLmg9ai3oHrW1r_-KocQzkd.xml

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resources/project/Project.xml

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resources/project/fjRQtWiSIy7hIlj-Kmk87M7s21k/NjSPEMsIuLUyIpr2u1Js5bVPsOsp.xml

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resources/project/qaw0eS1zuuY1ar9TdPn1GMfrjbQ/0Xjd6EFmVVFAUJrpsHqsPFwdsO4p.xml

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+<?xml version='1.0' encoding='UTF-8'?>
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resources/project/qaw0eS1zuuY1ar9TdPn1GMfrjbQ/1E_ORUYoUaqXIBh7b3Z8QCO6F5Ep.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<Info location="RPMvsV.csv" type="File" />

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