Hi expert,
I have two effiency maps, one for engine and one for generator and their operating curves like below. I want to obtain the maximum efficiency data, that is when speed from 0~600 rad/s, torque = the smaller value of maximum torque of genrator and engine(torque limitation), and effiency = efficiency of genrator * efficiency of engine.
The data file sizes are:
w_eg_row: 1*9 genrator speed
T_eg_col: 15*1 generator torque
eta_EG_map: 9*15 efficiency of generator
T_EG_max: 9*1 maximum torque versus speed
w_ce_row: 1*15 genrator speed
T_ce_col: 1*16 generator torque
eta_ce_map: 16*15 efficiency of generator
T_ce_max: 1*15 maximum torque versus speed

I don’t know how to process the data to get the result. Could you please provide the code?Hi expert,
I have two effiency maps, one for engine and one for generator and their operating curves like below. I want to obtain the maximum efficiency data, that is when speed from 0~600 rad/s, torque = the smaller value of maximum torque of genrator and engine(torque limitation), and effiency = efficiency of genrator * efficiency of engine.
The data file sizes are:
w_eg_row: 1*9 genrator speed
T_eg_col: 15*1 generator torque
eta_EG_map: 9*15 efficiency of generator
T_EG_max: 9*1 maximum torque versus speed
w_ce_row: 1*15 genrator speed
T_ce_col: 1*16 generator torque
eta_ce_map: 16*15 efficiency of generator
T_ce_max: 1*15 maximum torque versus speed

I don’t know how to process the data to get the result. Could you please provide the code? Hi expert,
I have two effiency maps, one for engine and one for generator and their operating curves like below. I want to obtain the maximum efficiency data, that is when speed from 0~600 rad/s, torque = the smaller value of maximum torque of genrator and engine(torque limitation), and effiency = efficiency of genrator * efficiency of engine.
The data file sizes are:
w_eg_row: 1*9 genrator speed
T_eg_col: 15*1 generator torque
eta_EG_map: 9*15 efficiency of generator
T_EG_max: 9*1 maximum torque versus speed
w_ce_row: 1*15 genrator speed
T_ce_col: 1*16 generator torque
eta_ce_map: 16*15 efficiency of generator
T_ce_max: 1*15 maximum torque versus speed

I don’t know how to process the data to get the result. Could you please provide the code? efficiency map MATLAB Answers — New Questions

​

I have a 10000×400 matrix, plotphys, I want to turn into a table and add variable names to. I understand that can be done easily with the array2table function. However adding 400 headings is a lot; luckily I want the headings uniform in that they would be labeled
‘phys state at tstep 1’, ‘phys state at tstep 2’, …, ‘phys state at tstep 400’
Is there a way I can basically automate the creation of the headings?
I tried this
head = join("phys state at tstep " + [1:1:400]);

phystable = array2table(plotphys, ‘VariableNames’, {head});
but that did not workI have a 10000×400 matrix, plotphys, I want to turn into a table and add variable names to. I understand that can be done easily with the array2table function. However adding 400 headings is a lot; luckily I want the headings uniform in that they would be labeled
‘phys state at tstep 1’, ‘phys state at tstep 2’, …, ‘phys state at tstep 400’
Is there a way I can basically automate the creation of the headings?
I tried this
head = join("phys state at tstep " + [1:1:400]);

phystable = array2table(plotphys, ‘VariableNames’, {head});
but that did not work I have a 10000×400 matrix, plotphys, I want to turn into a table and add variable names to. I understand that can be done easily with the array2table function. However adding 400 headings is a lot; luckily I want the headings uniform in that they would be labeled
‘phys state at tstep 1’, ‘phys state at tstep 2’, …, ‘phys state at tstep 400’
Is there a way I can basically automate the creation of the headings?
I tried this
head = join("phys state at tstep " + [1:1:400]);

phystable = array2table(plotphys, ‘VariableNames’, {head});
but that did not work table, headings MATLAB Answers — New Questions

​

I have a periodic signal with 6 peaks and 6 valleys. I am able to find all 6 peaks and all 6 valleys using the code below:
% plot periodic signal
plot(angle,signal)
hold on;
% fit to avoid noisy oscillations and find 6 global peaks
f = fit(angle,signal,’sin9′);
yfitted = feval(f,angle);
plot(angle,yfitted,’r’)
% find peaks and corresponding angles
[ypk0,idx0] = findpeaks(yfitted);
peaks = signal(idx0);
max_angles = angle(idx0);
% invert fitted signal to find 6 global valleys and corresponding angles
yfittedinv = max(yfitted) – yfitted;
[ypk,idx] = findpeaks(yfittedinv);
valleys = signal(idx);
min_angles = angle(idx);
Furthermore, I am able to find the global minimum (i.e., the lowest valley) using this line:
% find the global minimum
minangle = min_angles(valleys == min(valleys));
Both the arrays "max_angles" and "min_angles" have 6 elements. The question is how to reduce the number of elements in the array "min_angles" from 6 to 3, where I will have only the global minimum and the 2 non-neighbor valleys. The attached pic should help. I am able to find the green circle, but I also need to find the 2 red circles. Note that the global valley (green circle) is not always in the middle. It can be the first element of the array "min_angles", or it can be the last one. In the picture below, it’s number 4.I have a periodic signal with 6 peaks and 6 valleys. I am able to find all 6 peaks and all 6 valleys using the code below:
% plot periodic signal
plot(angle,signal)
hold on;
% fit to avoid noisy oscillations and find 6 global peaks
f = fit(angle,signal,’sin9′);
yfitted = feval(f,angle);
plot(angle,yfitted,’r’)
% find peaks and corresponding angles
[ypk0,idx0] = findpeaks(yfitted);
peaks = signal(idx0);
max_angles = angle(idx0);
% invert fitted signal to find 6 global valleys and corresponding angles
yfittedinv = max(yfitted) – yfitted;
[ypk,idx] = findpeaks(yfittedinv);
valleys = signal(idx);
min_angles = angle(idx);
Furthermore, I am able to find the global minimum (i.e., the lowest valley) using this line:
% find the global minimum
minangle = min_angles(valleys == min(valleys));
Both the arrays "max_angles" and "min_angles" have 6 elements. The question is how to reduce the number of elements in the array "min_angles" from 6 to 3, where I will have only the global minimum and the 2 non-neighbor valleys. The attached pic should help. I am able to find the green circle, but I also need to find the 2 red circles. Note that the global valley (green circle) is not always in the middle. It can be the first element of the array "min_angles", or it can be the last one. In the picture below, it’s number 4. I have a periodic signal with 6 peaks and 6 valleys. I am able to find all 6 peaks and all 6 valleys using the code below:
% plot periodic signal
plot(angle,signal)
hold on;
% fit to avoid noisy oscillations and find 6 global peaks
f = fit(angle,signal,’sin9′);
yfitted = feval(f,angle);
plot(angle,yfitted,’r’)
% find peaks and corresponding angles
[ypk0,idx0] = findpeaks(yfitted);
peaks = signal(idx0);
max_angles = angle(idx0);
% invert fitted signal to find 6 global valleys and corresponding angles
yfittedinv = max(yfitted) – yfitted;
[ypk,idx] = findpeaks(yfittedinv);
valleys = signal(idx);
min_angles = angle(idx);
Furthermore, I am able to find the global minimum (i.e., the lowest valley) using this line:
% find the global minimum
minangle = min_angles(valleys == min(valleys));
Both the arrays "max_angles" and "min_angles" have 6 elements. The question is how to reduce the number of elements in the array "min_angles" from 6 to 3, where I will have only the global minimum and the 2 non-neighbor valleys. The attached pic should help. I am able to find the green circle, but I also need to find the 2 red circles. Note that the global valley (green circle) is not always in the middle. It can be the first element of the array "min_angles", or it can be the last one. In the picture below, it’s number 4. findpeaks, findvalleys MATLAB Answers — New Questions

​

fluid=’cyclopentane’
T1=348.15;
P1=refpropm(‘P’,’T’,T1,’Q’,1,’fluid’);fluid=’cyclopentane’
T1=348.15;
P1=refpropm(‘P’,’T’,T1,’Q’,1,’fluid’); fluid=’cyclopentane’
T1=348.15;
P1=refpropm(‘P’,’T’,T1,’Q’,1,’fluid’); refprop, [setup error 101] MATLAB Answers — New Questions

​

I am running fgetl in a loop similar to the code below. When profiling the code, I noticed that fgetl(fid) takes the most time to execute compared to the rest of the code. After checking the fgetl documentation, I found the following note in the documentation:
fgetl is intended for use with files that contain newline characters. Given a file with no newline characters, fgetl may take a long time to execute.
However, the documentation does not provide a solution for files without newline characters. Since my file lacks newline characters, what would be the best alternative to fgetl?
fid = fopen(FileName);

while ischar(tline) %loops over 1e5 times
% read new line
tic
tline = fgetl(fid);
toc
% Do stuff with tline

endI am running fgetl in a loop similar to the code below. When profiling the code, I noticed that fgetl(fid) takes the most time to execute compared to the rest of the code. After checking the fgetl documentation, I found the following note in the documentation:
fgetl is intended for use with files that contain newline characters. Given a file with no newline characters, fgetl may take a long time to execute.
However, the documentation does not provide a solution for files without newline characters. Since my file lacks newline characters, what would be the best alternative to fgetl?
fid = fopen(FileName);

while ischar(tline) %loops over 1e5 times
% read new line
tic
tline = fgetl(fid);
toc
% Do stuff with tline

end I am running fgetl in a loop similar to the code below. When profiling the code, I noticed that fgetl(fid) takes the most time to execute compared to the rest of the code. After checking the fgetl documentation, I found the following note in the documentation:
fgetl is intended for use with files that contain newline characters. Given a file with no newline characters, fgetl may take a long time to execute.
However, the documentation does not provide a solution for files without newline characters. Since my file lacks newline characters, what would be the best alternative to fgetl?
fid = fopen(FileName);

while ischar(tline) %loops over 1e5 times
% read new line
tic
tline = fgetl(fid);
toc
% Do stuff with tline

end fgetl, fgets, loop MATLAB Answers — New Questions

​

I am trying to model and visualize two permanent magnet spheres using the below code snippet:

function twoMagnets_femodel_demo()
clc; clear; close all;
% ——————————-
% 1) Define geometry parameters
% ——————————-
% Let’s assume "1/2-inch magnets" => diameter = 0.5 inch => radius = 0.25 in
% 1 inch ~ 0.0254 m, so 0.25 in ~ 0.00635 m
R_sphere = 0.00635; % [m]

% Bounding box of ~5 cm each side
boxDim = 0.05; % [m]
% ——————————-
% 2) Build geometry parts
% ——————————-
% (a) Air region: bounding box
boxGm = multicuboid(boxDim, boxDim, boxDim);
% (b) Sphere #1
sphere1Gm = multisphere(R_sphere);
% (c) Sphere #2
sphere2Gm = multisphere(R_sphere);
% Translate spheres so that they’re centered in the box, side-by-side
% Let the box corners go from (0,0,0) to (0.05,0.05,0.05), so center ~ (0.025,0.025,0.025)
centerBox = [0.025, 0.025, 0.025];
offset1 = centerBox + [-R_sphere, 0, 0]; % shift left in x
offset2 = centerBox + [ R_sphere, 0, 0]; % shift right in x
sphere1Gm = translate(sphere1Gm, offset1);
sphere2Gm = translate(sphere2Gm, offset2);
% ——————————-
% 3) Combine geometries
% ——————————-
% addCell(…) is the new PDE Toolbox function that
% keeps each shape as a separate "cell" in the final geometry.
gm = addCell(boxGm, sphere1Gm);
gm = addCell(gm, sphere2Gm);
% Visualize & label
figure;
pdegplot(gm, FaceAlpha=0.2, CellLabels="on");
title("Bounding Box + Two Spheres");
axis equal
% At this point we should see "Cell #1 = bounding box, #2 = first sphere, #3 = second sphere"
% ——————————-
% 4) Create femodel for magnetostatics
% ——————————-
model = femodel(AnalysisType="magnetostatic", Geometry=gm);
% Specify vacuum permeability in SI (H/m)
model.VacuumPermeability = 4*pi*1e-7; % ~ 1.2566370614e-6
% ——————————-
% 5) Set material properties
% ——————————-
% We have 3 cells:
% 1 => bounding box (air)
% 2 => sphere #1
% 3 => sphere #2
%
% For air and the spheres, assume relative permeability ~ 1
model.MaterialProperties(1) = materialProperties(RelativePermeability=1);
model.MaterialProperties(2) = materialProperties(RelativePermeability=1);
model.MaterialProperties(3) = materialProperties(RelativePermeability=1);
% ——————————-
% 6) Assign magnetization
% ——————————-
% In new PDE Toolbox, you can set magnetization on the "CellLoad" for a subdomain (cell).
% Suppose sphere #1 is magnetized in +z; sphere #2 in -z.
% For a typical neodymium magnet, you might set M ~ 1e5 or 1e6 A/m.
M1 = [0; 0; 1e5];
M2 = [0; 0;-1e5];
model.CellLoad(2) = cellLoad(Magnetization=M1); % sphere1
model.CellLoad(3) = cellLoad(Magnetization=M2); % sphere2
% ——————————-
% 7) Boundary conditions
% ——————————-
% Typically, you’d set a "zero" magnetic potential (A = 0) on the outer faces
% of the bounding box to approximate an open boundary.
% Identify the face IDs of the bounding box:
% pdegplot(gm, FaceAlpha=0.1, CellLabels="on", FaceLabels="on")
% The bounding box typically has 6 faces with IDs [1..6].
% So we do:
model.FaceBC(1:6) = faceBC(MagneticPotential=[0;0;0]);
% (If you find different face numbering, adjust accordingly.)
% ——————————-
% 8) Generate mesh
% ——————————-
% We can specify "Hcell" to refine the mesh in certain cells, e.g. the magnets,
% or keep it uniform. For example, refine in cells 2 & 3 (the spheres):
internalCells = [2 3];
model = generateMesh(model, Hcell={internalCells, R_sphere/3});
% ——————————-
% 9) Solve
% ——————————-
R = solve(model);
% R is a MagnetostaticResults object with fields:
% R.MagneticPotential, R.MagneticField, R.MagneticFluxDensity, R.Mesh, etc.
% ——————————-
% 10) Postprocessing
% ——————————-
% Extract Bx, By, Bz at the mesh nodes
Bx = R.MagneticFluxDensity.Bx;
By = R.MagneticFluxDensity.By;
Bz = R.MagneticFluxDensity.Bz;
Bmag = sqrt(Bx.^2 + By.^2 + Bz.^2);
% Simple 3D plot of |B|
figure;
pdeplot3D(R.Mesh, ColorMapData=Bmag);
title("|B| flux density magnitude");
colorbar;
% Optionally, a vector plot:
figure;
pdeplot3D(R.Mesh, FlowData=[Bx By Bz]);
title("Magnetic Field Vectors");
end
While logically complete, the above code doesn’t work. The current error I am struggling with is that addCell() only works inside the original geometry. And throws the following error here:
Error using pde.DiscreteGeometry/addCell
Added cells must be located strictly inside a single cell of the original geometry.
Error in
TwoMagnets (line 38)
gm = addCell(boxGm, sphere1Gm);
^^^^^^^^^^^^^^^^^^^^^^^^^

Is there an example script on how to simulate permanent magnets using the latest PDE Toolbox?I am trying to model and visualize two permanent magnet spheres using the below code snippet:

function twoMagnets_femodel_demo()
clc; clear; close all;
% ——————————-
% 1) Define geometry parameters
% ——————————-
% Let’s assume "1/2-inch magnets" => diameter = 0.5 inch => radius = 0.25 in
% 1 inch ~ 0.0254 m, so 0.25 in ~ 0.00635 m
R_sphere = 0.00635; % [m]

% Bounding box of ~5 cm each side
boxDim = 0.05; % [m]
% ——————————-
% 2) Build geometry parts
% ——————————-
% (a) Air region: bounding box
boxGm = multicuboid(boxDim, boxDim, boxDim);
% (b) Sphere #1
sphere1Gm = multisphere(R_sphere);
% (c) Sphere #2
sphere2Gm = multisphere(R_sphere);
% Translate spheres so that they’re centered in the box, side-by-side
% Let the box corners go from (0,0,0) to (0.05,0.05,0.05), so center ~ (0.025,0.025,0.025)
centerBox = [0.025, 0.025, 0.025];
offset1 = centerBox + [-R_sphere, 0, 0]; % shift left in x
offset2 = centerBox + [ R_sphere, 0, 0]; % shift right in x
sphere1Gm = translate(sphere1Gm, offset1);
sphere2Gm = translate(sphere2Gm, offset2);
% ——————————-
% 3) Combine geometries
% ——————————-
% addCell(…) is the new PDE Toolbox function that
% keeps each shape as a separate "cell" in the final geometry.
gm = addCell(boxGm, sphere1Gm);
gm = addCell(gm, sphere2Gm);
% Visualize & label
figure;
pdegplot(gm, FaceAlpha=0.2, CellLabels="on");
title("Bounding Box + Two Spheres");
axis equal
% At this point we should see "Cell #1 = bounding box, #2 = first sphere, #3 = second sphere"
% ——————————-
% 4) Create femodel for magnetostatics
% ——————————-
model = femodel(AnalysisType="magnetostatic", Geometry=gm);
% Specify vacuum permeability in SI (H/m)
model.VacuumPermeability = 4*pi*1e-7; % ~ 1.2566370614e-6
% ——————————-
% 5) Set material properties
% ——————————-
% We have 3 cells:
% 1 => bounding box (air)
% 2 => sphere #1
% 3 => sphere #2
%
% For air and the spheres, assume relative permeability ~ 1
model.MaterialProperties(1) = materialProperties(RelativePermeability=1);
model.MaterialProperties(2) = materialProperties(RelativePermeability=1);
model.MaterialProperties(3) = materialProperties(RelativePermeability=1);
% ——————————-
% 6) Assign magnetization
% ——————————-
% In new PDE Toolbox, you can set magnetization on the "CellLoad" for a subdomain (cell).
% Suppose sphere #1 is magnetized in +z; sphere #2 in -z.
% For a typical neodymium magnet, you might set M ~ 1e5 or 1e6 A/m.
M1 = [0; 0; 1e5];
M2 = [0; 0;-1e5];
model.CellLoad(2) = cellLoad(Magnetization=M1); % sphere1
model.CellLoad(3) = cellLoad(Magnetization=M2); % sphere2
% ——————————-
% 7) Boundary conditions
% ——————————-
% Typically, you’d set a "zero" magnetic potential (A = 0) on the outer faces
% of the bounding box to approximate an open boundary.
% Identify the face IDs of the bounding box:
% pdegplot(gm, FaceAlpha=0.1, CellLabels="on", FaceLabels="on")
% The bounding box typically has 6 faces with IDs [1..6].
% So we do:
model.FaceBC(1:6) = faceBC(MagneticPotential=[0;0;0]);
% (If you find different face numbering, adjust accordingly.)
% ——————————-
% 8) Generate mesh
% ——————————-
% We can specify "Hcell" to refine the mesh in certain cells, e.g. the magnets,
% or keep it uniform. For example, refine in cells 2 & 3 (the spheres):
internalCells = [2 3];
model = generateMesh(model, Hcell={internalCells, R_sphere/3});
% ——————————-
% 9) Solve
% ——————————-
R = solve(model);
% R is a MagnetostaticResults object with fields:
% R.MagneticPotential, R.MagneticField, R.MagneticFluxDensity, R.Mesh, etc.
% ——————————-
% 10) Postprocessing
% ——————————-
% Extract Bx, By, Bz at the mesh nodes
Bx = R.MagneticFluxDensity.Bx;
By = R.MagneticFluxDensity.By;
Bz = R.MagneticFluxDensity.Bz;
Bmag = sqrt(Bx.^2 + By.^2 + Bz.^2);
% Simple 3D plot of |B|
figure;
pdeplot3D(R.Mesh, ColorMapData=Bmag);
title("|B| flux density magnitude");
colorbar;
% Optionally, a vector plot:
figure;
pdeplot3D(R.Mesh, FlowData=[Bx By Bz]);
title("Magnetic Field Vectors");
end
While logically complete, the above code doesn’t work. The current error I am struggling with is that addCell() only works inside the original geometry. And throws the following error here:
Error using pde.DiscreteGeometry/addCell
Added cells must be located strictly inside a single cell of the original geometry.
Error in
TwoMagnets (line 38)
gm = addCell(boxGm, sphere1Gm);
^^^^^^^^^^^^^^^^^^^^^^^^^

Is there an example script on how to simulate permanent magnets using the latest PDE Toolbox? I am trying to model and visualize two permanent magnet spheres using the below code snippet:

function twoMagnets_femodel_demo()
clc; clear; close all;
% ——————————-
% 1) Define geometry parameters
% ——————————-
% Let’s assume "1/2-inch magnets" => diameter = 0.5 inch => radius = 0.25 in
% 1 inch ~ 0.0254 m, so 0.25 in ~ 0.00635 m
R_sphere = 0.00635; % [m]

% Bounding box of ~5 cm each side
boxDim = 0.05; % [m]
% ——————————-
% 2) Build geometry parts
% ——————————-
% (a) Air region: bounding box
boxGm = multicuboid(boxDim, boxDim, boxDim);
% (b) Sphere #1
sphere1Gm = multisphere(R_sphere);
% (c) Sphere #2
sphere2Gm = multisphere(R_sphere);
% Translate spheres so that they’re centered in the box, side-by-side
% Let the box corners go from (0,0,0) to (0.05,0.05,0.05), so center ~ (0.025,0.025,0.025)
centerBox = [0.025, 0.025, 0.025];
offset1 = centerBox + [-R_sphere, 0, 0]; % shift left in x
offset2 = centerBox + [ R_sphere, 0, 0]; % shift right in x
sphere1Gm = translate(sphere1Gm, offset1);
sphere2Gm = translate(sphere2Gm, offset2);
% ——————————-
% 3) Combine geometries
% ——————————-
% addCell(…) is the new PDE Toolbox function that
% keeps each shape as a separate "cell" in the final geometry.
gm = addCell(boxGm, sphere1Gm);
gm = addCell(gm, sphere2Gm);
% Visualize & label
figure;
pdegplot(gm, FaceAlpha=0.2, CellLabels="on");
title("Bounding Box + Two Spheres");
axis equal
% At this point we should see "Cell #1 = bounding box, #2 = first sphere, #3 = second sphere"
% ——————————-
% 4) Create femodel for magnetostatics
% ——————————-
model = femodel(AnalysisType="magnetostatic", Geometry=gm);
% Specify vacuum permeability in SI (H/m)
model.VacuumPermeability = 4*pi*1e-7; % ~ 1.2566370614e-6
% ——————————-
% 5) Set material properties
% ——————————-
% We have 3 cells:
% 1 => bounding box (air)
% 2 => sphere #1
% 3 => sphere #2
%
% For air and the spheres, assume relative permeability ~ 1
model.MaterialProperties(1) = materialProperties(RelativePermeability=1);
model.MaterialProperties(2) = materialProperties(RelativePermeability=1);
model.MaterialProperties(3) = materialProperties(RelativePermeability=1);
% ——————————-
% 6) Assign magnetization
% ——————————-
% In new PDE Toolbox, you can set magnetization on the "CellLoad" for a subdomain (cell).
% Suppose sphere #1 is magnetized in +z; sphere #2 in -z.
% For a typical neodymium magnet, you might set M ~ 1e5 or 1e6 A/m.
M1 = [0; 0; 1e5];
M2 = [0; 0;-1e5];
model.CellLoad(2) = cellLoad(Magnetization=M1); % sphere1
model.CellLoad(3) = cellLoad(Magnetization=M2); % sphere2
% ——————————-
% 7) Boundary conditions
% ——————————-
% Typically, you’d set a "zero" magnetic potential (A = 0) on the outer faces
% of the bounding box to approximate an open boundary.
% Identify the face IDs of the bounding box:
% pdegplot(gm, FaceAlpha=0.1, CellLabels="on", FaceLabels="on")
% The bounding box typically has 6 faces with IDs [1..6].
% So we do:
model.FaceBC(1:6) = faceBC(MagneticPotential=[0;0;0]);
% (If you find different face numbering, adjust accordingly.)
% ——————————-
% 8) Generate mesh
% ——————————-
% We can specify "Hcell" to refine the mesh in certain cells, e.g. the magnets,
% or keep it uniform. For example, refine in cells 2 & 3 (the spheres):
internalCells = [2 3];
model = generateMesh(model, Hcell={internalCells, R_sphere/3});
% ——————————-
% 9) Solve
% ——————————-
R = solve(model);
% R is a MagnetostaticResults object with fields:
% R.MagneticPotential, R.MagneticField, R.MagneticFluxDensity, R.Mesh, etc.
% ——————————-
% 10) Postprocessing
% ——————————-
% Extract Bx, By, Bz at the mesh nodes
Bx = R.MagneticFluxDensity.Bx;
By = R.MagneticFluxDensity.By;
Bz = R.MagneticFluxDensity.Bz;
Bmag = sqrt(Bx.^2 + By.^2 + Bz.^2);
% Simple 3D plot of |B|
figure;
pdeplot3D(R.Mesh, ColorMapData=Bmag);
title("|B| flux density magnitude");
colorbar;
% Optionally, a vector plot:
figure;
pdeplot3D(R.Mesh, FlowData=[Bx By Bz]);
title("Magnetic Field Vectors");
end
While logically complete, the above code doesn’t work. The current error I am struggling with is that addCell() only works inside the original geometry. And throws the following error here:
Error using pde.DiscreteGeometry/addCell
Added cells must be located strictly inside a single cell of the original geometry.
Error in
TwoMagnets (line 38)
gm = addCell(boxGm, sphere1Gm);
^^^^^^^^^^^^^^^^^^^^^^^^^

Is there an example script on how to simulate permanent magnets using the latest PDE Toolbox? pde, matlab code, mesh MATLAB Answers — New Questions

​

Hi,
I want to extract RC values from HPPC test, and I found a good example on MathWorks:Characterize Battery Cell for Electric Vehicles, However I can find batt_BatteryCellCharacterization function, is there anything I need to do?Hi,
I want to extract RC values from HPPC test, and I found a good example on MathWorks:Characterize Battery Cell for Electric Vehicles, However I can find batt_BatteryCellCharacterization function, is there anything I need to do? Hi,
I want to extract RC values from HPPC test, and I found a good example on MathWorks:Characterize Battery Cell for Electric Vehicles, However I can find batt_BatteryCellCharacterization function, is there anything I need to do? battery, modelling MATLAB Answers — New Questions

​

I do a lot of script and tool development for Matlab/Simulink. This involves supporting multiple versions of Matlab, usually from R2016a+ (previously it was R2011b+). This means that I have almost a dozen different versions of Matlab installed on my computer. When one of my tools/scripts encounters a bug in a version of Matlab, or the Matlab/Simulink behaviour differs between versions, I need to be able to pinpoint which version the bug occurred in or the behaviour changed in. I usually can’t find the bugs listed on the Bug Reports support page, especially when the bugs are already fixed in later versions. Likewise, when the behaviour changes I check if it is noted in the Release Notes, but these are very high-level descriptions and I usually can’t find it mentioned.
Given that the aforementioned pages are not reliable, I usually need to figure out which version of Matlab has the bug fix or behaviour change. I typically follow this process:
I create a script to replicate the bug automatically (if possible).
One by one I open each version of Matlab, execute the script, and make note of when the bug occurs. Sometimes I have to download and install additional Matlab versions.
Then I develop a workaround for the bug or behaviour change by having the script check which version it is running on, and then perform extra steps to fix the buggy behavior or accommodate for inconsistent behaviours between the versions.
My questions is: Is it possible run a script on multiple versions of Matlab in order to make this process a little easier?I do a lot of script and tool development for Matlab/Simulink. This involves supporting multiple versions of Matlab, usually from R2016a+ (previously it was R2011b+). This means that I have almost a dozen different versions of Matlab installed on my computer. When one of my tools/scripts encounters a bug in a version of Matlab, or the Matlab/Simulink behaviour differs between versions, I need to be able to pinpoint which version the bug occurred in or the behaviour changed in. I usually can’t find the bugs listed on the Bug Reports support page, especially when the bugs are already fixed in later versions. Likewise, when the behaviour changes I check if it is noted in the Release Notes, but these are very high-level descriptions and I usually can’t find it mentioned.
Given that the aforementioned pages are not reliable, I usually need to figure out which version of Matlab has the bug fix or behaviour change. I typically follow this process:
I create a script to replicate the bug automatically (if possible).
One by one I open each version of Matlab, execute the script, and make note of when the bug occurs. Sometimes I have to download and install additional Matlab versions.
Then I develop a workaround for the bug or behaviour change by having the script check which version it is running on, and then perform extra steps to fix the buggy behavior or accommodate for inconsistent behaviours between the versions.
My questions is: Is it possible run a script on multiple versions of Matlab in order to make this process a little easier? I do a lot of script and tool development for Matlab/Simulink. This involves supporting multiple versions of Matlab, usually from R2016a+ (previously it was R2011b+). This means that I have almost a dozen different versions of Matlab installed on my computer. When one of my tools/scripts encounters a bug in a version of Matlab, or the Matlab/Simulink behaviour differs between versions, I need to be able to pinpoint which version the bug occurred in or the behaviour changed in. I usually can’t find the bugs listed on the Bug Reports support page, especially when the bugs are already fixed in later versions. Likewise, when the behaviour changes I check if it is noted in the Release Notes, but these are very high-level descriptions and I usually can’t find it mentioned.
Given that the aforementioned pages are not reliable, I usually need to figure out which version of Matlab has the bug fix or behaviour change. I typically follow this process:
I create a script to replicate the bug automatically (if possible).
One by one I open each version of Matlab, execute the script, and make note of when the bug occurs. Sometimes I have to download and install additional Matlab versions.
Then I develop a workaround for the bug or behaviour change by having the script check which version it is running on, and then perform extra steps to fix the buggy behavior or accommodate for inconsistent behaviours between the versions.
My questions is: Is it possible run a script on multiple versions of Matlab in order to make this process a little easier? version, bugs, release notes, bug reports MATLAB Answers — New Questions

​

Hi Matlabers,
I am trying to install the Rapbian imager for matlab, and while configuring my hardware in the process, i get the following error:
"cannot retrieve removable drives: ‘wmic’ is not recognized as an internal or external command, operable program or batch file"

I saw a question like this here before but the solution there wasn’t good for me.
I added the following to my Path
%SystemRoot%System32Wbem
but no good.
Please help!Hi Matlabers,
I am trying to install the Rapbian imager for matlab, and while configuring my hardware in the process, i get the following error:
"cannot retrieve removable drives: ‘wmic’ is not recognized as an internal or external command, operable program or batch file"

I saw a question like this here before but the solution there wasn’t good for me.
I added the following to my Path
%SystemRoot%System32Wbem
but no good.
Please help! Hi Matlabers,
I am trying to install the Rapbian imager for matlab, and while configuring my hardware in the process, i get the following error:
"cannot retrieve removable drives: ‘wmic’ is not recognized as an internal or external command, operable program or batch file"

I saw a question like this here before but the solution there wasn’t good for me.
I added the following to my Path
%SystemRoot%System32Wbem
but no good.
Please help! raspberry pi, system, path, packages, installation MATLAB Answers — New Questions

​

i have attached my matlb code for solving system of PDE ∂u/∂t=(∂^2 u)/〖∂η〗^2 +α (∂^3 u)/〖∂η〗^3 +δcφ+Grθ-Mu
∂θ/∂t=1/Pr (∂^2 θ)/〖∂η〗^2 +D_f (∂^2 φ)/〖∂η〗^2
∂φ/∂t=1/S_c (∂^2 φ)/〖∂η〗^2 +S_r (∂^2 θ)/〖∂η〗^2
when η→0
when η→0:u=sin⁡(wt),θ=1 ,φ=1
when η→∞:u→0,θ→0,φ→0
But,i’m confused how to set boundary conditions in this code. Also i want to set these skin friction and nusselt number expressions: C_f=-(∂u/∂η) at η=0
Nu〖Re〗_x^(-1)=-(∂θ/∂η) at η=0
in this code;
function yy= crank
n=105;
h=0.01;
m=0.1;
B=0; %B=0.0001;
Gr=2; %Gr=0.1=Delt. Gs=Dels
A=2; %A=alpha
Pr=5;

Gs=1; %3.5

Sc=1.5;
M=9; %M=30,12
Df=5;
Sr=10;
Ec=0.1; % 0.01-0.1(0-1)
t(1)=0;
s(1)=0;
for j=2:n
t(j)=t(j-1)+h;
end
for j=2:n
s(j)=s(j-1)+m;
end
k=1;
for j=1:n

aa(j,k)=exp(-0.15*Pr^2*t(j)*Ec^-0.1/Gr^0.1); % Guess M*Gr*Gs*S
bb(j,k)=exp(-t(j)*Sc/(Ec)^0.01*M); %bb(j,k)=exp(-Pr^2*t(j)/Ec);
cc(j,k)=exp(-Sc*2*t(j)/Ec^0.3);
end
a{1,k}=[1 0 0;0 1 0;0 0 1];
for j=2:n-1
a{j,k}=[-(1/h)-(1/h^2)-2*A-M Gr Gs;0 -(1/h)-(1/Pr*(h^2)) -Df/h^2;0 -Sr/h^2 -(1/h)-(1/Sc*h^2)];
end
a{n,k}=[1 0 0;0 1 0;0 0 1];
for j=2:n-1
b{j,k}=[(1/2*h^2)+(A/h^3) 0 0;0 1/2*Pr*h^2 Df/2*h^2;0 Sr/2*h^2 1/2*Sc*h^2]; % Lower diagonal entries
end
b{n,k}=[0 0 0;0 0 0;0 0 0];
c{1,k}=[0 0 0;0 0 0;0 0 0];
for j=2:n-1
c{j,k}=[(1/2*h^2)+(A/h^3) 0 0;0 1/2*Pr*h^2 Df/2*h^2;0 Sr/2*h^2 1/2*Sc*h^2];
end
r1(1,k)=0;
r2(1,k)=0;
r3(1,k)=0;
for j=2:n-1
r1(j,k)=-(exp(t(j))/h)-(1/2*h^2)*(1)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))-Gr*exp(-t(j))-Gs*exp(t(j))+M*exp(-t(j))-(A/2*h^3)*(-exp(-t(j+1))+2*exp(-t(j))-exp(-t(j-1)))…
+(aa(j,k)/h)-(1/2*h^2)*(1)*(aa(j+1,k)-2*aa(j,k)+aa(j-1,k))-(A/2*h^3)*( aa(j+1,k)^2-2*aa(j+1,k)*aa(j,k))-Gr*bb(j,k)-Gs*cc(j,k)+M*aa(j,k);

r2(j,k)=(exp((-t(j)))/h)-(1/2*Pr*h^2)*(exp(-t(j+1))-2* exp(-t(j))+exp(-t(j-1)))-Df*(1/2*h^2)*(exp(-t(j+1))-2* exp(-t(j))…
+exp(-t(j-1)))+(bb(j,k)/h)-(1/2*Pr*h^2)*(bb(j+1,k)-2*bb(j,k)+bb(j-1,k))-(Df/2*h^2)*(cc(j+1,k)-2*cc(j,k)+cc(j-1,k));

r3(j,k)=-(exp((-t(j)))/h)-(1/2*Sc*h^2)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))-(Sr/2*h^2)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))+ (cc(j,k)/h)…
-(1/2*Sc*h^2)*(cc(j+1,k)-2*cc(j,k)+cc(j-1,k))-(Sr/2*h^2)*(bb(j+1,k)-2*bb(j,k)+bb(j-1,k));

end
r1(n,k)= 0;
r2(n,k)=0;
r3(n,k)=0;
for j=1:n
rr{j,k}=[r1(j,k);r2(j,k);r3(j,k)];
end
gamma{1,k}=inv(a{1,k})*c{1,k};
for j=2:n-1
a{j,k}=a{j,k}-(b{j,k}*gamma{j-1,k});
gamma{j,k}=inv(a{j,k})*c{j,k};
end

y{1}=inv(a{1})*rr{1};
for j=2:n
y{j}=inv(a{j})*(rr{j}-b{j}*y{j-1});
end
x{n}=y{n};
for j=n-1:-1:1
x{j}=y{j}-(gamma{j})*x{j+1};
end
for j=n:-1:1
u(j,k)=x{j}(1,1);
z(j,k)=x{j}(2,1);
q(j,k)=x{j}(3,1);
end
for j=1:n
xx(j,k)= aa(j,k)+u(j,k);
yy(j,k)= bb(j,k)+z(j,k);
zz(j,k)= cc(j,k)+q(j,k);
end
for j=1:n-1
%U(j)=-((1+(1/B))*((xx(j+1)-xx(j))/h))
%U(j)=-((yy(j+1)-yy(j))/2*h)
end
%ee=meshgrid(xx);
%V=trapz(ee);
%eee=meshgrid(V);
%[XX,YY]=meshgrid(t,s);
%XXX=meshgrid(xx);
%surf(XX,YY,XXX)
%contour(eee)
figure(1)
plot(t,xx,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’-‘,’color’,’k’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘u’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on
figure(2)
plot(t,yy,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’-‘,’color’,’k’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘Theta(eta)’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on
figure(3)
plot(t,zz,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’–‘,’color’,’r’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘Phi(eta)’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold oni have attached my matlb code for solving system of PDE ∂u/∂t=(∂^2 u)/〖∂η〗^2 +α (∂^3 u)/〖∂η〗^3 +δcφ+Grθ-Mu
∂θ/∂t=1/Pr (∂^2 θ)/〖∂η〗^2 +D_f (∂^2 φ)/〖∂η〗^2
∂φ/∂t=1/S_c (∂^2 φ)/〖∂η〗^2 +S_r (∂^2 θ)/〖∂η〗^2
when η→0
when η→0:u=sin⁡(wt),θ=1 ,φ=1
when η→∞:u→0,θ→0,φ→0
But,i’m confused how to set boundary conditions in this code. Also i want to set these skin friction and nusselt number expressions: C_f=-(∂u/∂η) at η=0
Nu〖Re〗_x^(-1)=-(∂θ/∂η) at η=0
in this code;
function yy= crank
n=105;
h=0.01;
m=0.1;
B=0; %B=0.0001;
Gr=2; %Gr=0.1=Delt. Gs=Dels
A=2; %A=alpha
Pr=5;

Gs=1; %3.5

Sc=1.5;
M=9; %M=30,12
Df=5;
Sr=10;
Ec=0.1; % 0.01-0.1(0-1)
t(1)=0;
s(1)=0;
for j=2:n
t(j)=t(j-1)+h;
end
for j=2:n
s(j)=s(j-1)+m;
end
k=1;
for j=1:n

aa(j,k)=exp(-0.15*Pr^2*t(j)*Ec^-0.1/Gr^0.1); % Guess M*Gr*Gs*S
bb(j,k)=exp(-t(j)*Sc/(Ec)^0.01*M); %bb(j,k)=exp(-Pr^2*t(j)/Ec);
cc(j,k)=exp(-Sc*2*t(j)/Ec^0.3);
end
a{1,k}=[1 0 0;0 1 0;0 0 1];
for j=2:n-1
a{j,k}=[-(1/h)-(1/h^2)-2*A-M Gr Gs;0 -(1/h)-(1/Pr*(h^2)) -Df/h^2;0 -Sr/h^2 -(1/h)-(1/Sc*h^2)];
end
a{n,k}=[1 0 0;0 1 0;0 0 1];
for j=2:n-1
b{j,k}=[(1/2*h^2)+(A/h^3) 0 0;0 1/2*Pr*h^2 Df/2*h^2;0 Sr/2*h^2 1/2*Sc*h^2]; % Lower diagonal entries
end
b{n,k}=[0 0 0;0 0 0;0 0 0];
c{1,k}=[0 0 0;0 0 0;0 0 0];
for j=2:n-1
c{j,k}=[(1/2*h^2)+(A/h^3) 0 0;0 1/2*Pr*h^2 Df/2*h^2;0 Sr/2*h^2 1/2*Sc*h^2];
end
r1(1,k)=0;
r2(1,k)=0;
r3(1,k)=0;
for j=2:n-1
r1(j,k)=-(exp(t(j))/h)-(1/2*h^2)*(1)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))-Gr*exp(-t(j))-Gs*exp(t(j))+M*exp(-t(j))-(A/2*h^3)*(-exp(-t(j+1))+2*exp(-t(j))-exp(-t(j-1)))…
+(aa(j,k)/h)-(1/2*h^2)*(1)*(aa(j+1,k)-2*aa(j,k)+aa(j-1,k))-(A/2*h^3)*( aa(j+1,k)^2-2*aa(j+1,k)*aa(j,k))-Gr*bb(j,k)-Gs*cc(j,k)+M*aa(j,k);

r2(j,k)=(exp((-t(j)))/h)-(1/2*Pr*h^2)*(exp(-t(j+1))-2* exp(-t(j))+exp(-t(j-1)))-Df*(1/2*h^2)*(exp(-t(j+1))-2* exp(-t(j))…
+exp(-t(j-1)))+(bb(j,k)/h)-(1/2*Pr*h^2)*(bb(j+1,k)-2*bb(j,k)+bb(j-1,k))-(Df/2*h^2)*(cc(j+1,k)-2*cc(j,k)+cc(j-1,k));

r3(j,k)=-(exp((-t(j)))/h)-(1/2*Sc*h^2)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))-(Sr/2*h^2)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))+ (cc(j,k)/h)…
-(1/2*Sc*h^2)*(cc(j+1,k)-2*cc(j,k)+cc(j-1,k))-(Sr/2*h^2)*(bb(j+1,k)-2*bb(j,k)+bb(j-1,k));

end
r1(n,k)= 0;
r2(n,k)=0;
r3(n,k)=0;
for j=1:n
rr{j,k}=[r1(j,k);r2(j,k);r3(j,k)];
end
gamma{1,k}=inv(a{1,k})*c{1,k};
for j=2:n-1
a{j,k}=a{j,k}-(b{j,k}*gamma{j-1,k});
gamma{j,k}=inv(a{j,k})*c{j,k};
end

y{1}=inv(a{1})*rr{1};
for j=2:n
y{j}=inv(a{j})*(rr{j}-b{j}*y{j-1});
end
x{n}=y{n};
for j=n-1:-1:1
x{j}=y{j}-(gamma{j})*x{j+1};
end
for j=n:-1:1
u(j,k)=x{j}(1,1);
z(j,k)=x{j}(2,1);
q(j,k)=x{j}(3,1);
end
for j=1:n
xx(j,k)= aa(j,k)+u(j,k);
yy(j,k)= bb(j,k)+z(j,k);
zz(j,k)= cc(j,k)+q(j,k);
end
for j=1:n-1
%U(j)=-((1+(1/B))*((xx(j+1)-xx(j))/h))
%U(j)=-((yy(j+1)-yy(j))/2*h)
end
%ee=meshgrid(xx);
%V=trapz(ee);
%eee=meshgrid(V);
%[XX,YY]=meshgrid(t,s);
%XXX=meshgrid(xx);
%surf(XX,YY,XXX)
%contour(eee)
figure(1)
plot(t,xx,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’-‘,’color’,’k’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘u’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on
figure(2)
plot(t,yy,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’-‘,’color’,’k’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘Theta(eta)’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on
figure(3)
plot(t,zz,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’–‘,’color’,’r’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘Phi(eta)’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on i have attached my matlb code for solving system of PDE ∂u/∂t=(∂^2 u)/〖∂η〗^2 +α (∂^3 u)/〖∂η〗^3 +δcφ+Grθ-Mu
∂θ/∂t=1/Pr (∂^2 θ)/〖∂η〗^2 +D_f (∂^2 φ)/〖∂η〗^2
∂φ/∂t=1/S_c (∂^2 φ)/〖∂η〗^2 +S_r (∂^2 θ)/〖∂η〗^2
when η→0
when η→0:u=sin⁡(wt),θ=1 ,φ=1
when η→∞:u→0,θ→0,φ→0
But,i’m confused how to set boundary conditions in this code. Also i want to set these skin friction and nusselt number expressions: C_f=-(∂u/∂η) at η=0
Nu〖Re〗_x^(-1)=-(∂θ/∂η) at η=0
in this code;
function yy= crank
n=105;
h=0.01;
m=0.1;
B=0; %B=0.0001;
Gr=2; %Gr=0.1=Delt. Gs=Dels
A=2; %A=alpha
Pr=5;

Gs=1; %3.5

Sc=1.5;
M=9; %M=30,12
Df=5;
Sr=10;
Ec=0.1; % 0.01-0.1(0-1)
t(1)=0;
s(1)=0;
for j=2:n
t(j)=t(j-1)+h;
end
for j=2:n
s(j)=s(j-1)+m;
end
k=1;
for j=1:n

aa(j,k)=exp(-0.15*Pr^2*t(j)*Ec^-0.1/Gr^0.1); % Guess M*Gr*Gs*S
bb(j,k)=exp(-t(j)*Sc/(Ec)^0.01*M); %bb(j,k)=exp(-Pr^2*t(j)/Ec);
cc(j,k)=exp(-Sc*2*t(j)/Ec^0.3);
end
a{1,k}=[1 0 0;0 1 0;0 0 1];
for j=2:n-1
a{j,k}=[-(1/h)-(1/h^2)-2*A-M Gr Gs;0 -(1/h)-(1/Pr*(h^2)) -Df/h^2;0 -Sr/h^2 -(1/h)-(1/Sc*h^2)];
end
a{n,k}=[1 0 0;0 1 0;0 0 1];
for j=2:n-1
b{j,k}=[(1/2*h^2)+(A/h^3) 0 0;0 1/2*Pr*h^2 Df/2*h^2;0 Sr/2*h^2 1/2*Sc*h^2]; % Lower diagonal entries
end
b{n,k}=[0 0 0;0 0 0;0 0 0];
c{1,k}=[0 0 0;0 0 0;0 0 0];
for j=2:n-1
c{j,k}=[(1/2*h^2)+(A/h^3) 0 0;0 1/2*Pr*h^2 Df/2*h^2;0 Sr/2*h^2 1/2*Sc*h^2];
end
r1(1,k)=0;
r2(1,k)=0;
r3(1,k)=0;
for j=2:n-1
r1(j,k)=-(exp(t(j))/h)-(1/2*h^2)*(1)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))-Gr*exp(-t(j))-Gs*exp(t(j))+M*exp(-t(j))-(A/2*h^3)*(-exp(-t(j+1))+2*exp(-t(j))-exp(-t(j-1)))…
+(aa(j,k)/h)-(1/2*h^2)*(1)*(aa(j+1,k)-2*aa(j,k)+aa(j-1,k))-(A/2*h^3)*( aa(j+1,k)^2-2*aa(j+1,k)*aa(j,k))-Gr*bb(j,k)-Gs*cc(j,k)+M*aa(j,k);

r2(j,k)=(exp((-t(j)))/h)-(1/2*Pr*h^2)*(exp(-t(j+1))-2* exp(-t(j))+exp(-t(j-1)))-Df*(1/2*h^2)*(exp(-t(j+1))-2* exp(-t(j))…
+exp(-t(j-1)))+(bb(j,k)/h)-(1/2*Pr*h^2)*(bb(j+1,k)-2*bb(j,k)+bb(j-1,k))-(Df/2*h^2)*(cc(j+1,k)-2*cc(j,k)+cc(j-1,k));

r3(j,k)=-(exp((-t(j)))/h)-(1/2*Sc*h^2)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))-(Sr/2*h^2)*(exp(-t(j+1))-2*exp(-t(j))+exp(-t(j-1)))+ (cc(j,k)/h)…
-(1/2*Sc*h^2)*(cc(j+1,k)-2*cc(j,k)+cc(j-1,k))-(Sr/2*h^2)*(bb(j+1,k)-2*bb(j,k)+bb(j-1,k));

end
r1(n,k)= 0;
r2(n,k)=0;
r3(n,k)=0;
for j=1:n
rr{j,k}=[r1(j,k);r2(j,k);r3(j,k)];
end
gamma{1,k}=inv(a{1,k})*c{1,k};
for j=2:n-1
a{j,k}=a{j,k}-(b{j,k}*gamma{j-1,k});
gamma{j,k}=inv(a{j,k})*c{j,k};
end

y{1}=inv(a{1})*rr{1};
for j=2:n
y{j}=inv(a{j})*(rr{j}-b{j}*y{j-1});
end
x{n}=y{n};
for j=n-1:-1:1
x{j}=y{j}-(gamma{j})*x{j+1};
end
for j=n:-1:1
u(j,k)=x{j}(1,1);
z(j,k)=x{j}(2,1);
q(j,k)=x{j}(3,1);
end
for j=1:n
xx(j,k)= aa(j,k)+u(j,k);
yy(j,k)= bb(j,k)+z(j,k);
zz(j,k)= cc(j,k)+q(j,k);
end
for j=1:n-1
%U(j)=-((1+(1/B))*((xx(j+1)-xx(j))/h))
%U(j)=-((yy(j+1)-yy(j))/2*h)
end
%ee=meshgrid(xx);
%V=trapz(ee);
%eee=meshgrid(V);
%[XX,YY]=meshgrid(t,s);
%XXX=meshgrid(xx);
%surf(XX,YY,XXX)
%contour(eee)
figure(1)
plot(t,xx,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’-‘,’color’,’k’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘u’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on
figure(2)
plot(t,yy,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’-‘,’color’,’k’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘Theta(eta)’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on
figure(3)
plot(t,zz,’LineWidth’,2,’MarkerSize’,16,’linestyle’,’–‘,’color’,’r’)
xlabel(‘eta’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
ylabel(‘Phi(eta)’,’Interpreter’,’tex’,’FontSize’,16,’FontWeight’,’bold’);
grid on
hold on system of pde’s, crank nicloson method in matlab, skin friction and nusselt number MATLAB Answers — New Questions

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