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Content introduction
Heat conduction is an important physical phenomenon that describes how heat is transferred through matter. In many engineering and scientific applications, we need to model and analyze heat conduction to better understand and control thermodynamic processes. Two-dimensional transient heat conduction is a common heat conduction model that allows us to study temperature distributions as a function of time and space.
The basic assumption of the two-dimensional transient heat conduction model is that the temperature distribution inside a substance is two-dimensional and changes with time. This assumption holds true for many practical applications such as heat treatment, welding, and electronic device cooling. In these applications, we need to understand the temperature distribution inside the substance in order to better control the thermodynamic processes and thereby achieve better performance and efficiency.
The mathematical description of the two-dimensional transient heat conduction model is a partial differential equation, which describes the law of temperature distribution changing with time and space. This equation is often difficult to solve analytically, so numerical methods are needed to solve it. Commonly used numerical methods include finite element method, finite difference method and boundary element method. These methods can effectively solve two-dimensional transient heat conduction models and give accurate numerical solutions to the temperature distribution inside the material.
Two-dimensional transient heat conduction models are widely used. For example, during heat treatment, we need to model and analyze the temperature distribution inside the material in order to determine the optimal heat treatment parameters. During the welding process, we need to understand the temperature distribution in the welding area in order to control the welding quality. In terms of electronic device heat dissipation, we need to model and analyze the temperature distribution inside the electronic device in order to design a better heat dissipation system.
This Matlab submission provides a 2D transient heat conduction simulation tool for analyzing heat transfer in various materials of varying lengths and widths. It enables users to visualize temperature distribution over time and space and create temperature versus time graphs for specified locations.
feature
– 2D Transient Heat Conduction Simulation: Simulate 2D heat conduction in different materials of different lengths and widths
– Numerical stability: ensure stability checks and provide ulerts
– Temperature distribution visualization: Generate temperature distribution maps over time and space.
– Temperature vs. Time Graph: Create a graph of the temperature at a specific location over time.
– Customization: Easily configure material properties and simulation parameters.
– User-friendly interface: Intuitive GUI for seamless interaction.
In summary, two-dimensional transient heat conduction is a very important physical phenomenon that allows us to study temperature distributions that change with time and space. By solving the two-dimensional transient heat conduction model numerically, we can obtain an accurate numerical solution to the temperature distribution inside the material. These numerical solutions are useful for many engineering and scientific applications, such as heat treatment, welding, and electronic device cooling. Therefore, two-dimensional transient heat conduction is a very important research area worthy of further exploration and research.
Part of the code
function varargout = TwoDtransGUI(varargin)</code><code>% TWODTRANSGUI MATLAB code for TwoDtransGUI.fig</code><code>% TWODTRANSGUI, by itself, creates a new TWODTRANSGUI or raises the existing</code> <code>% singleton*.</code><code>%</code><code>% H = TWODTRANSGUI returns the handle to a new TWODTRANSGUI or the handle to</code><code>% the existing singleton*. </code><code>%</code><code>% TWODTRANSGUI('CALLBACK',hObject,eventData,handles,...) calls the local</code><code>% function named CALLBACK in TWODTRANSGUI.M with the given input arguments.</code><code>%</code><code>% TWODTRANSGUI('Property','Value',...) creates a new TWODTRANSGUI or raises the</code><code> % existing singleton*. Starting from the left, property value pairs are</code><code>% applied to the GUI before TwoDtransGUI_OpeningFcn gets called. An</code><code>% unrecognized property name or invalid value makes property application</code><code>% stop. All inputs are passed to TwoDtransGUI_OpeningFcn via varargin.</code><code>%</code><code>% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one</code><code>% instance to run (singleton)".</code><code>%</code><code>% See also: GUIDE, GUIDATA, GUIHANDLES</code><code>% Edit the above text to modify the response to help TwoDtransGUI</code><code>% Last Modified by GUIDE v2.5 17-Apr-2016 02:20:13</code><code>% Begin initialization code - DO NOT EDIT</code><code>gui_Singleton = 1;</code><code>gui_State = struct('gui_Name', mfilename, ...</code><code> 'gui_Singleton', gui_Singleton, ...</code><code> 'gui_OpeningFcn', @TwoDtransGUI_OpeningFcn, ...</code><code> 'gui_OutputFcn', @TwoDtransGUI_OutputFcn, ...</code><code> 'gui_LayoutFcn', [] , ...</code> <code> 'gui_Callback', []);</code><code>if nargin & amp; & amp; ischar(varargin{1})</code><code> gui_State.gui_Callback = str2func(varargin{1} );</code><code>end</code><code>?</code><code>if nargout</code><code> [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{: });</code><code>else</code><code> gui_mainfcn(gui_State, varargin{:});</code><code>end</code><code>% End initialization code - DO NOT EDIT</code><code>?</code><code>% --- Executes just before TwoDtransGUI is made visible.</code><code>function TwoDtransGUI_OpeningFcn(hObject, eventdata, handles, varargin)</code> <code>% This function has no output args, see OutputFcn.</code><code>% hObject handle to figure</code><code>% eventdata reserved - to be defined in a future version of MATLAB</code> <code>% handles structure with handles and user data (see GUIDATA)</code><code>% varargin command line arguments to TwoDtransGUI (see VARARGIN)</code><code>% Choose default command line output for TwoDtransGUI</code> code><code>handles.output = hObject;</code><code>% Update handles structure</code><code>guidata(hObject, handles);</code><code>% UIWAIT makes TwoDtransGUI wait for user response (see UIRESUME)</code><code>% uiwait(handles.figure1);</code><code>?</code><code>% --- Outputs from this function are returned to the command line. </code><code>function varargout = TwoDtransGUI_OutputFcn(hObject, eventdata, handles) </code><code>% varargout cell array for returning output args (see VARARGOUT);</code><code>% hObject handle to figure </code><code>% eventdata reserved - to be defined in a future version of MATLAB</code><code>% handles structure with handles and user data (see GUIDATA)</code><code>% Get default command line output from handles structure</code><code>varargout{1} = handles.output;</code><code>?</code><code>?</code><code>function handles = getpara(handles )</code><code>listStrings = get(handles.listbox1,'String');</code><code>domaintype = listStrings{get(handles.listbox1,'Value')};</code><code>switch domaintype</code><code> case 'Aluminum'</code><code> handles.data.alfa = 8.635e-5;</code><code> case 'Gold'</code><code> handles.data.alfa = 1.22e-4;</code><code> case 'Copper'</code><code> handles.data.alfa = 1.12e-4;</code><code> case 'Brass '</code><code> handles.data.alfa = 3.412e-5;</code><code> case 'Steel (0.5% C)'</code><code> handles.data.alfa = 1.474e -5;</code><code> case 'Steel (1.0% C)'</code><code> handles.data.alfa = 1.72e-5;</code><code> case 'Iron'</code> code><code> handles.data.alfa = 2.034e-5;</code><code> case 'Lead'</code><code> handles.data.alfa = 2.343e-5;</code><code> case 'Magnesium'</code><code> handles.data.alfa = 9.7e-5;</code><code>end</code><code>set(handles.mstxt,'String',. ..</code><code> sprintf('Material Property \
Thermal Diffusivity of Selected Material \
\
%g (m2/sec)',handles.data.alfa));</code><code>?</code><code>handles.data.plottime = str2double(get(handles.plottime,'String'));</code><code>?</code><code>%GEOMETRY INPUTS%</code><code>handles.data.lengthx = str2double(get(handles.lengthx,'String'));</code><code>handles.data.lengthy = str2double(get(handles.lengthy,'String'));</code><code>handles.data.chkx = str2double(get(handles.chkx,'String'));</code><code>handles.data.chky = str2double(get(handles.chky,'String' ));</code><code>handles.data.nodex = str2double(get(handles.nodex,'String'));</code><code>handles.data.nodey = handles.data.nodex;</code><code>?</code><code>handles.data.dx = handles.data.lengthx/(handles.data.nodex-1);</code><code>handles.data.dy = handles .data.lengthy/(handles.data.nodey-1);</code><code>handles.data.chkndx = round(handles.data.chkx/handles.data.dx);</code><code> handles.data.chkndy = round(handles.data.chky/handles.data.dy);</code><code>set(handles.gitxt,'String',...</code><code> sprintf( 'Geometry \
DX= %g (m)\
DY= %g (m)\
\
Monitoring Position\
(x,y)= %g,%g',...</code><code> handles .data.dx,handles.data.dy,handles.data.chkndx,handles.data.chkndy));</code><code>%TEMPERATURE INPUTS%</code><code>handles.data.temp_initial = str2double (get(handles.tini,'String'));</code><code>handles.data.temp_left_final = str2double(get(handles.tlf,'String'));</code><code>handles.data .temp_right_final = str2double(get(handles.tlr,'String'));</code><code>handles.data.temp_top_final = str2double(get(handles.tbt,'String'));</code><code>handles.data.temp_bottom_final = str2double(get(handles.ttp,'String'));</code><code>% TO CHECK MIN AND MAX TEMP FOR COLORBAR %</code><code>handles.data.ctvec = [ handles.data.temp_initial handles.data.temp_left_final ...</code><code> handles.data.temp_right_final handles.data.temp_top_final handles.data.temp_bottom_final];</code><code>handles.data. ctmax = max(handles.data.ctvec);</code><code>handles.data.ctmin = min(handles.data.ctvec);</code><code>% --------- ----------------------------------</code><code>%TIME INPUTS in sec%</code><code> handles.data.dt = str2double(get(handles.tstp,'String'));</code><code>handles.data.total_time = str2double(get(handles.ttime,'String'));</code><code>handles.data.convergance_criteria = str2double(get(handles.errv,'String'));</code><code>handles.data.plotupdatetime = handles.data.dt*handles.data.plottime;</code><code>set(handles.uptxt,'String',...</code><code> sprintf('Plot Update Time \
%g sec',handles.data.plotupdatetime));</code><code>% INITIALIZATION %</code><code>handles.data.fxx = (handles.data.alfa*handles.data.dt)/(handles.data.dx*handles.data.dx);</code> code><code>handles.data.fyy = (handles.data.alfa*handles.data.dt)/(handles.data.dy*handles.data.dy);</code><code>handles.data. fxy = handles.data.fxx + handles.data.fyy;</code><code>set(handles.ttxt,'String',...</code><code> sprintf('Numerical Stability \
Current \
Fourier Number = %g',handles.data.fxy));</code><code>handles.data.ldx = 0:handles.data.dx:handles.data.lengthx;</code><code>handles. data.ldy = 0:handles.data.dx:handles.data.lengthy;</code><code>% NUMERICAL SSTABILITY CHECK %</code><code>if handles.data.fxy > 0.5 </code><code> warnlg({'Numerical Stability Condition: ',</code><code> sprintf('FOURIER NUMBER \
((DIFFUSIVITY*TIME STEP)*(1/(DX^2)) + (1/(DX^ 2)))\
fo < 0.5'),</code><code> sprintf('Current Fourier Number = %g',handles.data.fxy)},'WARNING !!');</code><code>end</code><code>%MONITORING POSITION CHECK %</code><code>if handles.data.chkndx > handles.data.nodex || handles.data.chkndy > handles.data.nodey</code><code> warnlg({'Monitoring Position Out of Bounds ',</code><code> sprintf('Place (X,Y) distance of monitoring position within the limits of specified dimensions\
0 < x < %g\ n 0 < y < %g'...</code><code> ,handles.data.lengthx,handles.data.lengthy)},'WARNING !!');</code><code>end</code><code>?</code><code>?</code><code>?</code><code>?</code><code>?</code><code>function twodconduction(handles) </code><code>set(handles.stop,'UserData',0);</code><code>alfa = handles.data.alfa;</code><code>plottime = handles.data.plottime; </code><code>lengthx = handles.data.lengthx;</code><code>lengthy = handles.data.lengthy;</code><code>chkx = handles.data.chkx;</code><code>chky = handles.data.chky;</code><code>nodex = handles.data.nodex;</code><code>nodey = handles.data.nodey;</code><code>dx = handles .data.dx;</code><code>dy = handles.data.dy;</code><code>chkndx = handles.data.chkndx;</code><code>chkndy = handles.data.chkndy; </code><code>?</code><code>temp_initial = handles.data.temp_initial;</code><code>temp_left_final = handles.data.temp_left_final;</code><code>temp_right_final = handles.data .temp_right_final;</code><code>temp_top_final = handles.data.temp_top_final;</code><code>temp_bottom_final = handles.data.temp_bottom_final;</code><code>?</code><code>?</code><code>ctvec = handles.data.ctvec;</code><code>ctmax = handles.data.ctmax;</code><code>ctmin = handles.data.ctmin;</code><code>?</code><code>dt = handles.data.dt;</code><code>total_time = handles.data.total_time;</code><code>convergance_criteria = handles.data.convergance_criteria;</code><code>plotupdatetime = handles.data.plotupdatetime;</code><code>?</code><code>fxx = handles.data.fxx;</code><code>fyy = handles.data.fyy; </code><code>fxy = handles.data.fxy;</code><code>?</code><code>ldx = handles.data.ldx;</code><code>ldy = handles.data .ldy;</code><code>?</code><code>% INITIALIZING MATRIX %</code><code>for i=1:nodex;</code><code> for j=1:nodey</code><code> t(i,j) = temp_initial;</code><code> end</code><code>end </code><code>% CALCULATION OF TEMPETATURE PROFILE %</code><code>nt = 0;</code><code>k = 1;</code><code>shp = 0;</code><code>x = 0:dx:lengthx;</code><code>y = 0:dy:lengthy;</code><code>[x,y] = meshgrid(x,y);</code><code>while nt < total_time</code><code> if get(handles. stop,'UserData') == 1</code><code> break</code><code> end</code><code> if nt == 0</code><code> T = t;</code> code><code> T(1,:) = temp_top_final;</code><code> T(nodey,:) = temp_bottom_final;</code><code> T(:,1) = temp_left_final;</code> <code> T(:,nodex) = temp_right_final;</code><code> end</code><code> for i = 2:nodey-1</code><code> for j = 2:nodex-1 </code><code> T(i,j) = (t(i,j)*(1-(2*fxy))) + ((fxx*(t(i-1,j) + t(i + 1,j)) + (fyy*(t(i,j-1) + t(i,j + 1)))));</code><code> if i == chkndy</code><code> if j == chkndx</code><code> Tchk(k) = T(i,j);</code><code> end</code><code> end</code><code> end </code><code> end</code><code> err = max(max((abs(T-t))));</code><code> tmax = max(max(T));</code><code> if err < convergance_criteria</code><code> % MESSAGE BOX %</code><code> msgbox({'STEADY STATE ACHIEVED',</code><code> sprintf('Time for steady state = %g',nt)},'RESULT');</code><code> k = k + 1;</code><code> break</code><code> end</code><code> if shp == plottime</code><code> contourf(handles.contour,x,y,T,20);</code><code> caxis(handles.contour,[ctmin,ctmax]);</code> <code> colorbar('peer',handles.contour);</code><code> xlabel(handles.contour,'DISTANCE x (m)'),</code><code> ylabel(handles.contour,' DISTANCE Y (m)'),</code><code> axis(handles.contour,'equal','tight'),</code><code> title(handles.contour,...</code> <code> sprintf('TEMPERATURE PROFILE FOR TIME (SEC) = %g\
Error = %g\
Check Node Temp = %g',nt,err,Tchk(k)));</code><code> time = 1:k;</code><code> time = time.*dt;</code><code> plot(handles.axes2,time,Tchk)</code><code> grid on;</code><code> xlabel(handles.axes2,'TIME (sec)');</code><code> ylabel(handles.axes2,'TEMPERATURE (Celcius)');</code><code> title(handles.axes2, ...</code><code> sprintf('TEMPERATURE PROFILE FOR NODE AT DISTANCE (m)\
= %g,%g',chkndx,chkndy));</code><code> pause(0.01)</code><code> shp = 0;</code><code> end</code><code> t = T;</code><code> nt = nt + dt;</code><code> k = k + 1;</code><code> shp = shp + 1;</code><code>end</code><code>contourf(handles.contour,x,y,T,20);</code> code><code>caxis(handles.contour,[ctmin,ctmax]);</code><code>colorbar('peer',handles.contour),</code><code>xlabel(handles.contour,' DISTANCE x (m)'),</code><code>ylabel(handles.contour,'DISTANCE Y (m)'),</code><code>axis(handles.contour,'equal','tight' ),</code><code>title(handles.contour,...</code><code> sprintf('TEMPERATURE PROFILE FOR TIME (SEC) = %g\
Error = %g\
Check Node Temp = %g ',nt,err,Tchk(k-1)));</code><code>?</code><code>% --- Executes on button press in pushbutton1.</code><code>function pushbutton1_Callback (hObject, eventdata, handles)</code><code>% hObject handle to pushbutton1 (see GCBO)</code><code>% eventdata reserved - to be defined in a future version of MATLAB</code><code> ?
Operation results
References
[1] Zhang Sen. Fluid-solid-thermal multi-physics coupling analysis and structural optimization of automotive ventilated disc brakes [D]. Shandong University of Science and Technology, 2017.
[2] Zhang Sen. Fluid-solid-thermal multi-physics coupling analysis and structural optimization of automotive ventilated disc brakes [D]. Shandong University of Science and Technology [2023-11-01].
[3] Zhou Fenglin, Yuan Xiaohan, Yu Jianghong, et al. Transient heat conduction analysis of heat dissipation structure based on time domain boundary element method [J]. Journal of Hunan University of Technology, 2022(003):036.