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1-D Steady Heat conduction FDM

shivam choubey
shivam choubey

This document contains the analysis of two 1-D steady heat conduction problems using the Finite Difference Method (FDM). The first case considers a metal rod with a base temperature of 100属C and a tip temperature of 30属C. The second case considers the same rod but with the tip insulated, so the temperature gradient is calculated to the second last node. Both cases are solved for varying nodal discretizations and the temperature profiles along the rod length are plotted.

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www.engineeringwithsandeep.com| Student Assignment Assignment No. 07 1-D Steady Heat conduction FDM 14.04.2021 Shivam Choubey Student No: CFDB30321004
www.engineeringwithsandeep.com| Student Assignment Case1: T base =100 C and T tip = 30 C %% 1-D Steady Heat conduction FDM Code % 1-D steady heat conduction problem % metal rod which is 20 cm long %Case1: T base =100 C and T tip = 30 C clc clear all; L=20/100;% length convert into meter N=80;%N=10 ;N=20;N=40;N=50;N=80; dx=linspace(0,L,N); Tb=100; Tend=30; T=zeros(N,1);%Initialization T(1)=Tb;% base temp T(N)=Tend;%Tip temp
www.engineeringwithsandeep.com| Student Assignment k=100;% Correction loop for j=1:k for i=2:N-1 T(i)=(T(i+1)+T(i-1))/2; end T(N)=Tend;%Tip temp end plot(dx,T); hold on xlabel("Length (m)") ylabel("Temp") title("Length Vs Temp") legend("N=10","N=20","N=40","N=50","N=80") hold on
www.engineeringwithsandeep.com| Student Assignment Case 2: T base =100C and Tip is insulated %% 1-D Steady Heat conduction FDM Code % 1-D steady heat conduction problem % metal rod which is 20 cm long %Case1: T base =100 C and T tip = 0 C clc clear all; L=20/100;% length convert into meter N=100;%N=40 N=50 N=80 N=100 dx=linspace(0,L,N); Tb=100; Tend=0; T=zeros(N,1);%Initialization T(1)=Tb;% base temp T(N)=Tend;%Tip temp k=100;% Correction loop for j=1:k
www.engineeringwithsandeep.com| Student Assignment for i=2:N-1 T(i)=(T(i+1)+T(i-1))/2; end %T(N)=Tend;%Tip temp T(N)=T(N-1);%condition for insulated tip end plot(dx,T); hold on xlabel("Length (m)") ylabel("Temp") title("Length Vs Temp") legend("N=10","N=20","N=40","N=50","N=80","N=100") hold on

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1-D Steady Heat conduction FDM

  • 1. www.engineeringwithsandeep.com| Student Assignment Assignment No. 07 1-D Steady Heat conduction FDM 14.04.2021 Shivam Choubey Student No: CFDB30321004
  • 2. www.engineeringwithsandeep.com| Student Assignment Case1: T base =100 C and T tip = 30 C %% 1-D Steady Heat conduction FDM Code % 1-D steady heat conduction problem % metal rod which is 20 cm long %Case1: T base =100 C and T tip = 30 C clc clear all; L=20/100;% length convert into meter N=80;%N=10 ;N=20;N=40;N=50;N=80; dx=linspace(0,L,N); Tb=100; Tend=30; T=zeros(N,1);%Initialization T(1)=Tb;% base temp T(N)=Tend;%Tip temp
  • 3. www.engineeringwithsandeep.com| Student Assignment k=100;% Correction loop for j=1:k for i=2:N-1 T(i)=(T(i+1)+T(i-1))/2; end T(N)=Tend;%Tip temp end plot(dx,T); hold on xlabel("Length (m)") ylabel("Temp") title("Length Vs Temp") legend("N=10","N=20","N=40","N=50","N=80") hold on
  • 4. www.engineeringwithsandeep.com| Student Assignment Case 2: T base =100C and Tip is insulated %% 1-D Steady Heat conduction FDM Code % 1-D steady heat conduction problem % metal rod which is 20 cm long %Case1: T base =100 C and T tip = 0 C clc clear all; L=20/100;% length convert into meter N=100;%N=40 N=50 N=80 N=100 dx=linspace(0,L,N); Tb=100; Tend=0; T=zeros(N,1);%Initialization T(1)=Tb;% base temp T(N)=Tend;%Tip temp k=100;% Correction loop for j=1:k
  • 5. www.engineeringwithsandeep.com| Student Assignment for i=2:N-1 T(i)=(T(i+1)+T(i-1))/2; end %T(N)=Tend;%Tip temp T(N)=T(N-1);%condition for insulated tip end plot(dx,T); hold on xlabel("Length (m)") ylabel("Temp") title("Length Vs Temp") legend("N=10","N=20","N=40","N=50","N=80","N=100") hold on