M=1.4; %mach speed
l=1.68; %length , m
t=0.15 ; %thickness, m
dx=0.168; %delta x, m
dy=0.015; %delta y, m
dz=0.68668; %delta z, m
Ta=216.66; %free stream temperature, K
K=1.401; %specific heat ratio
pr=0.72178; %prandtl number
r=(pr)^(1/3); %recovery factor
Tstag=Ta*(1+((K-1)/2)*((M*(cosd(20)))^(2))); %stagnation temperature
Taw=Ta*(1+r*((K-1)/2)*M^(2)); %adiabatic wall temperaure
Ka=121.0 % Aluminum,Thermal Conductivity, W/m-k
Kt=6.7 %Titanium, Thermal Conductivity, W/m-k
Kc=30.758 %Carbon-carbon,Thermal Conductivity, W/m-k
%matrix 1x4 of each node
N_1=[ 0 21 0 0];
N_2=[ 0 30 21 0];
N_3=[ 0 44 30 0];
N_4=[ 0 54 44 0];
N_5=[ 0 60 54 0];
N_6=[ 0 0 60 0 ];
N_7=[ 0 0 56 60];
N_8=[0 0 48 56 ];
N_9=[0 0 36 48];
N_10=[0 0 29 36];
N_11=[0 0 0 29];
N_12=[21 37 0 0];
N_13=[ 37 49 0 0];
N_14=[49 57 0 0];
N_15=[ 57 61 0 0];
N_16=[61 0 0 0 ];
N_17=[59 0 0 61];
N_18=[53 0 0 59];
N_19=[ 43 0 0 53];
N_20=[29 0 0 43];
N_21=[2 22 12 1];
N_22=[ 30 23 37 21];
N_23=[ 31 24 38 22];
N_24=[32 25 39 23];
N_25=[33 26 40 24];
N_26=[34 27 41 25];
N_27=[35 28 42 26];
N_28=[36 29 43 27];
N_29=[ 10 11 20 28];
N_30=[ 3 31 22 2];
N_31=[44 32 23 30];
N_32=[ 45 33 24 31];
N_33=[ 46 34 25 32];
N_34=[ 47 35 26 33];
N_35=[ 48 36 27 34];
N_36=[ 9 10 28 35];
N_37=[ 22 38 13 12];
N_38=[ 23 39 49 37];
N_39=[ 24 40 50 30];
N_40=[ 25 41 51 39];
N_41=[26 42 52 40];
N_42=[27 43 53 41];
N_43=[28 20 19 42];
N_44=[ 4 45 31 3];
N_45=[54 46 32 44];
N_46=[ 55 47 33 45];
N_47=[ 56 48 34 46];
N_48=[ 8 9 35 47];
N_49=[ 38 50 14 13];
N_50=[ 39 51 57 49];
N_51=[ 40 52 58 50];
N_52=[ 41 53 59 51];
N_53=[ 42 19 18 52];
N_54=[ 5 55 45 4 ];
N_55=[ 60 7 55 5 ];
N_56=[ 7 8 47 55];
N_57=[ 50 58 15 14];
N_58=[51 59 61 57];
N_59=[ 52 18 17 58];
N_60=[ 6 7 55 5];
N_61=[58 17 16 15];
% 61x4 matrix of nodes
C=[N_1;N_2;N_3;N_4;N_5;N_6;N_7;N_8;N_9;N_10;N_11;N_12;N_13;N_14;...
N_15;N_16;N_17;N_18;N_19;N_20;N_21;N_22;N_23;N_24;N_25;N_26;N_27;N_28;N_29;...
N_30;N_31;N_32;N_33;N_34;N_35;N_36;N_37;N_38;N_39;N_40;N_41;N_42;N_43;...
N_44;N_45;N_46;N_47;N_48;N_49;N_50;N_51;N_52;N_53;N_54;N_55;N_56;N_57;N_58;...
N_59;N_60;N_61]
k=0.168:0.168:1.68; %distance from 0.168 to 1.68, increment of 0.168
for x=1:length(k) %for loop to find heat transfer coefficient at different distances
if k(x)>=0.03 && k(x)<=0.06
h(x)=1.437*k(x)^(-0.279)
elseif k(x)>=0.07 && k(x)<=0.83
h(x)=5.313*k(x)^(-0.121)
else k(x)>=0.85 && k(x)<=1.68
h(x)=(-2.0945)*k(x)+7.0609
end
end
h(x)
% for i=2:1:5
alr=Ka*(dy/dx) %Thermal Conductivity times y distance /x distance
alb=Ka*(dx/dy) %Thermal Conductivity times x distance /ydistance
N=zeros(1,61) %constant value matrixs
A=zeros(61,61); %61 x 61 matrix
for i=2:1:5 %for loop for node 2 to 5 to solve 61x61 matrix
A(i,i)=((h(i-1))*(dz))+(alb+alr)
A(i,C(i,2))=alr
A(i,C(i,3))=alb
N(i,1)=(h(i-1))*(dz)*Taw %solve for 61x1 matrix for constant vaule
end
for i=6 %solve for node 6
A(i,i)=2*(h(6)*dz/2)+alb
A(i,C(i,3))=alb
N(1,i)=2*(h(6)*dz/2)*Taw %solve for node 6 constant vaule
end
for i=7:1:10 %for loop for node 7 to 10 to solve 61x61 matrix
A(i,i)=(h(i-1)*(dz))+(alb+alr)
A(i,C(i,3))=alr
A(i,C(i,4))=alb
N(1,i)=(h(i-1)*(dz))*Taw %solve for 61x1 matrix for constant vaule
end
for i=11 %solve for node 6 for
A(i,i)=2*(h(10)*dz/2)+alr
A(i,C(i,4))=alr
N(1,i)=2*(h(10)*dz/2)*Taw
end
for i=12:1:15
A(i,i)=(h(i-11)*(dz))+(alb+alr)
A(i,C(i,1))=alr
A(i,C(i,2))=alb
N(1,i)=(h(i-11)*(dz))*Taw
end
for i=16
A(i,i)=2*(h(6)*dz/2)+alb
A(i,C(i,1))=alb
N(1,i)=2*(h(6)*dz/2)*Taw
end
for i=17:1:20
A(i,i)=(h(i-11)*(dz))+(alb+alr)
A(i,C(i,1))=alr
A(i,C(i,4))=alb
N(1,i)=(h(i-11)*(dz))*Taw
end
for i=21:1:61
A(i,i)=(2*alr)+(2*alb)
A(i,C(i,1))=alr
A(i,C(i,2))=alb
A(i,C(i,3))=alr
A(i,C(i,4))=alb
end
Ta1(1)=Tstag
Ta1(2:61)=N(2:61)*inv(A(2:61,2:61))
how to plot an intensity plot of temperaure in the x-y plane
