Fortran Programming--Heat Equation 2D SS NoGen (Elliptic PDE)

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PROGRAM HeatEquation_2D_SS_NoGen

! This program have been written by Pedram Niakan

!_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-__-_-_-_-_-_-NOMENCLATOR_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_

! T[i,j] ---> Temprature @ desired node(i,j)

! i,j ---> Respectively row & column of a node ((n-1)*(m-1)) ---> Number of cells

! m,n ---> Respectively number of rows & columns

! deltaX,deltaY ---> Respectively Length & Height of a cell ! BCS,BCW,BCN,BCS---> Boundry condidtions

! Tinf ---> Temprature of neighbor fluid For convection (@ Boundry) ! qe,qw,qn,qs ---> Heat Flux (@ Boundry) qe,qw,qn,qs<0 represents outgoing of heat from plate &

! cooling and qe,qw,qn,qs>0 represents incoming of heat in to the plate & heating

! k,h ---> Respectively conduction [watt/k-m] & convection [watt/k-m^2] coefficients

! probable ---> Probable values of temperature for solution of discreted equation ! !_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-__-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-__-_-_-_-_-_-_-_-_-_-_-_-_-_ IMPLICIT NONE REAL,ALLOCATABLE :: T(:,:),probable(:,:) INTEGER :: i,j,n,m,q,BCE,BCW,BCN,BCS REAL :: X,deltaX,Y,deltaY,k,h,er !---

DESCRIPTION---WRITE (*,*) "Discrete Equation for 2D,SS,NoGen Heat Transfer @ a rectangle plate:"

WRITE (*,*) ""

WRITE (*,*) " 2 2"

WRITE (*,*) "T[i+1,j]+T[i-1,j] T[i,j+1]+T[i,j-1] (deltaX)+ (deltaY)"

WRITE (*,*) "_________________ + _________________ = 2._________________ * T[i,j]"

WRITE (*,*) " 2 2 2 2"

WRITE (*,*) " (deltaX) (deltaY) (deltaX)*(deltaY)" WRITE (*,*) "" !--- ---OPEN(1,FILE="INPUT(HeatEquation_2D_SS_NoGen).TXT",STATUS="REPLACE") OPEN(2,FILE="OUTPUT(HeatEquation_2D_SS_NoGen).TXT",STATUS="REPLACE")

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READ (*,*) X

WRITE (*,*) "Please enter number of Nodes @ X-Direction:" READ (*,*) n

WRITE (*,*) "Please enter heigth of model @ Y-Direction:" READ (*,*) Y

WRITE (*,*) "Please enter number of Nodes @ Y-Direction:" READ (*,*) m

WRITE (*,*) "Enter thermophysics properties k[watt/kelv-m] & h [watt/kelv-m^2]:"

READ (*,*) k,h deltaX=X/(n-1) deltaY=Y/(m-1)

WRITE (*,*) "Enter allowed value for error:" READ (*,*) er

ALLOCATE (T(1:n,1:m),probable(1:n,1:m))

!Declaration of probable values {0} for nodes DO i=1,n DO j=1,m T(i,j)=0 probable(i,j)=0 END DO END DO

!DECLARATION OF BOUNDRY CONDITIONS q=0

!Declaration of boundry condition @ side E

WRITE (*,*) "Declaration of boundry condition type @ side E:" WRITE (*,*) ""

10 WRITE (*,*)"Select one of below numbers:" WRITE (*,*)" 1 Temperatur"

WRITE (*,*)" 2 Heat Flux" WRITE (*,*)" 3 Convection" READ (*,*) BCE

!Declaration of boundry condition @ side W

WRITE (*,*) "Declaration of boundry condition type @ side W:" WRITE (*,*) ""

WRITE (*,*)" 2 Heat Flux" WRITE (*,*)" 3 Convection" READ (*,*) BCW

!Declaration of boundry condition @ side N

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WRITE (*,*) ""

WRITE (*,*)" 2 Heat Flux" WRITE (*,*)" 3 Convection" READ (*,*) BCN

!Declaration of boundry condition @ side S

WRITE (*,*) "Declaration of boundry condition type @ side S:" WRITE (*,*) ""

WRITE (*,*)" 2 Heat Flux" WRITE (*,*)" 3 Convection" READ (*,*) BCS

50 IF (BCE==1) THEN

CALL Temperatur (q,n,m,BCE,BCW,BCN,BCS,T) ELSE IF (BCE==2) THEN

CALL HeatFlux (q,n,deltaX,m,deltaY,k,BCE,BCW,BCN,BCS,T) ELSE IF (BCE==3) THEN

CALL Convection (q,n,deltaX,m,deltaY,k,h,BCE,BCW,BCN,BCS,T) ELSE

WRITE (*,*)"Enter a correct number for EAST!" GO TO 10

END IF

60 IF (BCW==1) THEN

CALL Temperatur (q,n,m,BCE,BCW,BCN,BCS,T) ELSE IF (BCW==2) THEN

CALL HeatFlux (q,n,deltaX,m,deltaY,k,BCE,BCW,BCN,BCS,T) ELSE IF (BCW==3) THEN

WRITE (*,*)"Enter a correct number for WEST!" GO TO 20

END IF

70 IF (BCN==1) THEN

CALL Temperatur (q,n,m,BCE,BCW,BCN,BCS,T) ELSE IF (BCN==2) THEN

CALL HeatFlux (q,n,deltaX,m,deltaY,k,BCE,BCW,BCN,BCS,T) ELSE IF (BCN==3) THEN

WRITE (*,*)"Enter a correct number for NORTH!" GO TO 30

END IF

80 IF (BCS==1) THEN

CALL Temperatur (q,n,m,BCE,BCW,BCN,BCS,T) ELSE IF (BCS==2) THEN

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ELSE IF (BCS==3) THEN

WRITE (*,*)"Enter a correct number for SOUTH!" GO TO 40

END IF

!Using Try & Error method 90 DO i=2,n-1 DO j=2,m-1 T(i,j)=(((T(i+1,j)+T(i-1,j))/(deltaX**2))+((T(i,j+1)+T(i,j-1))/ (deltaY**2)))*(.5*(deltaX**2)*(deltaY**2)/(deltaX**2+deltaY**2)) WRITE (*,*) "T(",i,",",j,")=",T(i,j) q=1 END DO END DO DO i=2,n-1 DO j=2,m-1 IF (ABS(T(i,j)-probable(i,j))>er) THEN probable(i,j)=T(i,j) GO TO 50 END IF END DO END DO WRITE (2,*)"varibles:x,y"

WRITE (2,*)"zone f=point,i=",n,",j=",m DO j=1,m

DO i=1,n

WRITE (*,*)"T(",i,",",j,")= ",T(i,j) WRITE (2,100)i,j,T(i,j)

100 FORMAT (15x,I10,I10,f20.6) END DO

END DO PAUSE

END PROGRAM HeatEquation_2D_SS_NoGen

!

CONTAINS !---

---SUBROUTINE Temperatur (q,n,m,BCE,BCW,BCN,BCS,T) INTEGER,INTENT(IN):: q,n,m,BCE,BCW,BCN,BCS REAL :: Te,Tw,Tn,Ts INTEGER :: i,j REAL,DIMENSION(1:n,1:m),INTENT(INOUT) :: T IF (BCE==1) THEN IF (q==0) THEN

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READ (*,*) Te END IF DO j=1,m T(n,j)=Te END DO END IF IF (BCW==1) THEN IF (q==0) THEN

WRITE (*,*) "Enter the Temperatur @ WEST SIDE:" READ (*,*) Tw END IF DO j=1,m T(1,j)=Tw END DO END IF IF (BCN==1) THEN IF (q==0) THEN

WRITE (*,*) "Enter the Temperatur @ NORTH SIDE:" READ (*,*) Tn END IF DO i=1,n T(i,m)=Tn END DO END IF IF (BCS==1) THEN IF (q==0) THEN

WRITE (*,*) "Enter the Temperatur @ SOUTH SIDE:" READ (*,*) Ts END IF DO i=1,n T(i,1)=Ts END DO END IF RETURN

END SUBROUTINE Temperatur

SUBROUTINE HeatFlux (q,n,deltaX,m,deltaY,k,BCE,BCW,BCN,BCS,T) INTEGER,INTENT(IN) :: q,n,m,BCE,BCW,BCN,BCS REAL,INTENT(IN) :: deltaX,deltaY,k INTEGER :: i,j REAL :: qe,qw,qn,qs REAL,DIMENSION(1:n,1:m),INTENT(INOUT) :: T IF (BCE==2) THEN IF (q==0) THEN

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READ (*,*) qe END IF DO j=1,m T(n,j)=qe*deltaX/k+T(n-1,j) END DO END IF IF (BCW==2) THEN IF (q==0) THEN

WRITE (*,*) "Enter the HeatFlux @ WEST SIDE:" READ (*,*) qw END IF DO j=1,m T(1,j)=qw*deltaX/k+T(2,j) END DO END IF IF (BCN==2) THEN IF (q==0) THEN

WRITE (*,*) "Enter the HeatFlux @ NORTH SIDE:" READ (*,*) qn END IF DO i=1,n T(i,m)=qn*deltaY/k+T(i,m-1) END DO END IF IF (BCS==2) THEN IF (q==0) THEN

WRITE (*,*) "Enter the HeatFlux @ SOUTH SIDE:" READ (*,*) qs END IF DO i=1,n T(i,1)=qs*deltaY/k+T(i,2) END DO END IF RETURN

END SUBROUTINE HeatFlux

SUBROUTINE Convection (q,n,deltaX,m,deltaY,k,h,BCE,BCW,BCN,BCS,T) INTEGER,INTENT(IN):: q,n,m,BCE,BCW,BCN,BCS REAL,INTENT(IN) :: deltaX,deltaY,k,h INTEGER :: i,j REAL :: Tinf_e,Tinf_w,Tinf_n,Tinf_s REAL,DIMENSION(1:n,1:m),INTENT(INOUT) :: T IF (BCE==3) THEN IF (q==0) THEN

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READ (*,*) Tinf_e END IF DO j=1,m T(n,j)=(T(n-1,j)+(h*deltaX/k)*Tinf_e)/(h*deltaX/k+1) END DO END IF IF (BCW==3) THEN IF (q==0) THEN

WRITE (*,*) "Enter the Tinf_w @ WEST SIDE:" READ (*,*) Tinf_w END IF DO j=1,m T(1,j)=(T(2,j)+(h*deltaX/k)*Tinf_w)/(h*deltaX/k+1) END DO END IF IF (BCN==3) THEN IF (q==0) THEN

WRITE (*,*) "Enter the Tinf_n @ NORTH SIDE:" READ (*,*) Tinf_n END IF DO i=1,n T(i,m)=(T(i,m-1)+(h*deltaX/k)*Tinf_n)/(h*deltaY/k+1) END DO END IF IF (BCS==3) THEN IF (q==0) THEN

WRITE (*,*) "Enter the Tinf_s @ SOUTH SIDE:" READ (*,*) Tinf_s END IF DO i=1,n T(i,1)=(T(i,2)+(h*deltaX/k)*Tinf_s)/(h*deltaY/k+1) END DO END IF RETURN