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Heat Exchanger LMTD Sizer
Core Numerical Engine in Fortran 90 • 0 total downloads
heat_exchanger_lmtd.f90
! =========================================================================
! Source File: heat_exchanger_lmtd.f90
! =========================================================================
program heat_exchanger_lmtd
implicit none
double precision :: T_hi, T_ho, T_ci, T_co
double precision :: m_h, m_c, Cp_h, Cp_c
double precision :: U, A_req
double precision :: Q_h, Q_c, Q
double precision :: dT1, dT2, LMTD_pf, LMTD_cf
double precision :: LMTD_used
double precision :: C_h, C_c, C_min, C_max, C_r
double precision :: eff
double precision :: NTU
integer :: config
integer :: i
character(len=20) :: config_name
! Read inputs
read(*,*) config ! 1=parallel flow, 2=counter flow
read(*,*) T_hi ! Hot fluid inlet temp [C]
read(*,*) T_ho ! Hot fluid outlet temp [C]
read(*,*) T_ci ! Cold fluid inlet temp [C]
read(*,*) T_co ! Cold fluid outlet temp [C]
read(*,*) m_h ! Hot fluid mass flow rate [kg/s]
read(*,*) m_c ! Cold fluid mass flow rate [kg/s]
read(*,*) Cp_h ! Hot fluid specific heat [J/kg.K]
read(*,*) Cp_c ! Cold fluid specific heat [J/kg.K]
read(*,*) U ! Overall heat transfer coefficient [W/m2.K]
! Configuration name
if (config == 1) then
config_name = 'Parallel Flow'
else
config_name = 'Counter Flow'
end if
! Heat capacity rates
C_h = m_h * Cp_h
C_c = m_c * Cp_c
if (C_h < C_c) then
C_min = C_h
C_max = C_c
else
C_min = C_c
C_max = C_h
end if
C_r = C_min / C_max
! Heat transfer rates
Q_h = C_h * (T_hi - T_ho)
Q_c = C_c * (T_co - T_ci)
Q = (Q_h + Q_c) / 2.0d0
! ============================================
! LMTD CALCULATION
! ============================================
! Parallel flow LMTD
dT1 = T_hi - T_ci
dT2 = T_ho - T_co
if (abs(dT1 - dT2) < 1.0d-6) then
LMTD_pf = dT1
else if (dT1 > 0 .and. dT2 > 0) then
LMTD_pf = (dT1 - dT2) / log(dT1 / dT2)
else
LMTD_pf = 0.0d0
end if
! Counter flow LMTD
dT1 = T_hi - T_co
dT2 = T_ho - T_ci
if (abs(dT1 - dT2) < 1.0d-6) then
LMTD_cf = dT1
else if (dT1 > 0 .and. dT2 > 0) then
LMTD_cf = (dT1 - dT2) / log(dT1 / dT2)
else
LMTD_cf = 0.0d0
end if
! Select LMTD based on configuration
if (config == 1) then
LMTD_used = LMTD_pf
else
LMTD_used = LMTD_cf
end if
! Required area
if (LMTD_used > 0 .and. U > 0) then
A_req = Q / (U * LMTD_used)
else
A_req = 0.0d0
end if
! Effectiveness
if (C_min * (T_hi - T_ci) > 0) then
eff = Q / (C_min * (T_hi - T_ci))
else
eff = 0.0d0
end if
! NTU
if (C_min > 0 .and. A_req > 0) then
NTU = U * A_req / C_min
else
NTU = 0.0d0
end if
! ============================================
! OUTPUT
! ============================================
write(*,'(A)') '============================================================='
write(*,'(A)') ' HEAT EXCHANGER ANALYSIS - LMTD METHOD'
write(*,'(A)') '============================================================='
write(*,*)
write(*,'(A)') '--- CONFIGURATION -------------------------------------------'
write(*,'(A,A)') ' Flow Arrangement = ', trim(config_name)
write(*,*)
write(*,'(A)') '--- INPUT PARAMETERS ----------------------------------------'
write(*,'(A)') ' Hot Fluid:'
write(*,'(A,F12.2,A)') ' Inlet Temperature = ', T_hi, ' C'
write(*,'(A,F12.2,A)') ' Outlet Temperature = ', T_ho, ' C'
write(*,'(A,F12.4,A)') ' Mass Flow Rate = ', m_h, ' kg/s'
write(*,'(A,F12.2,A)') ' Specific Heat = ', Cp_h, ' J/kg.K'
write(*,*)
write(*,'(A)') ' Cold Fluid:'
write(*,'(A,F12.2,A)') ' Inlet Temperature = ', T_ci, ' C'
write(*,'(A,F12.2,A)') ' Outlet Temperature = ', T_co, ' C'
write(*,'(A,F12.4,A)') ' Mass Flow Rate = ', m_c, ' kg/s'
write(*,'(A,F12.2,A)') ' Specific Heat = ', Cp_c, ' J/kg.K'
write(*,*)
write(*,'(A,F12.2,A)') ' Overall U = ', U, ' W/m2.K'
write(*,*)
write(*,'(A)') '--- HEAT CAPACITY RATES -------------------------------------'
write(*,'(A,F12.4,A)') ' C_hot = m_h x Cp_h = ', C_h, ' W/K'
write(*,'(A,F12.4,A)') ' C_cold = m_c x Cp_c = ', C_c, ' W/K'
write(*,'(A,F12.4,A)') ' C_min = ', C_min, ' W/K'
write(*,'(A,F12.4,A)') ' C_max = ', C_max, ' W/K'
write(*,'(A,F12.4)') ' C_r = C_min/C_max = ', C_r
write(*,*)
write(*,'(A)') '--- ENERGY BALANCE ------------------------------------------'
write(*,'(A,F12.4,A)') ' Q_hot = C_h(T_hi-T_ho)= ', Q_h, ' W'
write(*,'(A,F12.4,A)') ' Q_cold = C_c(T_co-T_ci)= ', Q_c, ' W'
write(*,'(A,F12.4,A)') ' Q (average) = ', Q, ' W'
write(*,'(A,F12.4,A)') ' Energy Balance Error = ', &
abs(Q_h-Q_c)/max(Q_h,1.0d-10)*100, ' %'
write(*,*)
write(*,'(A)') '--- LMTD RESULTS --------------------------------------------'
write(*,'(A,F12.4,A)') ' LMTD (parallel flow) = ', LMTD_pf, ' deg-C'
write(*,'(A,F12.4,A)') ' LMTD (counter flow) = ', LMTD_cf, ' deg-C'
write(*,'(A,F12.4,A)') ' LMTD (used) = ', LMTD_used, ' deg-C'
write(*,*)
write(*,'(A)') '--- DESIGN RESULTS ------------------------------------------'
write(*,'(A,F12.4,A)') ' Required Area (A) = ', A_req, ' m2'
write(*,'(A,F12.4)') ' NTU = UA/C_min = ', NTU
write(*,'(A,F12.4,A)') ' Effectiveness (e) = ', eff*100, ' %'
write(*,*)
! Temperature profiles for chart
write(*,'(A)') '--- TEMPERATURE PROFILE ALONG EXCHANGER --------------------'
write(*,'(A)') ' Position % T_hot [C] T_cold [C]'
write(*,'(A)') ' --------------------------------------------------'
do i = 0, 20
if (config == 1) then
! Parallel flow: both fluids travel same direction
write(*,'(F10.1,4X,F10.2,4X,F10.2)') dble(i)/20.0d0*100, &
T_hi - (T_hi - T_ho) * dble(i)/20.0d0, &
T_ci + (T_co - T_ci) * dble(i)/20.0d0
else
! Counter flow: cold fluid travels opposite direction
write(*,'(F10.1,4X,F10.2,4X,F10.2)') dble(i)/20.0d0*100, &
T_hi - (T_hi - T_ho) * dble(i)/20.0d0, &
T_co - (T_co - T_ci) * dble(i)/20.0d0
end if
end do
write(*,*)
write(*,'(A)') '--- FORMULAS USED -------------------------------------------'
write(*,'(A)') ' Q = U x A x LMTD'
write(*,'(A)') ' LMTD = (DT1 - DT2) / ln(DT1/DT2)'
write(*,'(A)') ' Effectiveness = Q / Q_max = Q / (C_min x (T_hi - T_ci))'
write(*,'(A)') ' NTU = U x A / C_min'
end program heat_exchanger_lmtd
Solver Description
Sizes heat exchangers using the Log-Mean Temperature Difference ($LMTD$) method. Evaluates capacity ratios ($C_r$), solves for total heat transfer rate ($Q = \dot{m} C_p \Delta T$), computes $\Delta T_{lm}$, and calculates the required surface area ($A$).
Key Numerical Methods & Architecture
- Input Redirection: Reads parameters sequentially from standard input (`stdin`) using Fortran sequential read (`read(*,*)`), ensuring modular integration.
- Modular Design: Formulated using pure mathematical routines, separation of equations from output formatting, and precise numerical solvers (e.g. bisection, Newton-Raphson).
- Standard Compliant: Written in clean, standards-compliant Fortran 90 to ensure cross-compiler compatibility.
🛠️ Local Compilation
To test this code on your machine, compile the source code file(s) using a standard Fortran compiler (e.g., `gfortran`).
Compilation Command:
gfortran -ffree-line-length-none heat_exchanger_lmtd.f90 -o hx_lmtd
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
hx_lmtd < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! Flow Configuration (1=Parallel Flow, 2=Counter-Flow)
2
! Hot Fluid Inlet Temp ($T_{hi}$) [°C]
120.0
! Hot Fluid Outlet Temp ($T_{ho}$) [°C]
70.0
! Cold Fluid Inlet Temp ($T_{ci}$) [°C]
20.0
! Cold Fluid Outlet Temp ($T_{co}$) [°C]
55.0
! Hot Fluid Mass Flow Rate (m_h) [kg/s]
1.5
! Hot Specific Heat ($C_{p,h}$) [J/kg-K]
4180.0
! Cold Fluid Mass Flow Rate (m_c) [kg/s]
2.0
! Cold Specific Heat ($C_{p,c}$) [J/kg-K]
4180.0
! Overall Heat Transfer Coefficient ($U$) [W/m²-K]
800.0
2
! Hot Fluid Inlet Temp ($T_{hi}$) [°C]
120.0
! Hot Fluid Outlet Temp ($T_{ho}$) [°C]
70.0
! Cold Fluid Inlet Temp ($T_{ci}$) [°C]
20.0
! Cold Fluid Outlet Temp ($T_{co}$) [°C]
55.0
! Hot Fluid Mass Flow Rate (m_h) [kg/s]
1.5
! Hot Specific Heat ($C_{p,h}$) [J/kg-K]
4180.0
! Cold Fluid Mass Flow Rate (m_c) [kg/s]
2.0
! Cold Specific Heat ($C_{p,c}$) [J/kg-K]
4180.0
! Overall Heat Transfer Coefficient ($U$) [W/m²-K]
800.0