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Heat & Mass Transfer Analogy
Core Numerical Engine in Fortran 90 • 67 total downloads
heat_mass_analogy.f90
! =========================================================================
! Source File: heat_mass_analogy.f90
! =========================================================================
program heat_mass_analogy
implicit none
! Inputs
integer :: geom_type ! 1 = External flow over flat plate, 2 = Internal flow inside tube
double precision :: U_vel ! Free-stream or mean velocity, m/s
double precision :: L_c ! Characteristic length (L for plate, D for tube), m
double precision :: rho ! Density, kg/m3
double precision :: mu ! Dynamic viscosity, Pa.s
double precision :: k_f ! Thermal conductivity, W/m.K
double precision :: Cp ! Specific heat, J/kg.K
double precision :: D_AB ! Binary mass diffusivity, m2/s
! Physical properties & Dimensionless Numbers
double precision :: nu, alpha
double precision :: Re, Pr, Sc, Le
double precision :: Cf, Nu_avg, Sh_avg
double precision :: h_avg, hm_avg
double precision :: ratio_actual, ratio_theory
! Profile variables
integer :: i, n_points
double precision :: x, dx, Re_x, Nu_x, Sh_x, h_x, hm_x, f_factor
character(len=50) :: geom_name
integer :: iostat_val
! Read inputs
read(*,*,iostat=iostat_val) geom_type
if (iostat_val /= 0) then
write(*,*) 'ERROR: Invalid geometry selection.'
stop
end if
read(*,*,iostat=iostat_val) U_vel
read(*,*,iostat=iostat_val) L_c
read(*,*,iostat=iostat_val) rho
read(*,*,iostat=iostat_val) mu
read(*,*,iostat=iostat_val) k_f
read(*,*,iostat=iostat_val) Cp
read(*,*,iostat=iostat_val) D_AB
if (iostat_val /= 0) then
write(*,*) 'ERROR: Failed to read all analogy parameters.'
stop
end if
! Basic validations
if (U_vel <= 0.0d0) then
write(*,*) 'ERROR: Velocity must be positive.'
stop
end if
if (L_c <= 0.0d0) then
write(*,*) 'ERROR: Characteristic length must be positive.'
stop
end if
if (rho <= 0.0d0 .or. mu <= 0.0d0 .or. k_f <= 0.0d0 .or. Cp <= 0.0d0 .or. D_AB <= 0.0d0) then
write(*,*) 'ERROR: Physical properties must be positive.'
stop
end if
! Compute physical properties
nu = mu / rho
alpha = k_f / (rho * Cp)
! Compute dimensionless numbers
Re = U_vel * L_c / nu
Pr = nu / alpha
Sc = nu / D_AB
Le = alpha / D_AB ! Le = Sc / Pr
! Setup geometry cases
if (geom_type == 1) then
geom_name = "External Flow over Flat Plate"
! Transition Reynolds number is 5.0e5
if (Re <= 5.0d5) then
! Fully laminar flow
Cf = 1.328d0 / sqrt(Re)
Nu_avg = 0.664d0 * sqrt(Re) * Pr**(1.0d0/3.0d0)
Sh_avg = 0.664d0 * sqrt(Re) * Sc**(1.0d0/3.0d0)
else
! Mixed laminar/turbulent flow
Cf = 0.074d0 / (Re**0.2d0) - 1740.0d0 / Re
Nu_avg = (0.037d0 * Re**0.8d0 - 871.0d0) * Pr**(1.0d0/3.0d0)
Sh_avg = (0.037d0 * Re**0.8d0 - 871.0d0) * Sc**(1.0d0/3.0d0)
end if
h_avg = Nu_avg * k_f / L_c
hm_avg = Sh_avg * D_AB / L_c
ratio_theory = rho * Cp * Le**(2.0d0/3.0d0)
else if (geom_type == 2) then
geom_name = "Internal Flow in Circular Tube"
if (Re <= 2300.0d0) then
! Laminar fully developed pipe flow (constant wall temp assumption)
Cf = 16.0d0 / Re ! f = 64/Re, Cf = f/4
Nu_avg = 3.66d0
Sh_avg = 3.66d0
ratio_theory = rho * Cp * Le**(2.0d0/3.0d0)
else
! Turbulent flow - Petukhov correlation for friction factor
! f = (0.790 * ln(Re) - 1.64)**(-2)
f_factor = (0.790d0 * log(Re) - 1.64d0)**(-2)
Cf = f_factor / 4.0d0
! Dittus-Boelter correlation (standard heating: exponent = 0.4)
Nu_avg = 0.023d0 * Re**0.8d0 * Pr**0.4d0
Sh_avg = 0.023d0 * Re**0.8d0 * Sc**0.4d0
ratio_theory = rho * Cp * Le**(0.6d0) ! Modified exponent due to Dittus-Boelter exponent 0.4
end if
h_avg = Nu_avg * k_f / L_c
hm_avg = Sh_avg * D_AB / L_c
else
write(*,*) 'ERROR: Invalid geometry selection code.'
stop
end if
ratio_actual = h_avg / hm_avg
! Output results
write(*,*) '============================================================'
write(*,*) ' HEAT & MASS TRANSFER ANALOGY SOLVER'
write(*,*) '============================================================'
write(*,*)
write(*,'(A,A)') ' Configuration Type = ', trim(geom_name)
write(*,'(A,F12.4,A)') ' Velocity (U) = ', U_vel, ' m/s'
write(*,'(A,F12.4,A)') ' Characteristic Length = ', L_c, ' m'
write(*,*)
write(*,'(A)') '--- FLUID & DIFFUSION PROPERTIES ---------------------------'
write(*,'(A,F12.4,A)') ' Density (rho) = ', rho, ' kg/m3'
write(*,'(A,ES12.4,A)') ' Viscosity (mu) = ', mu, ' Pa.s'
write(*,'(A,F12.4,A)') ' Thermal Cond (kf) = ', k_f, ' W/m.K'
write(*,'(A,F12.2,A)') ' Specific Heat (Cp) = ', Cp, ' J/kg.K'
write(*,'(A,ES12.4,A)') ' Mass Diffusivity D_AB = ', D_AB, ' m2/s'
write(*,*)
write(*,'(A)') '--- DIMENSIONLESS NUMBERS ----------------------------------'
write(*,'(A,ES12.4)') ' Reynolds Number (Re) = ', Re
write(*,'(A,F12.4)') ' Prandtl Number (Pr) = ', Pr
write(*,'(A,F12.4)') ' Schmidt Number (Sc) = ', Sc
write(*,'(A,F12.4)') ' Lewis Number (Le) = ', Le
write(*,*)
write(*,'(A)') '--- ANALOGY RESULTS (AVERAGE VALUES) -----------------------'
write(*,'(A,F12.6)') ' Skin Friction Coeff (Cf) = ', Cf
write(*,'(A,F12.4)') ' Average Nusselt Number = ', Nu_avg
write(*,'(A,F12.4)') ' Average Sherwood Number = ', Sh_avg
write(*,'(A,F12.4,A)') ' Average Heat HTC (h) = ', h_avg, ' W/m2.K'
write(*,'(A,ES12.4,A)') ' Average Mass MTC (hm) = ', hm_avg, ' m/s'
write(*,*)
write(*,'(A)') '--- CHILTON-COLBURN RATIO VERIFICATION ---------------------'
write(*,'(A,ES12.4,A)') ' Actual Ratio h/hm = ', ratio_actual, ' J/m3.K'
write(*,'(A,ES12.4,A)') ' Theoretical rho*Cp*Le^n = ', ratio_theory, ' J/m3.K'
write(*,'(A,F12.2,A)') ' Analogy Deviation = ', abs(ratio_actual - ratio_theory)/ratio_theory * 100.0d0, ' %'
write(*,*)
! ============================================
! LOCAL PROFILE DATA (along flow path)
! ============================================
write(*,'(A)') '--- LOCAL PROFILE ALONG SURFACE ----------------------------'
write(*,'(A)') ' x [m] Re_x Nu_x Sh_x h_x [W/m2.K] hm_x [m/s]'
write(*,'(A)') ' ----------------------------------------------------------------------'
n_points = 40
dx = L_c / dble(n_points)
do i = 1, n_points
x = dble(i) * dx
Re_x = U_vel * x / nu
if (geom_type == 1) then
! Flat Plate boundary layer development
if (Re_x <= 5.0d5) then
! Local laminar Nusselt & Sherwood
Nu_x = 0.332d0 * sqrt(Re_x) * Pr**(1.0d0/3.0d0)
Sh_x = 0.332d0 * sqrt(Re_x) * Sc**(1.0d0/3.0d0)
else
! Local turbulent Nusselt & Sherwood
Nu_x = 0.0296d0 * Re_x**0.8d0 * Pr**(1.0d0/3.0d0)
Sh_x = 0.0296d0 * Re_x**0.8d0 * Sc**(1.0d0/3.0d0)
end if
h_x = Nu_x * k_f / x
hm_x = Sh_x * D_AB / x
else
! Internal Flow - tube entrance region thermal development
! Use simplified thermal entrance correlation for laminar/turbulent
if (Re <= 2300.0d0) then
! Laminar entrance region
Nu_x = 3.66d0 + (0.0668d0 * (L_c/x) * Re * Pr) / (1.0d0 + 0.04d0 * ((L_c/x) * Re * Pr)**(2.0d0/3.0d0))
Sh_x = 3.66d0 + (0.0668d0 * (L_c/x) * Re * Sc) / (1.0d0 + 0.04d0 * ((L_c/x) * Re * Sc)**(2.0d0/3.0d0))
else
! Turbulent entrance (approximate entrance region effect)
Nu_x = Nu_avg * (1.0d0 + (L_c/x)**0.7d0) ! Simplistic entry-region factor
Sh_x = Sh_avg * (1.0d0 + (L_c/x)**0.7d0)
end if
h_x = Nu_x * k_f / L_c
hm_x = Sh_x * D_AB / L_c
end if
write(*,'(F8.4,2X,ES12.4,2X,F10.2,3X,F10.2,4X,F10.4,4X,ES12.4)') &
x, Re_x, Nu_x, Sh_x, h_x, hm_x
end do
write(*,*)
write(*,'(A)') '--- CORRELATIONS USED ---------------------------------------'
if (geom_type == 1) then
write(*,'(A)') ' Flat Plate Laminar (Re <= 5e5): Nu_x = 0.332 Re_x^0.5 Pr^1/3, Sh_x = 0.332 Re_x^0.5 Sc^1/3.'
write(*,'(A)') ' Flat Plate Turbulent (Re > 5e5): Nu_x = 0.0296 Re_x^0.8 Pr^1/3, Sh_x = 0.0296 Re_x^0.8 Sc^1/3.'
else
write(*,'(A)') ' Laminar Tube (Re <= 2300): Nu = 3.66 (Fully Developed Constant Temperature).'
write(*,'(A)') ' Turbulent Tube (Re > 2300): Dittus-Boelter correlation Nu = 0.023 Re^0.8 Pr^n.'
end if
write(*,'(A)') ' Boundary layers assumed analogous under Chilton-Colburn definition.'
end program heat_mass_analogy
Solver Description
Solves convective heat and mass transfer boundary layers using transport analogies. Supports laminar/turbulent external flow over a flat plate and internal tube flow. Computes Reynolds, Prandtl, Schmidt, and Lewis numbers. Uses Chilton-Colburn analogy (\ = \) to relate Nusselt and Sherwood numbers. Outputs heat and mass transfer coefficients, transfer rates, and Stanton numbers.
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 -O3 heat_mass_analogy.f90 -o heat_mass_analogy
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
heat_mass_analogy < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! Flow Configuration (1=External Plate, 2=Internal Tube)
1
! Mean Velocity [m/s]
5.0
! Characteristic Length L or Diameter D [m]
0.5
! Fluid Density [kg/m3]
1.204
! Fluid Dynamic Viscosity [Pa-s]
1.825e-5
! Thermal Conductivity k [W/m-K]
0.02514
! Specific Heat Cp [J/kg-K]
1007.0
! Binary Diffusivity D_AB [m2/s]
2.6e-5
1
! Mean Velocity [m/s]
5.0
! Characteristic Length L or Diameter D [m]
0.5
! Fluid Density [kg/m3]
1.204
! Fluid Dynamic Viscosity [Pa-s]
1.825e-5
! Thermal Conductivity k [W/m-K]
0.02514
! Specific Heat Cp [J/kg-K]
1007.0
! Binary Diffusivity D_AB [m2/s]
2.6e-5