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Flat Plate Convection
Core Numerical Engine in Fortran 90 • 60 total downloads
flat_plate_convection.f90
! =========================================================================
! Source File: flat_plate_convection.f90
! =========================================================================
program flat_plate_convection
implicit none
! Variables
double precision :: L, T_s, T_inf, U_inf, rho, mu, nu, k_f, Pr, Cp
double precision :: Re_L, Re_x, Re_crit, x_crit
double precision :: Nu_lam, Nu_turb, Nu_mixed, h_avg
double precision :: Q_total, A, W
double precision :: delta_lam, delta_turb, Cf_lam, Cf_turb
double precision :: delta_t_lam
character(len=20) :: flow_regime
integer :: i, n_points
double precision :: x, dx, local_Re, local_Nu, local_h
double precision :: local_Cf, local_delta
! Read inputs
read(*,*) L ! Plate length [m]
read(*,*) W ! Plate width [m]
read(*,*) T_s ! Surface temperature [°C]
read(*,*) T_inf ! Free stream temperature [°C]
read(*,*) U_inf ! Free stream velocity [m/s]
read(*,*) rho ! Fluid density [kg/m³]
read(*,*) mu ! Dynamic viscosity [Pa·s]
read(*,*) k_f ! Thermal conductivity [W/m·K]
read(*,*) Pr ! Prandtl number
read(*,*) Cp ! Specific heat [J/kg·K]
! Calculate properties
nu = mu / rho
A = L * W
Re_crit = 5.0d5
! Reynolds number at trailing edge
Re_L = U_inf * L / nu
! Determine flow regime
if (Re_L < Re_crit) then
flow_regime = 'Laminar'
else
flow_regime = 'Mixed (Lam+Turb)'
end if
! Critical length (transition point)
x_crit = Re_crit * nu / U_inf
if (x_crit > L) x_crit = L
! ============================================
! AVERAGE NUSSELT NUMBER CALCULATIONS
! ============================================
! Laminar correlation (entire plate laminar): Nu = 0.664 Re^0.5 Pr^(1/3)
Nu_lam = 0.664d0 * Re_L**0.5d0 * Pr**(1.0d0/3.0d0)
! Turbulent correlation (entire plate turbulent): Nu = 0.037 Re^0.8 Pr^(1/3)
Nu_turb = 0.037d0 * Re_L**0.8d0 * Pr**(1.0d0/3.0d0)
! Mixed correlation: Nu = (0.037 Re^0.8 - 871) Pr^(1/3)
if (Re_L > Re_crit) then
Nu_mixed = (0.037d0 * Re_L**0.8d0 - 871.0d0) * Pr**(1.0d0/3.0d0)
else
Nu_mixed = Nu_lam
end if
! Average heat transfer coefficient
h_avg = Nu_mixed * k_f / L
! Total heat transfer
Q_total = h_avg * A * abs(T_s - T_inf)
! Boundary layer thicknesses at trailing edge
if (Re_L < Re_crit) then
delta_lam = 5.0d0 * L / sqrt(Re_L)
delta_turb = 0.0d0
Cf_lam = 1.328d0 / sqrt(Re_L)
Cf_turb = 0.0d0
else
delta_lam = 5.0d0 * x_crit / sqrt(Re_crit)
delta_turb = 0.37d0 * L / Re_L**0.2d0
Cf_lam = 1.328d0 / sqrt(Re_crit)
Cf_turb = 0.074d0 / Re_L**0.2d0
end if
! Thermal boundary layer thickness (laminar)
delta_t_lam = delta_lam / Pr**(1.0d0/3.0d0)
! ============================================
! OUTPUT RESULTS
! ============================================
write(*,'(A)') '============================================================'
write(*,'(A)') ' FORCED CONVECTION - FLOW OVER A FLAT PLATE'
write(*,'(A)') '============================================================'
write(*,*)
write(*,'(A)') '--- INPUT PARAMETERS ----------------------------------------'
write(*,'(A,F12.4,A)') ' Plate Length (L) = ', L, ' m'
write(*,'(A,F12.4,A)') ' Plate Width (W) = ', W, ' m'
write(*,'(A,F12.4,A)') ' Surface Area (A) = ', A, ' m²'
write(*,'(A,F12.2,A)') ' Surface Temperature = ', T_s, ' °C'
write(*,'(A,F12.2,A)') ' Free Stream Temperature = ', T_inf, ' °C'
write(*,'(A,F12.4,A)') ' Free Stream Velocity = ', U_inf, ' m/s'
write(*,*)
write(*,'(A)') '--- FLUID PROPERTIES ----------------------------------------'
write(*,'(A,ES12.4,A)') ' Density (ρ) = ', rho, ' kg/m³'
write(*,'(A,ES12.4,A)') ' Dynamic Viscosity (μ) = ', mu, ' Pa·s'
write(*,'(A,ES12.4,A)') ' Kinematic Viscosity (ν) = ', nu, ' m²/s'
write(*,'(A,F12.4,A)') ' Thermal Conductivity = ', k_f, ' W/m·K'
write(*,'(A,F12.4)') ' Prandtl Number (Pr) = ', Pr
write(*,*)
write(*,'(A)') '--- FLOW ANALYSIS -------------------------------------------'
write(*,'(A,ES12.4)') ' Reynolds Number (Re_L) = ', Re_L
write(*,'(A,ES12.4)') ' Critical Re = ', Re_crit
write(*,'(A,A)') ' Flow Regime = ', trim(flow_regime)
write(*,'(A,F12.4,A)') ' Transition Point (x_cr) = ', x_crit, ' m'
write(*,*)
write(*,'(A)') '--- HEAT TRANSFER RESULTS -----------------------------------'
write(*,'(A,F12.4)') ' Average Nusselt Number = ', Nu_mixed
write(*,'(A,F12.4,A)') ' Average h = ', h_avg, ' W/m²·K'
write(*,'(A,F12.4,A)') ' Total Heat Transfer (Q) = ', Q_total, ' W'
write(*,*)
write(*,'(A)') '--- BOUNDARY LAYER ------------------------------------------'
if (Re_L < Re_crit) then
write(*,'(A,F12.6,A)') ' δ at trailing edge = ', delta_lam*1000, ' mm'
write(*,'(A,F12.6,A)') ' δ_thermal at trailing = ', delta_t_lam*1000, ' mm'
write(*,'(A,ES12.4)') ' Average Cf (laminar) = ', Cf_lam
else
write(*,'(A,F12.6,A)') ' δ_lam at transition = ', delta_lam*1000, ' mm'
write(*,'(A,F12.6,A)') ' δ_turb at trailing edge = ', delta_turb*1000, ' mm'
write(*,'(A,ES12.4)') ' Cf_lam (at transition) = ', Cf_lam
write(*,'(A,ES12.4)') ' Cf_turb (average) = ', Cf_turb
end if
write(*,*)
! ============================================
! LOCAL PROFILE DATA (for chart)
! ============================================
write(*,'(A)') '--- LOCAL PROFILE ALONG PLATE --------------------------------'
write(*,'(A)') ' x [m] Re_x Nu_x h_x [W/m2.K] d [mm]'
write(*,'(A)') ' ------------------------------------------------------------'
n_points = 40
dx = L / dble(n_points)
do i = 1, n_points
x = dble(i) * dx
local_Re = U_inf * x / nu
if (local_Re < Re_crit) then
! Laminar
local_Nu = 0.332d0 * sqrt(local_Re) * Pr**(1.0d0/3.0d0)
local_delta = 5.0d0 * x / sqrt(local_Re)
local_Cf = 0.664d0 / sqrt(local_Re)
else
! Turbulent
local_Nu = 0.0296d0 * local_Re**0.8d0 * Pr**(1.0d0/3.0d0)
local_delta = 0.37d0 * x / local_Re**0.2d0
local_Cf = 0.0592d0 / local_Re**0.2d0
end if
local_h = local_Nu * k_f / x
write(*,'(F8.4,2X,ES12.4,2X,F10.2,4X,F10.4,4X,F10.4)') &
x, local_Re, local_Nu, local_h, local_delta*1000
end do
write(*,*)
write(*,'(A)') '--- CORRELATIONS USED ---------------------------------------'
write(*,'(A)') ' Laminar: Nu_x = 0.332 Re_x^0.5 Pr^(1/3)'
write(*,'(A)') ' Turbulent: Nu_x = 0.0296 Re_x^0.8 Pr^(1/3)'
write(*,'(A)') ' Average: Nu_L = (0.037 Re_L^0.8 - 871) Pr^(1/3)'
write(*,'(A)') ' Valid for: 0.6 < Pr < 60, Re_crit = 5×10⁵'
end program flat_plate_convection
Solver Description
Convective heat transfer over a flat plate is analyzed using empirical correlations that relate the local and average Nusselt numbers ($Nu_L$) to the Reynolds ($Re_L$) and Prandtl ($Pr$) numbers. The transition from laminar to turbulent flow is assumed to occur at the critical Reynolds number ($Re_{crit} = 5 \times 10^5$).
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 flat_plate_convection.f90 -o flat_plate_conv
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
flat_plate_conv < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! Plate Length L [m]
1.0
! Plate Width W [m]
0.5
! Surface Temp Ts [°C]
80.0
! Free Stream Temp Tinf [°C]
20.0
! Free Stream Velocity U [m/s]
5.0
! Fluid Density [kg/m3]
1.092
! Dynamic Viscosity [Pa-s]
1.963e-5
! Thermal Conductivity k [W/m-K]
0.02735
! Prandtl Number Pr
0.7228
! Specific Heat Cp [J/kg-K]
1007.0
1.0
! Plate Width W [m]
0.5
! Surface Temp Ts [°C]
80.0
! Free Stream Temp Tinf [°C]
20.0
! Free Stream Velocity U [m/s]
5.0
! Fluid Density [kg/m3]
1.092
! Dynamic Viscosity [Pa-s]
1.963e-5
! Thermal Conductivity k [W/m-K]
0.02735
! Prandtl Number Pr
0.7228
! Specific Heat Cp [J/kg-K]
1007.0