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Convection Over a Sphere
Core Numerical Engine in Fortran 90 • 30 total downloads
sphere_convection.f90
! =========================================================================
! Source File: sphere_convection.f90
! =========================================================================
program sphere_convection
implicit none
double precision :: D, V, Ti, Ts, rho, mu, kf, Pr, cp, beta
integer :: fl_type
double precision :: Tf, dT, nu, Re, NuW, NuR, h, Q, As, g, pi, mu_s, temp_val
integer :: iostat_val, i
double precision :: Vs, Res, NuWs, NuRs, hs, Qs
g = 9.80665d0
pi = 3.141592653589793d0
! Read inputs sequentially
read(*,*,iostat=iostat_val) D
read(*,*,iostat=iostat_val) V
read(*,*,iostat=iostat_val) Ti
read(*,*,iostat=iostat_val) Ts
read(*,*,iostat=iostat_val) fl_type
! Read custom parameters
read(*,*,iostat=iostat_val) rho
read(*,*,iostat=iostat_val) mu
read(*,*,iostat=iostat_val) kf
read(*,*,iostat=iostat_val) Pr
read(*,*,iostat=iostat_val) cp
read(*,*,iostat=iostat_val) temp_val ! mu_s from php
if (iostat_val /= 0) then
write(*,*) 'ERROR: Failed to read all input values.'
stop
end if
! Evaluate bulk properties at free-stream temperature T_inf = Ti
if (fl_type == 1) then
! Air
rho = 1.177d0
mu = 1.85d-5
kf = 0.0263d0
Pr = 0.71d0
cp = 1007d0
mu_s = 1.85d-5 * ((Ts + 273.15d0) / (Ti + 273.15d0))**0.7d0
else if (fl_type == 2) then
! Water
rho = 997d0
mu = 8.9d-4
kf = 0.613d0
Pr = 6.13d0
cp = 4180d0
mu_s = 2.414d-5 * 10.0d0**(247.8d0 / (Ts + 273.15d0 - 140.0d0))
else
! Engine Oil
rho = 870d0
mu = 0.05d0
kf = 0.14d0
Pr = 500d0
cp = 2000d0
mu_s = 0.05d0 * exp(-0.04d0 * (Ts - Ti))
end if
! Override custom mu_s if provided
if (temp_val > 0.0d0) mu_s = temp_val
nu = mu / rho
Re = rho * V * D / mu
! Nusselt Whitaker correlation (Eq. 7.56)
NuW = 2.0d0 + (0.4d0 * Re**0.5d0 + 0.06d0 * Re**(2.0d0/3.0d0)) * Pr**0.4d0 * (mu / mu_s)**0.25d0
! Nusselt Ranz-Marshall correlation
NuR = 2.0d0 + 0.6d0 * Re**0.5d0 * Pr**(1.0d0/3.0d0)
h = NuW * kf / D
As = pi * D**2
dT = abs(Ts - Ti)
Q = h * As * dT
write(*,'(A)') '============================================'
write(*,'(A)') ' CONVECTION OVER SPHERE ENGINE'
write(*,'(A)') '============================================'
write(*,*)
write(*,'(A,ES14.4)') ' Reynolds Re = ', Re
write(*,'(A,F12.4)') ' Whitaker Nu = ', NuW
write(*,'(A,F12.4)') ' Ranz Nu = ', NuR
write(*,'(A,F12.4,A)') ' Coeff h = ', h, ' W/m2K'
write(*,'(A,F12.4,A)') ' Transfer Q = ', Q, ' W'
write(*,*)
write(*,'(A)') '--- VELOCITY SWEEP ---'
write(*,'(A)') ' V[m/s] Re Nu_Whitaker Nu_Ranz h[W/m2K] Q[W]'
write(*,'(A)') ' -------------------------------------------------------------------------'
do i=1,25
Vs = 0.05d0 + (max(V,0.2d0)*4.0d0 - 0.05d0)*dble(i-1)/24.0d0
Res = rho * Vs * D / mu
NuWs = 2.0d0 + (0.4d0 * Res**0.5d0 + 0.06d0 * Res**(2.0d0/3.0d0)) * Pr**0.4d0 * (mu / mu_s)**0.25d0
NuRs = 2.0d0 + 0.6d0 * Res**0.5d0 * Pr**(1.0d0/3.0d0)
hs = NuWs * kf / D
Qs = hs * As * dT
write(*,'(2X,F8.3,2X,ES10.3,2X,F11.3,2X,F11.3,2X,F10.4,2X,F12.4)') Vs, Res, NuWs, NuRs, hs, Qs
end do
write(*,*)
end program sphere_convection
Solver Description
Models forced convection heat transfer over spheres. Computes Nusselt numbers using Whitaker correlation (which incorporates a correction for temperature-dependent viscosity variations across the boundary layer) and Ranz-Marshall correlation.
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 sphere_convection.f90 -o sphere_convection
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
sphere_convection < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! Sphere diameter D [m]
0.05
! Free stream velocity V [m/s]
5.0
! Free stream temperature Tinf [C]
25.0
! Surface temperature Ts [C]
100.0
! Fluid type (1=Air, 2=Water, 3=Oil)
1
! Custom density [kg/m3] (0=auto)
0.0
! Custom viscosity [Pa-s] (0=auto)
0.0
! Custom thermal conductivity [W/m-K] (0=auto)
0.0
! Custom Prandtl number (0=auto)
0.0
! Custom specific heat [J/kg-K] (0=auto)
0.0
! Custom surface dynamic viscosity [Pa-s] (0=auto)
0.0
0.05
! Free stream velocity V [m/s]
5.0
! Free stream temperature Tinf [C]
25.0
! Surface temperature Ts [C]
100.0
! Fluid type (1=Air, 2=Water, 3=Oil)
1
! Custom density [kg/m3] (0=auto)
0.0
! Custom viscosity [Pa-s] (0=auto)
0.0
! Custom thermal conductivity [W/m-K] (0=auto)
0.0
! Custom Prandtl number (0=auto)
0.0
! Custom specific heat [J/kg-K] (0=auto)
0.0
! Custom surface dynamic viscosity [Pa-s] (0=auto)
0.0