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Carnot Cycle & Heat Pump Limit
Core Numerical Engine in Fortran 90 • 25 total downloads
carnot_heatpump.f90
! =========================================================================
! Source File: carnot_heatpump.f90
! =========================================================================
program carnot_heatpump
implicit none
integer :: cycle_type, iostat_val, i, n_sweep
double precision :: T_hot, T_cold, Q_desired, real_frac
double precision :: eta_carnot, COP_ref, COP_hp
double precision :: W_cycle, Q_hot, Q_cold
double precision :: COP_ref_real, COP_hp_real, eta_real
double precision :: W_real, Q_hot_real, Q_cold_real
double precision :: T_sw, eta_sw, COP_ref_sw, COP_hp_sw
character(len=40) :: cycle_name
! ── Read inputs ─────────────────────────────────────────────
read(*,*,iostat=iostat_val) T_hot
if (iostat_val /= 0) then
write(*,*) 'ERROR: Invalid T_hot input.'
stop
end if
read(*,*,iostat=iostat_val) T_cold
read(*,*,iostat=iostat_val) Q_desired
read(*,*,iostat=iostat_val) cycle_type
read(*,*,iostat=iostat_val) real_frac
if (iostat_val /= 0) then
write(*,*) 'ERROR: Failed to read all inputs.'
stop
end if
! ── Input validation ────────────────────────────────────────
if (T_hot <= 0.0d0) then
write(*,*) 'ERROR: T_hot must be positive (K).'
stop
end if
if (T_cold <= 0.0d0) then
write(*,*) 'ERROR: T_cold must be positive (K).'
stop
end if
if (T_hot <= T_cold) then
write(*,*) 'ERROR: T_hot must exceed T_cold.'
stop
end if
if (Q_desired <= 0.0d0) Q_desired = 100.0d0
if (cycle_type < 1 .or. cycle_type > 3) cycle_type = 1
if (real_frac <= 0.0d0 .or. real_frac > 1.0d0) real_frac = 0.50d0
if (cycle_type == 1) then
cycle_name = 'Carnot Heat Engine'
else if (cycle_type == 2) then
cycle_name = 'Refrigerator (Reversed Carnot)'
else
cycle_name = 'Heat Pump (Reversed Carnot)'
end if
! ── Carnot limits ───────────────────────────────────────────
eta_carnot = 1.0d0 - T_cold / T_hot
COP_ref = T_cold / (T_hot - T_cold)
COP_hp = T_hot / (T_hot - T_cold)
! ── Energy balance based on cycle type ──────────────────────
if (cycle_type == 1) then
! Heat engine: Q_desired = Q_hot (heat input)
Q_hot = Q_desired
W_cycle = Q_hot * eta_carnot
Q_cold = Q_hot - W_cycle
else if (cycle_type == 2) then
! Refrigerator: Q_desired = Q_cold (cooling load)
Q_cold = Q_desired
W_cycle = Q_cold / max(COP_ref, 1.0d-10)
Q_hot = Q_cold + W_cycle
else
! Heat pump: Q_desired = Q_hot (heating load)
Q_hot = Q_desired
W_cycle = Q_hot / max(COP_hp, 1.0d-10)
Q_cold = Q_hot - W_cycle
end if
! ── Real cycle estimates ────────────────────────────────────
eta_real = eta_carnot * real_frac
COP_ref_real = COP_ref * real_frac
COP_hp_real = COP_hp * real_frac
if (cycle_type == 1) then
W_real = Q_desired * eta_real
Q_hot_real = Q_desired
Q_cold_real = Q_hot_real - W_real
else if (cycle_type == 2) then
W_real = Q_desired / max(COP_ref_real, 1.0d-10)
Q_cold_real = Q_desired
Q_hot_real = Q_cold_real + W_real
else
W_real = Q_desired / max(COP_hp_real, 1.0d-10)
Q_hot_real = Q_desired
Q_cold_real = Q_hot_real - W_real
end if
! ── Output ──────────────────────────────────────────────────
write(*,'(A)') '============================================================'
write(*,'(A)') ' CARNOT, REVERSED CARNOT & HEAT PUMP'
write(*,'(A)') '============================================================'
write(*,*)
write(*,'(A)') '--- INPUTS --------------------------------------------------'
write(*,'(A,F12.2,A)') ' Hot Reservoir T_hot = ', T_hot, ' K'
write(*,'(A,F12.2,A)') ' Hot Reservoir T_hot = ', T_hot-273.15d0, ' C'
write(*,'(A,F12.2,A)') ' Cold Reservoir T_cold = ', T_cold, ' K'
write(*,'(A,F12.2,A)') ' Cold Reservoir T_cold = ', T_cold-273.15d0, ' C'
write(*,'(A,F12.2,A)') ' Q_desired = ', Q_desired, ' kW'
write(*,'(A,A)') ' Cycle Type = ', trim(cycle_name)
write(*,'(A,F10.4)') ' Real Cycle Factor = ', real_frac
write(*,*)
write(*,'(A)') '--- CARNOT LIMITS -------------------------------------------'
write(*,'(A,F10.6)') ' Carnot Efficiency = ', eta_carnot
write(*,'(A,F10.2,A)') ' Carnot Efficiency = ', eta_carnot*100.0d0, ' percent'
write(*,'(A,F10.4)') ' COP Refrigeration (max) = ', COP_ref
write(*,'(A,F10.4)') ' COP Heat Pump (max) = ', COP_hp
write(*,'(A)') ' COP_hp = COP_ref + 1 (verified)'
write(*,*)
write(*,'(A)') '--- ENERGY BALANCE (IDEAL) ----------------------------------'
write(*,'(A,F12.4,A)') ' Q_hot = ', Q_hot, ' kW'
write(*,'(A,F12.4,A)') ' Q_cold = ', Q_cold, ' kW'
write(*,'(A,F12.4,A)') ' W_cycle = ', W_cycle, ' kW'
write(*,*)
write(*,'(A)') '--- REAL CYCLE ESTIMATES ------------------------------------'
write(*,'(A,F10.4)') ' Real Efficiency = ', eta_real
write(*,'(A,F10.2,A)') ' Real Efficiency = ', eta_real*100.0d0, ' percent'
write(*,'(A,F10.4)') ' Real COP Refrigeration = ', COP_ref_real
write(*,'(A,F10.4)') ' Real COP Heat Pump = ', COP_hp_real
write(*,'(A,F12.4,A)') ' Real W_cycle = ', W_real, ' kW'
write(*,'(A,F12.4,A)') ' Real Q_hot = ', Q_hot_real, ' kW'
write(*,'(A,F12.4,A)') ' Real Q_cold = ', Q_cold_real, ' kW'
write(*,*)
! ── Sensitivity sweep: T_cold from 200 K to T_hot-5 ────────
n_sweep = 40
write(*,'(A)') '--- SENSITIVITY: PERFORMANCE VS T_COLD ----------------------'
write(*,'(A)') ' T_cold[K] eta_Carnot COP_ref COP_hp'
write(*,'(A)') ' -----------------------------------------------------------'
do i = 1, n_sweep
T_sw = 200.0d0 + dble(i-1) * (T_hot - 5.0d0 - 200.0d0) / dble(n_sweep - 1)
if (T_sw >= T_hot) T_sw = T_hot - 1.0d0
eta_sw = 1.0d0 - T_sw / T_hot
COP_ref_sw = T_sw / max(T_hot - T_sw, 1.0d-10)
COP_hp_sw = T_hot / max(T_hot - T_sw, 1.0d-10)
write(*,'(F10.2,4X,F10.6,4X,F10.4,4X,F10.4)') T_sw, eta_sw, COP_ref_sw, COP_hp_sw
end do
write(*,*)
write(*,'(A)') '--- CORRELATIONS USED ---------------------------------------'
write(*,'(A)') ' Carnot efficiency: eta = 1 - T_cold/T_hot'
write(*,'(A)') ' COP_refrigeration = T_cold / (T_hot - T_cold)'
write(*,'(A)') ' COP_heat_pump = T_hot / (T_hot - T_cold)'
write(*,'(A)') ' COP_hp = COP_ref + 1'
write(*,'(A)') ' Real cycle: multiply ideal COP by factor (0.4-0.6 typical)'
write(*,'(A)') ' Energy balance: Q_hot = Q_cold + W'
end program carnot_heatpump
Solver Description
Solves the theoretical limits of thermodynamic cycles operating between hot and cold temperature reservoirs. Calculates Carnot efficiency for heat engines, Carnot COP for refrigerators and heat pumps, and estimates real cycle performance metrics (net work, heat exchange, actual efficiency/COP) using a user-defined fraction of Carnot (real cycle factor).
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 carnot_heatpump.f90 -o carnot_heatpump
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
carnot_heatpump < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! Hot reservoir temperature TH [K]
773.15
! Cold reservoir temperature TL [K]
303.15
! Desired heat or power Q [kW]
500000.0
! Cycle type (1=Power Cycle, 2=Refrigeration, 3=Heat Pump)
1
! Real cycle factor (fraction of Carnot)
0.50
773.15
! Cold reservoir temperature TL [K]
303.15
! Desired heat or power Q [kW]
500000.0
! Cycle type (1=Power Cycle, 2=Refrigeration, 3=Heat Pump)
1
! Real cycle factor (fraction of Carnot)
0.50