Multi-Physics Engineering Suite & Supplier Reference Platform

Thermodynamic Cycle Equations & 2D CoolProp Mesh Isentropic Compression

• Fluid State Properties & Live-Drag Parity: Solved via Helmholtz Energy Equations of State (CoolProp 8.0) and client-side 2D CoolProp isoline mesh interpolators (interpHFromPS / interpHFromPT + exact (∂h/∂s)_p = T high-entropy extrapolation, ≤ 0.025 % deviation vs. Python CoolProp 8.0 across 12-point curved compression polylines).
• Isentropic Efficiency: At η_is = 1.00, compression path 1 → 2 follows the exact CoolProp isentrope s = s₁; irreversible compressor work scales as h₂ = h₁ + (h_2s − h₁) / η_is.
• Scope: Thermodynamic refrigerant cycle state points only (no motor, inverter, or mechanical shaft losses; no EN 378 / ASHRAE 34 charge limits or EN 14511 seasonal ratings).
• R744 (CO₂): In temperature mode, high-side pressure is solved via a 19-point optimal COP search above p_crit for the specified gas-cooler outlet temperature; in pressure mode, gas-cooler outlet defaults to T_crit + 15 K.
• ORC: Feed pump and expander use the selected isentropic efficiency, with automatic cavitation warning at saturated pump inlet.

Darcy-Weisbach Hydraulics & Friction Factor

• One continuous expression: f = 64/Re in laminar flow (Hagen-Poiseuille), Colebrook/Moody values in turbulent flow, no jump at Re = 2300. Between Re 2300 and 4000 the flow regime is uncertain; the value is an interpolation (about ±20 %) and is marked in the chart and as a warning.
• Roughness: ε = 1.5 µm (drawn copper / stainless tube) as default assumption, editable (0 = hydraulically smooth); validity up to ε/D = 0.05.
• Minor losses: Σζ of bends, tees and fittings is entered by the user (default 0); inlet length, manifolds and height differences are not modelled.
• Hydraulic and pump power: P_hyd = V̇ · Δp, P_shaft = P_hyd / η_pump (η_pump = 55 % assumption, editable).
• Plausibility: warnings above 3 m/s (guideline for cooling circuits) and above about 2 bar pressure drop (typical circulation pumps).
• Fluid properties: ρ, μ, c_p of the selected coolant from CoolProp 8.0 tables at the entered fluid temperature (linear interpolation, viscosity in ln μ; the glycol tables end at 100 °C, water above 95 °C at p_sat + 50 kPa); outside the table range the value is clamped and a warning is shown, below the freezing point an error. The synthetic thermal fluid option uses the CoolProp TD12 incompressible fit.
• Method: Churchill 1977, VDI Heat Atlas (friction in pipes) — no standard is claimed.

Linear-elastic beam theory (Euler-Bernoulli bending + Timoshenko shear)

• Shear deformation: always included (Timoshenko); it is about 3 % of the deflection at L/h = 10, 11 % at L/h = 5 and dominates below L/h = 1. Below L/h = 10 a note is shown, below L/h = 5 the result is marked as indicative (local stresses at supports and load points).
• Self-weight (optional): added as a uniform load W = m · g (centre load: M += W·L/8, cantilever: M += W·L/2).
• Large deformation: linear theory only; from w/L > 0.1 a warning is shown (the real deflection is smaller, the stress higher).
• Deflection limit: L/300 as editable guideline (cantilever: 2·L/300); not a code requirement. Safety factor warnings below 1.5 (guideline) and 1 (yielding).
• Material data (minimum values, condition and thickness dependent, verify with the material certificate): EN AW-6063-T6 R_p0.2 170 MPa for t ≤ 10 mm (EN 755-2); S235JR R_eH 235 MPa for t ≤ 16 mm (EN 10025-2); Cu-ETP R240 R_p0.2 180 MPa (EN 1652); Ti-6Al-4V annealed 828 MPa (ASTM B348 minimum). E: 69 / 210 / 117 / 114 GPa (typical).
• Method: textbook beam theory (e.g. Gross/Hauger/Schröder/Wall, Technische Mechanik 2); no standard verification (no EN 1993 / DIN 1025 section checks).

Trace Width: IPC-2152 (Brooks & Adam fit) and IPC-2221 · Spacing: IEC 60664-1:2020 Table Lookup

• IPC-2152 method: Brooks & Adam (2015) curve fit to the IPC-2152 external-trace data (PCD&F, 29 May 2015, Eq. 5; same coefficients in KiCad's track-width calculator). The article states no explicit validity range; the fit was validated for 2 oz external traces. The checked range (external traces, 0.5–3 oz copper, ΔT ≤ 100 K) is assumed to be the range of the published IPC-2152 curves — a warning is shown outside. IPC-2152 board-thickness and copper-plane modifiers are not applied (planes and thicker boards lower ΔT, so this is on the safe side). Internal layers: IPC-2152 data show internal traces running cooler than external ones, so the external fit is used as a conservative bound.
• IPC-2221: the classic IPC-D-275 chart fit (internal k = 0.024 ≙ 2.60 × area), thickness 1.378 mil/oz; extrapolated outside 0–35 A, ≤ 10.2 mm (400 mil), 0.5–3 oz. It is a historic fit and gives clearly smaller widths than the IPC-2152 fit at high currents (25 A, 2 oz, 20 K: 8.4 mm instead of 22.8 mm); a warning is shown from 25 % difference, the larger value is the safer design value.
• IEC 60664-1:2020 (Ed. 3.0; table numbers as in Ed. 3.1:2025): Table F.1 rows 50–1000 V (the Ed. 3 DC rows 1250/1500 V are not covered), Table F.2 case A 0.33–12 kV, altitude factors 2000–5000 m (next higher altitude row, no interpolation), Table F.5 creepage: general columns 10–2500 V, printed-wiring columns 25–1000 V (outside: general column, conservative). Creepage between table rows: linear interpolation, rounded up to the decimals of the table values. Reinforced insulation: clearance at the next higher preferred impulse voltage (330, 500, 800, 1500, 2500, 4000, 6000, 8000, 12000 V), creepage × 2. Every table cell is confirmed by ≥ 2 independent public sources (list in shared_engine/norm_tables.js).
• Not covered: functional insulation, clearances for steady-state / recurring peak voltages (Table F.8), homogeneous-field case B, voltages above the verified rows, solid insulation and partial discharge. AC is in scope up to 1000 V, DC up to 1500 V.
• Sources and reservation: the trace width is a fit to IPC-2152 data (PCD&F 2015), not a calculation by the standard; the spacing tables come from public secondary sources of IEC 60664-1:2020 (14 sources, 8 cells with deviating values documented) and are not verified against the standard text. For safety proofs use the standards themselves.
• Practicality: a warning is shown above a 50 mm trace width (use copper pours, parallel layers, busbars).

Reference matrix: creepage, pollution degree 2, material group IIIa (basic insulation)

Psychrometric Formulations & Condensation Prevention

• Constants (Hyland & Wexler 1983, ASHRAE Fundamentals 2009, Ch. 1, eq. 5, 6): C1 = −5.6745359·10³, C2 = 6.3925247, C3 = −9.677843·10⁻³, C4 = 6.2215701·10⁻⁷, C5 = 2.0747825·10⁻⁹, C6 = −9.484024·10⁻¹³, C7 = 4.1635019; C8 = −5.8002206·10³, C9 = 1.3914993, C10 = −4.8640239·10⁻², C11 = 4.1764768·10⁻⁵, C12 = −1.4452093·10⁻⁸, C13 = 6.5459673. Supercooled water below 0 °C: Murphy & Koop (2005). Enhancement factor: Buck (1981).
• Accuracy: compared with CoolProp 8.0 (HAPropsSI) on a grid of −20…80 °C, 1…100 % RH, 0.5…2.5 bar: up to 50 °C the dew point differs by ≤ 0.05 K, the humidity ratio by ≤ 0.2 % and the enthalpy by ≤ 0.5 kJ/kg; up to 80 °C by ≤ 0.07 K and ≤ 0.8 % (ideal-mixture model, steam-rich air).
• RH below 0 °C: by default RH refers to saturation over ice (ASHRAE, CoolProp). Hygrometers calibrated over liquid water (WMO convention) read lower values for the same state: choose “over liquid water” in the model assumptions (at −20 °C: 80 % over water = 97 % over ice).
• Wet bulb near 0 °C: two solutions exist (liquid-water wick and frozen wick). The liquid-water wick is shown; the ice-bulb value is added as a note when both exist (up to ≈ 0.7 K apart).
• Not valid: when RH · f · p_ws exceeds 95 % of the total pressure the water would boil; the results are shown as “n/a”.
• Cold plate protection: a cooled surface below the dew point collects condensate. The ampel is red at a margin ≤ 0 K, amber below the required margin (default 2 K, an assumption), green above. The input is the surface temperature, not the coolant temperature; sensor tolerance and surface temperature gradients are not part of the margin.
• Source: ASHRAE Handbook — Fundamentals 2009, Chapter 1 (eq. 5, 6, 33, 35). No standard is claimed.

Moist Air Density & Transport Properties

• Constants: M_a = 28.96546 g/mol, M_v = 18.01528 g/mol, R = 8.314472 J/(mol·K); a₀ = 1.58123·10⁻⁶ K/Pa, a₁ = −2.9331·10⁻⁸ Pa⁻¹, a₂ = 1.1043·10⁻¹⁰ K⁻¹Pa⁻¹, d = 1.83·10⁻¹¹ K²/Pa² (CIPM-2007, Picard et al. 2008). The vapour and cross terms of CIPM-2007 are not used. p_ws and f: Hyland & Wexler (1983) / Buck (1981), same as the Dew Point tool.
• Transport: dry air μ = 18.2176 μPa·s · (T/293.15)^1.5 · (293.15 + 119.25)/(T + 119.25) and k = 0.025904 W/(m·K) · (T/293.15)^1.5 · (293.15 + 164.62)/(T + 164.62) (Sutherland form, fitted to CoolProp 8.0 dry air, ≤ 0.4 % from −40 to 200 °C); steam: IAPWS dilute-gas correlations (R12-08, R15-11).
• Accuracy (compared with CoolProp 8.0 humid air, −30 … 100 °C, 0.3 … 3 bar, 0 … 100 % RH): density ≤ 0.36 % up to 60 °C and 2 bar, ≈ 1 % in hot, nearly saturated air (real-gas effects of steam are not modelled); μ ≤ 2.2 % and k ≤ 3.1 % up to 60 °C and 2 bar, up to 4 % and 5 % at 100 °C. Pressure dependence of μ and k (< 1 % at 3 bar) is neglected.
• Humid air paradox: water vapour (18.02 g/mol) is lighter than dry air (28.97 g/mol); more humidity lowers the density.
• Reference density: ρ₀ = 1.2041 kg/m³ is dry air at 20 °C and 101.325 kPa (R_d = 287.058 J/(kg·K)). Against the ISA sea-level density 1.225 kg/m³ the ratios would be 1.7 % lower.
• Altitude: at 2000 m the ISA pressure is 0.795 bar; with 25 °C and 50 % RH the density is 23 % below ρ₀ (76.6 %), with the ISA temperature (2 °C) 16 % below (83.6 %). “Use ISA temperature” sets the temperature and the ISA reference density is shown as a tile.
• RH limit: if RH · f · p_ws exceeds 95 % of the total pressure (water would boil), RH is limited and a notice is shown.
• Sources: ASHRAE Fundamentals 2009 Ch. 1; CIPM-2007 (Picard et al., Metrologia 45 (2008) 149); IAPWS R12-08 / R15-11; Wilke, J. Chem. Phys. 18 (1950) 517; ISA troposphere formula of ISO 2533 (used only to 11 km, the standard itself is not reproduced).

Liquid Sizing, Choked Flow & Cavitation Index

• Inherent characteristics (idealised): linear K_v = K_vs·h; equal percentage K_v = K_vs·R^(h−1), R = 50 (2 % of K_vs at h = 0, not zero); quick opening K_v = K_vs·√h. Real valves deviate; the installed characteristic (valve authority) is not modelled.
• σ and cavitation: σ ≤ σ_ch means choked flow. Cavitation starts earlier at σ_i, which is manufacturer-specific and not computed; enter it under the model assumptions to get a second threshold.
• Media (20 °C): water ρ 998.2 kg/m³, p_v 0.0234 bar (IAPWS-95); MEG 40 % ρ 1051.9 kg/m³ (CoolProp INCOMP), p_v ≈ 0.019 bar (Raoult estimate); ISO VG 46 oil and diesel: assumed values (p_v 0.001 and 0.005 bar). p_c of water (220.64 bar) is used for all media (effect on Δp_max < 0.01 %). ρ and p_v can be overridden.
• Validity: turbulent liquid flow, no reducers (F_P = 1), no Reynolds-number correction (F_R = 1). Viscous media (ISO VG 46 oil) give lower flows than calculated; the tool warns.
• F_L: typical values 0.90 / 0.75 / 0.60 are manufacturer-specific and depend on the stroke; Δp_max scales with F_L². Enter manufacturer data under the model assumptions.
• Equivalent orifice: sharp-edged orifice with C_d (assumption 0.61, turbulent) that passes the same flow at the same Δp; not an ISO 5167 orifice-plate design.
• Source: equation form of IEC 60534-2-1 for liquids (the standard text is not reproduced). Check the result against the manufacturer sizing data.

Radial Conduction & Outside Film

Outside Film (mode “Computed”)

Condensation Check & Minimum Thickness

• Sign convention: Q' > 0 is heat loss of a warm line, Q' < 0 is heat gain of a cold line. The dew-point margin and t_min are evaluated for cold lines only.
• Material values: λ₁₀, the coefficient c and the service-temperature limits are typical order-of-magnitude values of the material classes, not data-sheet values; enter the declared value of your product. Mineral wool: c ≈ 0.35 %/K, elastomeric foam 0.25 %/K, PIR/PUR 0.20 %/K, aerogel and cellular glass 0.30 %/K; typical service limits: wool 250 °C, foams 110 °C. The linear λ(T) model is an approximation above a mean temperature of about 150 °C.
• Outside film: still indoor air at 1.013 bar, dry-air properties at film temperature; ε = 0.9 for painted, plastic or matt jackets (bright aluminium: 0.05…0.2). Outdoor wind raises h_ext and is not modelled; use the fixed mode.
• Neglected: pipe wall and inner film (the insulation inner surface is at T_fluid), jacket, joints, hangers and supports, moisture in the insulation, vapour diffusion and the latent heat of condensation. For cold lines a vapour barrier or closed-cell insulation is required. The critical radius only matters when r₁ < r_crit (small pipes with high λ or low h_ext); the tool warns in that case.
• Accuracy: against an independent CoolProp-based solution of the same model the heat flow agrees within 0.01 % and the surface temperature within 0.05 K. The real uncertainty is dominated by λ (±10…20 %), h_ext (±20 %) and the installation. The dew-point margin is flagged as unreliable below the combined uncertainty of the RH reading (±3 % RH) and the film coefficient.
• Sources: Fourier radial conduction in a cylinder (any heat-transfer text); Churchill & Chu, Int. J. Heat Mass Transfer 18 (1975) 1049–1053; Hyland & Wexler (1983) for the dew point; ISO 12241, ASTM C680 and VDI 2055 describe complete calculation procedures and are not implemented here.

Free Expansion & Bonded Strip (Timoshenko 1925)

• Stresses: linear inside each layer; the extreme values lie at the outer surfaces and at the interface (the stress jumps at the interface because E differs). Tension is positive. The bonded stress is far below E·α·ΔT of each layer, because the strip bends and relieves the mismatch.
• Concave side: on heating the layer with the lower α is on the concave side, on cooling the layer with the higher α. Layer 1 is drawn on top. δ is shown as a magnitude.
• Reference strength: maximum |σ| of a layer against R_p0.2 (metals, PEEK); maximum tensile stress against the flexural strength (ceramics, silicon, FR4). Typical values, editable; they depend on temper, grade and surface by a factor of 2…3 (copper: annealed ≈ 70, half-hard 250, hard 310 MPa). Above the strength the elastic result is not valid.
• Validity: the tool warns at κL > π (more than a half circle), withholds the deflection at κL > 2π (more than a full circle), warns at δ/h > 0.5 (wide plates become doubly curved at about δ/h > 1, the strip result then over-predicts the deflection), above the glass transition of FR4 (≈ 130 °C) and PEEK (143 °C onset) and outside −60 … +250 °C.
• Material data: mean values near room temperature (20…100 °C), constant in ΔT. Cross-checked with supplier data sheets for 6061-T6, 6063-T6, C11000, Ti-6Al-4V, 316L, Invar 36, Kovar, PEEK, FR4, silicon and the ceramics; the spread between sources and grades is 2…20 % (Invar α 1.2…1.6, Si₃N₄ α 2.7…3.4, PEEK α 45…55 ppm/K, ceramics E ±10 %). Polymers and ceramics are grade- and direction-dependent.
• Accuracy: against a 2D plane-stress finite-element solution of the free strip (L/h = 25…50) the deflection agrees within 1 % and the interface stresses within 1.5 MPa; the equilibrium solution reproduces Timoshenko's closed form to rounding error.
• Sources: S. Timoshenko, Analysis of bi-metal thermostats, J. Opt. Soc. Am. 11 (1925) 233–255; thin-film limit: Stoney (1909); material data: supplier data sheets and handbook values as listed above.

Permissible Assembly Preload (tension + thread torsion)

Tightening Torque

Tightening Factor and Setting Torque

• What the tiles mean: F_M,zul and M_A,zul belong together (upper end of the scatter band). The wrench is set to M_A,nom: with a symmetric scatter the preload then lies between F_M,min = F_M,zul/α_A and F_M,zul. Setting M_A,zul directly would let the scatter push the equivalent stress above ν · R_p0.2min (for α_A = 1.6 to about 1.11 · R_p0.2min at ν = 90 %).
• Torque split: head bearing friction about 45…50 %, thread friction 35…40 %, pitch (the part that stretches the bolt) 12…16 % for μ_G = μ_K = 0.12; the values are computed from the inputs.
• Tightening factor α_A: VDI 2230 guide values for torque-controlled tightening: setpoint determined by tests 1.4…1.6 (scatter ±17…23 %), setpoint from estimated friction 1.6…2.0 (class B) or 1.7…2.5 (class A), impact wrench or hand tightening 2.5…4. The upper end of the range is used (it guarantees F_M,min). Methods without torque control (rotation-angle or yield-point controlled 1.2…1.4, hydraulic 1.1…1.4, ultrasonic 1.1…1.2) are not offered; enter α_A manually for them.
• Friction: μ_G and μ_K are the values at the moment of tightening and the largest source of error. VDI 2230 friction classes: A 0.04…0.10, B 0.08…0.16, C 0.14…0.24, D 0.20…0.35, E ≥ 0.30 (unlubricated Zn/Fe, austenitic steel, Al/Mg). If μ is uncertain, use the lowest probable value for the yield check.
• Property classes: ISO 898-1 minimum yield strength: 8.8 640 MPa up to M16 and 660 MPa above, 10.9 940 MPa, 12.9 1100 MPa. Stainless classes A2-70 (450 MPa) and A4-80 (600 MPa) belong to ISO 3506-1, which tabulates them up to M24; for M30 and M36 the property class must be agreed with the supplier. Unlubricated stainless threads gall.
• Head diameter: D_Km uses the minimum bearing diameter d_w of hexagon head screws (ISO 4014/4017, grade A to M24, B above) and the medium clearance hole d_h (ISO 273): M10 12.8 mm, M16 20.0 mm, M20 25.1 mm. Washers, flange or socket heads change D_Km and with it the head torque (M_K ∝ D_Km); enter your own value under Model assumptions.
• Engagement length: guideline for cut internal threads (coarse thread, tolerance 6g/6H, without countersink and run-out) from practical trials of a fastener-supplier engineering table, in multiples of d (e.g. 0.9 d for S355 with class 8.8, 1.4 d for grey cast iron with 12.9). Where the table lists it, the theoretical value of the VDI 2230 stripping formula is shown too; it is higher and the safer choice. Not a calculation: the exact length follows from the VDI 2230 stripping check with the actual strength of the internal thread; there is no guideline for stainless screws or for class 12.9 in aluminium.
• Accuracy: against the rounded table values of a VDI 2230:2015 data sheet (M10, M16, M20 in 8.8, 10.9 and 12.9; μ = 0.12, ν = 90 %) F_M agrees within 0.5 % and M_A within the rounding of the table; the numerical solution of the von Mises condition reproduces F_M,zul within 0.1 %. The rounded constants 0.16 and 0.58 differ from the exact thread torque by up to 0.4 %.
• Sources: VDI 2230 Blatt 1 (2003, 2015) “Systematic calculation of highly stressed bolted joints”; ISO 898-1:2013; ISO 3506-1; ISO 724, ISO 4014/4017, ISO 273.

Rate, Stresses and Lengths (DIN EN 13906-1)

Buckling (Wahl, DIN 2089-1)

Natural Frequency

• Stress factor: DIN EN 13906-1 uses the Bergsträsser factor; the Wahl factor K_W = (4w − 1)/(4w − 4) + 0.615/w is 0.5 % (w = 20) to 1.4 % (w = 4) higher. The correction is for cyclic loading; the static check uses the uncorrected τ.
• Permissible stress: τ_zul = 0.5 · R_m at the working stroke and τ_c,zul = 0.56 · R_m at solid length are the design rules for cold-formed, not preset springs of patented-drawn steel wire. For stainless wire and CuBe2 no standard value was checked: 0.45 · R_m is used (assumption, editable). The result is a guideline check, not a fatigue proof.
• Tensile strength: steel: EN 10270-1 Table 3, grade SH/DH, lower value, interpolated (d = 3 mm: 1840 MPa; 10 mm: 1410 MPa); wire of grades SL, SM and DM is weaker. Stainless 1.4310: EN 10270-3 Table 2, grade NS, minimum value, table ends at 10 mm. CuBe2: 1280 MPa, lower end of the CW101C range 1280…1480 MPa, depends on the temper. Straightened rods can be up to 10 % weaker. Enter your own R_m under Model assumptions.
• Moduli: G = 81.5 GPa (steel); stainless 70…73 GPa depending on strength (upper value used); CuBe2 47 GPa estimated from E = 125…130 GPa. E for buckling: 206 / 190 / 127.5 GPa; density 7850 / 7900 / 8250 kg/m³. G scales the rate directly (editable).
• Accuracy of R: the standard formula omits the deflection from direct shear (+1/(2w²): 0.8 % at w = 8, 3.1 % at w = 4) and the pitch angle; n_t = n + 2 assumes one inactive end coil on each side. Manufacturing tolerances (DIN 2095) come on top. Valid for 4 ≤ w ≤ 20.
• Lengths: L_c is calculated without the wire tolerance (the standard uses d_max). The stroke is limited to L₀ − L_c; above s_n = L₀ − L_n the minimum coil clearance S_a is not kept.
• Buckling: end support ν = 0.5 both ends clamped, 0.7 one clamped and one guided, 1 both ends on flat plates, 2 one end free. The spring cannot buckle if L₀/D_m ≤ √C₂/ν (about 2.6/ν for steel, the known rule L₀/D < 2.63 for plate-supported springs); beyond that, s_K is the critical deflection and the spring must be guided if s > s_K.
• Natural frequency: exact solution for a uniform spring fixed at one end with the payload at the other (reduces to m + m_F/3 for light springs); the surge frequency is the first natural frequency of the free spring between fixed ends; excitation near f_surge/k causes surge and breaks springs.
• Sources: DIN EN 13906-1 (cylindrical helical springs, calculation and design), DIN 2089-1, DIN 2095, EN 10270-1, EN 10270-3; A. M. Wahl, Mechanical Springs.

DIN 43671 Ampacity (Table Lookup)

Thermal Model (Secondary Estimate)

Voltage Drop and Loss

• DIN 43671:1975-12 table: continuous current of copper bars E-Cu F30, indoor, 35 °C air, 65 °C final bar temperature, bars vertical (width vertical), gap between bars = bar thickness (4 bars: 2 + 2), AC up to 60 Hz (includes skin and proximity effect) and DC; 26 standard sizes 12 × 2 … 200 × 10 mm. Values are used only where ≥ 2 independent sources agree (Deutsches Kupferinstitut DKI & DIN 43671 reference handbooks): all single-bar AC/DC values (DC painted 100 × 5 / 120 × 10 / 160 × 10 / 200 × 10: bare value used, conservative), AC 2–4 bars except 25 × 5 painted (3 bars) and 100 × 10 bare (4 bars), where the sources disagree. DC 2–4 bars: one source only — not covered.
• Temperature factor k2: the DIN 43671 k2 diagram is approximated by √((ϑ_S − ϑ_U)/30 K); it reproduces the published read-offs at 35 °C air (bar 55/75/85/105/125 °C → 0.80/1.17/1.29–1.32/1.55/1.75) within ±2.5 %. Used only inside the diagram range (air 0–60 °C, bar 50–125 °C). Factors k1 (conductivity), k3 (horizontal bars), k4 and k5 (altitude) were found in one source only and are not applied.
• Skin effect: the DIN 43671 AC columns already contain skin and proximity effect. For the thermal model under AC, k_s = R_ac/R_dc is taken from the DIN single-bar ratings of the same size, k_s = (I_DC/I_AC)² at equal heating (e.g. 50 × 10: 1.05, 100 × 10: 1.15, 200 × 10: 1.28); for other sizes the k_s input is used (typically 1.05–1.15 for copper bars thicker than 10 mm at 50 Hz; the field shows which value is in use). DC: k_s = 1.
• Thermal model — convection and radiation: the heat transfer coefficient follows from the geometry and the temperature rise (free convection after Churchill & Chu, air properties at the film temperature, plus radiation to surroundings at air temperature), it is not a constant. The only fitted quantities are the effective emissivities (bare 0.27, painted 0.75); with them the model gives 30 K ± 1.5 K at the DIN 43671 table current for all 226 tabulated cells (26 sizes, AC/DC, bare/painted, 1–4 bars; 4.8 % at most). That is the accuracy within the table conditions; for other air temperatures, mounting (horizontal bars, enclosures, neighbouring bars) and non-standard sizes expect about ±15 % in temperature rise. Round conductors: horizontal cylinder in free air, no insulation.
• Bar packages: the cooling of a bar in a package of n bars is reduced by the package factor φ_n = (I_n/(n·I_1))² taken from the DIN 43671 AC columns of the same size and surface (painted falls back to bare where the painted value is missing). Between standard sizes φ_n is interpolated; for round conductors the mean of the table is used (generic, warning). φ_n can be entered under Model assumptions. DC packages use the AC package factor (the DC columns for 2–4 bars are not covered).
• Plausibility check of the table: because the model is physically independent of the table, it also serves as a check of the tabulated currents: no cell deviates by more than 1.4 K from 30 K, i.e. a transcription error of more than about 3 % in current would be visible.
• Material data: copper 58 MS/m (ρ₂₀ = 17.241 nΩ·m, 100 % IACS, annealed — hard-drawn bars are slightly less conductive), α = 0.00393 K⁻¹ (IEC 60028); aluminium EN AW-6101B, temper T7: conductivity ≥ 32 MS/m (ρ₂₀ = 31.25 nΩ·m; T6: ≥ 30 MS/m), α ≈ 0.0040 K⁻¹ (typical value, not verified for this alloy) — the former value 28.3 nΩ·m was that of E-Al 1350 (61 % IACS), not of 6101B.
• Voltage drop: only the ohmic part unless a reactance X' is entered (3-phase only, typically 0.1–0.3 mΩ/m for busbars; depends on spacing). The resistance is taken at the model temperature of the conductor. Voltage drop and loss are not limited by the DIN rating.
• Not covered: aluminium DIN 43670 (the public tables found disagree), non-standard sizes and round conductors (thermal model only), insulated cables (IEC 60364-5-52, VDE 0298-4), enclosures and forced ventilation, short-circuit strength (DIN EN 60865), harmonics.
• Sources: DIN 43671:1975-12; S. W. Churchill, H. H. S. Chu, Int. J. Heat Mass Transfer 18 (1975) 1049 (vertical plate) and 1323 (horizontal cylinder); IEC 60028; EN 573-3 and EN 755-2 (EN AW-6101B); Incropera/DeWitt, Fundamentals of Heat and Mass Transfer (air properties).

Material Indices on the Axes

• Reading the chart: on log axes an index appears as a straight line of slope 1 (k/ρ, E/ρ, k/α) or 2 (E^½/ρ against E and ρ); materials towards the upper left (or the corner of the wanted property pair) are better for that index. Materials without a value on one axis (for example soft thermal-interface materials have no meaningful modulus or strength) and values ≤ 0 on a log axis (carbon fibre has a negative CTE) are not plotted; the list is given above the chart.
• Strength σ: yield strength (0.2 % proof) for metals and most polymers, flexural strength for ceramics and semiconductors, tensile strength for the epoxy, indium foil, pyrolytic graphite and the carbon laminate; strengths of brittle materials depend on surface and size (Weibull) and are not comparable with metal yield strengths in design.
• State per material: temper, grade, direction and temperature are shown under the tiles (for example 6063-T6, CW614N R430, CuBe age-hardened, in-plane for pyrolytic graphite and PBN, along the fibres for the carbon laminate). Anisotropic materials show one direction only.
• Data basis: rounded handbook values at 20…25 °C: ASM Handbook Vol. 2 and Aluminum Association Aluminum Standards and Data (Al and Cu alloys), EN 10025-2, EN 10088-2, EN 12164, CRC Materials Science and Engineering Handbook, ASM Engineered Materials Handbook Vol. 4, Ashby (polymers). Checked against published data sheets for 6063-T6, brass CW614N, PBN and indium foil. Maximum service temperature is an indicative continuous-use limit in air (or inert atmosphere where stated), not a standard value.
• Not covered: temperature dependence, processing and supplier-specific grades, cost, selection lines and optimisation (Pareto fronts), electrical resistivity.
• References: M. F. Ashby, Materials Selection in Mechanical Design, 5th Edition; ASM Handbook Vol. 2.

Summer cooling (design point)

Winter heating (design point)

• Air flows: the fresh airflow is referred to the outdoor state, the supply airflow to the cabin state; the mass flows follow from the dry-air density of the respective state (not a fixed 1.18 kg/m³). The fresh air is part of the supply air and is mixed with the recirculated air ahead of the evaporator, so it loads the coil but not the cabin: the supply air only has to carry the cabin-side sensible load.
• Ventilation latent load: only if the outdoor air is more humid than the cabin (no credit for drying; the cabin humidity is not controlled upwards). If the required supply air would be supersaturated at T_sup, the evaporator can only deliver saturated air and the cabin humidity settles below the set value; this is reported.
• Editable assumptions: R_si = 0.13 and R_se = 0.04 m²K/W (horizontal heat flow as used for building components in ISO 6946; the outer resistance of a moving vehicle is lower), occupants 80 W sensible + 60 W latent (seated work, 1 met = 58.2 W/m² × 1.8 m² ≈ 105 W per person; 1…2 met typical), cabin 50 % RH, minimum supply temperature 5 °C (evaporator icing, draught), ambient pressure 101.325 kPa. λ of the insulation: typical values (PU foam 0.024, mineral wool 0.038, EPS 0.035, silica aerogel 0.015 W/(m·K)); own value possible.
• Solar input: g is the total solar energy transmittance of the glazing (in automotive glazing: TTS, a measured quantity per ISO 13837, depends on the test convention); I_sol is the irradiance on the glazing plane — enter an effective area-weighted value (inclined windscreen and roof windows receive less than 1000 W/m² at normal incidence).
• Not included: solar heating of opaque panels (sol-air temperature), thermal mass and pull-down time, infiltration and leakage, engine / drivetrain / electronics heat, door openings, transient behaviour. U_wall neglects thermal bridges and the resistance of the sheet-metal skin.
• Accuracy: the psychrometric state values agree with CoolProp humid air to ≤ 0.3 %; the model result is dominated by the inputs (g, I_sol, R_se, leakage) and is not quantified here. For a specification, verify with the test methods of ISO 10263-4 / -6.
• Standards referred to: ISO 10263-4 (Earth-moving machinery — Operator enclosure environment — HVAC test method and performance), ISO 10263-6 (… determination of effect of solar heating), ISO 13837 (Road vehicles — Safety glazing materials — Method for determining solar transmittance), ISO 6946 (surface resistances); moist-air relations after ASHRAE Handbook — Fundamentals, Chapter 1.

Air duct (incompressible, dry air)

• Validity: incompressible flow — the result is marked invalid for Ma > 0.3 or when Δp_total exceeds 10 % of the absolute pressure. Colebrook–White: ε/D ≤ 0.05, Re ≥ 4000. Huebscher: aspect ratio up to about 8; laminar flow in rectangular ducts is indicative only.
• Roughness ε: typical values are about 0.09–0.15 mm for galvanised sheet-metal duct and 1–3 mm for flexible duct (ASHRAE Handbook — Fundamentals, Duct Design). Ambient pressure is an editable assumption; humidity of the air is neglected (< 1 % in ρ).
• Accuracy: in the turbulent range the friction factor, ρ and μ agree with a Colebrook–White calculation with CoolProp air properties to within 0.2 % (checked on a grid of circular and rectangular ducts, −20 … 80 °C). Real ducts deviate by 10–20 % (seams, joints, fittings, actual roughness).

Natural-gas pipe (Renouard)

• Check: d = 0.6, L = 112 m, Q = 20 Nm³/h, D = 68.8 mm gives Δp = 0.505 mbar (low-pressure form).
• Validity: Q/D < 150, turbulent flow (Re > 4000), Ma < 0.3 at the pipe end, medium-pressure form up to about 4 bar gauge. A flow that would leave no overpressure at the pipe end is reported as not deliverable. Switching between the two forms at 50 mbar changes the result by a few percent.
• Accuracy: Renouard is an empirical correlation. Against an isothermal Darcy–Weisbach calculation (Colebrook–White, CoolProp methane/ethane, ε = 10…45 µm) it deviates by about −30 … +30 % within its validity range (median +9 … +20 %, i.e. conservative for smooth pipes). Use the result for sizing, not for guarantee values.

Water & steam (IAPWS-IF97, release R7-97(2012))

• State lookup (T, p): Region 1 (compressed liquid, Gibbs g(p,T)), Region 2 (superheated vapour, g(p,T)), Region 3 (near-critical / supercritical, Helmholtz f(ρ,T); ρ(p,T) by root bracketing on the basic equation, stable branch from p_s(T)), Region 4 (saturation p_s(T), T_s(p)), Region 5 (1073.15–2273.15 K, p ≤ 50 MPa) and the B23 boundary. Valid 0…800 °C at p ≤ 1000 bar and 800…2000 °C at p ≤ 500 bar; inputs outside are rejected with a notice.
• Saturation modes: given T (0 … 373.946 °C) or p (0.00611 … 220.64 bar) the tool returns T_s, p_s, v′, v″, ρ, h′, h″, h_fg = h″ − h′, s′, s″, c_p and, for a vapour quality x, the wet-steam values v = v′ + x·(v″ − v′), h, s, u (the same linear mixing rule).
• Accuracy: deviation from the IAPWS verification tables ≤ 3·10⁻⁹ (table rounding); vs. iapws 1.5.5 / CoolProp IF97 ≤ 5·10⁻¹³ in ρ (CoolProp's Region 3 backward v(p,T) differs by up to 0.24 % near the critical point); IF97 vs. the IAPWS-95 reference EOS (CoolProp "Water"): Δρ/ρ ≤ 3.4·10⁻⁵ (Region 1), ≤ 3.2·10⁻⁴ (Region 2), ≤ 1.1·10⁻⁴ (Region 5), up to 1.8 % right at the critical point (Region 3; h up to about 10 kJ/kg, c_p up to about 24 %). Below 0.01 °C and about 1.3 bar the stable phase is ice; the liquid values are then metastable. Metastable vapour, backward equations and transport properties are not implemented.

Saturation tables (CoolProp 8.0.0 HEOS)

• Reference state (h, s): IIR convention for all 12 fluids: h = 200 kJ/kg and s = 1 kJ/(kg·K) for the saturated liquid of the pure refrigerant at 0 °C. For the blends the IIR states of the pure components apply, so h_L(0 °C) = 206.5 (R454B), 202.4 (R513A) and 200.1 kJ/kg (R515A). Differences such as Δh_vap and the superheat do not depend on the reference state; for absolute values from other tables add the constant offset between the two reference states.
• Accuracy of the interpolation (random off-grid temperatures, all 12 fluids, compared with CoolProp): for T ≤ T_c − 15 K p, ρ, c_p, μ_L, k_L ≤ 0.05 % and h ≤ 0.005 kJ/kg; closer than 15 K to T_c p, ρ ≤ 0.1 %, h ≤ 0.1 kJ/kg, μ_L, k_L ≤ 0.5 % and c_p up to about 4 % (c_p diverges at T_c). Superheat enthalpy (ΔT_sh between the table nodes 0.25 … 30 K): ≤ 0.15 kJ/kg for T ≤ T_c − 15 K, ≤ 0.2 kJ/kg closer to T_c. The uncertainty of the equations of state themselves is not included.
• Range: the table starts at −60 °C (R600a and R513A −50 °C, R515A −40 °C, R744 −56 °C, R1233zd(E) −30 °C) and ends 0.5 K below T_c. CoolProp's mixture solver does not converge at every node close to T_c: the blends end at 70 °C (R454B, T_c = 78.3 °C), 90.5 °C (R513A, T_c = 95.4 °C) and 106.5 °C (R515A, T_c = 108.4 °C); grid nodes missing inside the range (gaps ≤ 4 K) are bridged by the interpolation. T_ref outside the table has no value.
• Pressures of blends: p_bub (liquid line) and p_dew (vapour line) differ at the same temperature by up to 6.3 % (R454B, zeotropic), 1.2 % (R513A) and 0.4 % (R410A); both are listed for these three fluids, for the other fluids they are identical. The superheat is taken at the dew pressure.
• Normal boiling point = bubble-point temperature at 1.01325 bar. R744 has none: it sublimes at −78.5 °C at 1 atm (triple point 5.18 bar).
• GWP: indicative 100-year values as published in manufacturer and ASHRAE 34 listings: HFCs and blends on the IPCC AR4 basis (blend values mass-weighted), HFOs from AR5 (R1234yf “< 1” is entered as 1). Regulations define their own reference values.
• Transport properties (μ_L, k_L, Pr_L): CoolProp models for the pure fluids and R410A; R1233zd(E): extended corresponding states for μ_L (checked against literature data within ±1 %) and Perkins & Huber (2017) for k_L. For the blends R454B, R513A and R515A the values are estimated from the pure components (Grunberg–Nissan / Filippov mixing rules; compared with CoolProp's pseudo-pure R410A: μ_L +0.2 … +4.0 %, k_L −3.3 … −6.5 %), so expect up to about ±5 % for μ_L and ±7 % for k_L; they are marked “est.”. Surface tension σ (CSV only) of blends: mole-fraction average of the pure components; R1233zd(E): Kondou et al. (2015).
• CSV schema: comment lines (fluid, source, reference state, GWP basis, superheat definition, transport source), then one column per property with the unit in the column name, ready for OpenFOAM, ANSYS Fluent, MATLAB or EES.
• Source: CoolProp 8.0.0 (Bell, Wronski, Quoilin, Lemort, Ind. Eng. Chem. Res. 53 (2014) 2498); pure-fluid equations of state e.g. R134a: Tillner-Roth & Baehr (1994), R744: Span & Wagner (1996), R32: Tillner-Roth & Yokozeki (1997), R1234yf: Richter et al. (2011); R410A as pseudo-pure fluid (Lemmon 2003); the blend models R454B, R513A and R515A use Helmholtz mixing rules whose accuracy is lower than for the pure fluids. Refrigerant designations according to ANSI/ASHRAE Standard 34.

B-Rep Tessellation, Signed-Tetrahedron Volume Integration & ISO 128 Section Projection

3D CAD geometries are tessellated in-memory; volume, surface area and mass are computed from the closed triangle mesh (typically within 0.3 % for smooth bodies). All solids of a file are summed without a Boolean union, so overlapping solids count twice. The volume is exact only for closed meshes; an open mesh reports surface area and bounding box. Mass = volume × density of the selected material (handbook densities, about ±1 %).

Three clipping planes (X, Y, Z) reveal the internal cross-section; the Z plane drives the section view A–A in the style of ISO 128 (45° hatching, simplified dimensions in the style of ISO 129, drawing scale shown). Imported files keep their coordinate axes: bounding box is X × Y × Z of the file; the Y cut is horizontal, and the Z cut / section A–A is perpendicular to the depth axis.

Critical Heat Flux (Zuber 1959 / Lienhard–Dhir 1973, flat horizontal plate)

Nucleate Pool Boiling Wall Superheat ΔT_e = T_wall − T_sat

• Correlation choice: Auto uses Rohsenow for water (where C_s,f = 0.013 for water on polished copper is a textbook pair constant) and Cooper (1984) for methanol, R134a and R1233zd(E) (reduced-pressure correlation, valid for p_r = 0.001–0.9 and M = 2–200 g/mol).
• Surface & wick structure: Only Smooth Polished Copper with water (C_s,f = 0.013, CHF ×1.00) is a literature value; the sintered-wick and micro-grooved presets are editable engineering assumptions.
• Minimum film-boiling heat flux: Dashed branch beyond CHF uses Zuber/Berenson q″_min = 0.09 · ρ_v · Δh_lv · [σ·g·(ρ_l − ρ_v)/(ρ_l + ρ_v)²]^(1/4).