Math & Numbers

Compute the effectiveness (ε) of a heat exchanger by the ε-NTU method. C*=C_min/C_max (0..1), NTU=U·A/C_min, q_max=C_min·(T_h,in-T_c,in), and ε=q_actual/q_max. Supports four arrangements: Parallel flow ε=[1-exp(-NTU(1+C*))]/(1+C*); Counter flow ε=[1-exp(-NTU(1-C*))]/[1-C*·exp(-NTU(1-C*))], or NTU/(1+NTU) when C*=1; Shell-and-tube 1-2 ε=2/[1+C*+√(1+C*²)·(1+exp(-NTU√(1+C*²)))/(1-exp(-NTU√(1+C*²)))]; Crossflow (both unmixed) ε=1-exp{(NTU^0.22/C*)·[exp(-C*·NTU^0.78)-1]}. When C*=0 (phase change on one side, boiler/condenser) every arrangement gives ε=1-exp(-NTU). Optionally supply T_h,in and T_c,in to recover the actual heat-transfer rate q=ε·q_max and both outlet temperatures. Temperatures are used only as differences: Δ°C=ΔK and Δ°F×5/9=ΔK.

Math & Numbers

Estimate the heating (heat-loss) load of a room by the simplified steady-state method. Envelope transmission loss Q_trans = Σ(A_i·U_i·ΔT) over surfaces entered one per line as 'area,U' (U in W/(m²·K)). Cold-air infiltration loss Q_inf = 0.018·ACH·V·ΔT (W), where 0.018 W·h/(m³·K) ≈ ρ·c_p/3600. Total load = Q_trans + Q_inf, optionally multiplied by a safety factor (default 1.0). ΔT = indoor - outdoor (heating, >0). Temperature in °C/K/°F (only differences matter), area in m²/ft².

Development

Audit SPDX 2.3 or CycloneDX 1.5 component licenses and emit SARIF with failing dependency paths

Security

Show each HMAC step of HKDF Extract+Expand for protocol key derivation, including PRK, T(n), and OKM.

Math & Numbers

Compute 1-D steady-state heat conduction through a flat slab (Fourier's law): heat flux q = k·ΔT/d (W/m²), heat flow rate Q = k·A·ΔT/d (W), and thermal resistance R = d/(k·A) (K/W). k is the thermal conductivity (W/(m·K)); ΔT is the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9); d the slab thickness; A the cross-section area. ΔT may be negative (indicating reverse heat flow), but k, d and A must be positive. Thickness in m/cm/mm, area in m²/cm².

Math & Numbers

Compute convective heat transfer (Newton's law of cooling): heat flux q = h·ΔT (W/m²), heat flow rate Q = h·A·ΔT (W), and convective thermal resistance R_conv = 1/(h·A) (K/W). h is the convective heat-transfer coefficient (W/(m²·K)); ΔT is the temperature difference between the surface and the fluid (K; a °C difference equals a K difference, a °F difference is converted by ×5/9); A the heat-transfer area. ΔT may be negative (indicating reverse heat flow), but h and A must be positive. Area in m²/cm².

Math & Numbers

Compute the Log Mean Temperature Difference (LMTD) of a heat exchanger for parallel or counter flow. Parallel flow: ΔT₁ = T_h,in - T_c,in and ΔT₂ = T_h,out - T_c,out; counter flow: ΔT₁ = T_h,in - T_c,out and ΔT₂ = T_h,out - T_c,in. LMTD = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂), or ΔT₁ when ΔT₁ = ΔT₂. A non-positive terminal difference (temperature cross) is physically impossible and is rejected. Optionally, with the overall heat transfer coefficient U (W/(m²·K)) and the heat transfer area A (m²), the heat transfer rate Q = U·A·LMTD (W) is returned. Temperatures are used only as differences: Δ°C = ΔK and Δ°F ×5/9 = ΔK; the LMTD is reported in K.

Math & Numbers

Compute thermal radiation from a blackbody/grey body (Stefan-Boltzmann law): blackbody emissive power E_b = σ·T⁴ (W/m²), total radiated power Q_rad = ε·σ·A·T⁴ (W); with an optional surrounding temperature T₀ it also computes the net radiative exchange Q_net = ε·σ·A·(T⁴-T₀⁴) (W). σ = 5.670374419e-8 W/(m²·K⁴); ε is the emissivity (0 < ε ≤ 1, blackbody ε=1); T is the ABSOLUTE temperature (K) — °C and °F are first converted to K (this is an absolute temperature, not a difference); A is the radiating area. Area in m²/cm².

Math & Numbers

Compute the LC (RLC series/parallel) resonant frequency: f₀ = 1/(2π·√(L·C)). Resonant frequency is identical for series and parallel RLC; R only affects Q and bandwidth. Solves for f₀, L, or C from the other two, and returns angular resonance ω₀ and characteristic impedance √(L/C). L in H/mH/µH, C in F/µF/nF/pF, f in Hz/kHz/MHz.

Math & Numbers

Compute the Reynolds number Re = ρ·v·D/μ (dynamic viscosity) or Re = v·D/ν (kinematic viscosity, ν = μ/ρ) and classify the flow regime: Re < 2300 laminar, 2300 ≤ Re < 4000 transitional, Re ≥ 4000 turbulent. Diameter accepted in m/cm/mm. In dynamic mode the kinematic viscosity ν = μ/ρ is also returned. For internal pipe flow and general fluid-mechanics regime analysis.

Math & Numbers

Estimate copper cable current-carrying capacity per the simplified IEC 60364-5-52 reference method. Combines cross-section, insulation (PVC 70°C / XLPE 90°C), installation method, and ambient temperature to derive the corrected allowable ampacity (A).

Math & Numbers

Compute the reactive power produced by a known capacitor: Q_c = 2π·f·C·U². Supports single-phase, three-phase star (Y) and delta (Δ) connections. Returns Q_c in var/kvar, capacitive reactance Xc, and capacitor current Ic. Complementary to the power-factor-correction tool (which sizes a capacitor for a target cosφ).