Wire Overload Heat Calculator

ANA›Life Services Authority›National Calculator Authority›Wire Overload Heat Calculator

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Wire Overload Heat Calculator

Calculates the heat generated (power dissipation) in a wire during overload conditions, the temperature rise above ambient, and the time to reach a critical temperature using I²R heating principles.

Overload Current (A)

Wire Resistance (Ω)

Wire Length (m)

Resistivity ρ (Ω·m) (copper ≈ 1.72e-8)

Cross-Sectional Area (mm²)

Wire Mass (kg) (optional for temp rise)

Specific Heat Capacity (J/kg·K) (copper ≈ 385)

Overload Duration (s)

Ambient Temperature (°C)

Max Allowable Temperature (°C) (PVC insulation ≈ 70)

Calculate

Results will appear here.

function wirCalc() { const resultDiv = document.getElementById('wir-result');

// --- Read inputs --- const I = parseFloat(document.getElementById('wir-current').value); const R_input = parseFloat(document.getElementById('wir-resistance').value); const L = parseFloat(document.getElementById('wir-length').value); const rho = parseFloat(document.getElementById('wir-resistivity').value); const A_mm2 = parseFloat(document.getElementById('wir-area').value); const m = parseFloat(document.getElementById('wir-mass').value); const c = parseFloat(document.getElementById('wir-specific-heat').value); const t = parseFloat(document.getElementById('wir-time').value); const T_amb = parseFloat(document.getElementById('wir-ambient').value); const T_max = parseFloat(document.getElementById('wir-max-temp').value);

// --- Validation --- const errors = []; if (isNaN(I) || I 0) { R = R_input; R_source = "user-supplied resistance"; } else if (!isNaN(rho) && rho > 0 && !isNaN(L) && L > 0 && !isNaN(A_mm2) && A_mm2 > 0) { const A_m2 = A_mm2 * 1e-6; R = (rho * L) / A_m2; R_source = "computed from ρ, L, A"; } else { errors.push("Provide either Wire Resistance directly, OR all three of: Resistivity, Wire Length, and Cross-Sectional Area."); }

if (errors.length > 0) { resultDiv.innerHTML = 'Input Errors:' + errors.map(e => '').join('') + ''; return; }

// --- Core Calculations ---

// 1. Power dissipated (W) — Joule heating: P = I² × R const P = I * I * R;

// 2. Heat energy generated over duration (J): Q = P × t let Q = NaN, deltaT_time = NaN, T_final = NaN; let timeProvided = !isNaN(t) && t > 0; if (timeProvided) { Q = P * t; }

// 3. Temperature rise (°C) if mass provided: ΔT = Q / (m × c) let massProvided = !isNaN(m) && m > 0; if (timeProvided && massProvided) { deltaT_time = Q / (m * c); T_final = T_amb + deltaT_time; }

// 4. Time to reach max allowable temperature: t_crit = (m × c × ΔT_max) / P let t_crit = NaN; const deltaT_max = T_max - T_amb; if (massProvided) { t_crit = (m * c * deltaT_max) / P; }

// 5. Current density (A/mm²) let J = NaN; if (!isNaN(A_mm2) && A_mm2 > 0) { J = I / A_mm2; }

// 6. Resistance per unit length (Ω/m) let R_per_m = NaN; if (!isNaN(rho) && rho > 0 && !isNaN(A_mm2) && A_mm2 > 0) { R_per_m = rho / (A_mm2 * 1e-6); }

// --- Safety Assessment --- let safetyHTML = ""; if (timeProvided && massProvided) { if (T_final > T_max) { safetyHTML = '⚠️ DANGER: Wire reaches ' + T_final.toFixed(1) + ' °C after ' + t.toFixed(2) + ' s — exceeds max allowable ' + T_max.toFixed(1) + ' °C. Risk of insulation damage or fire.'; } else { safetyHTML = '✅ SAFE: Wire reaches ' + T_final.toFixed(1) + ' °C after ' + t.toFixed(2) + ' s — within max allowable ' + T_max.toFixed(1) + ' °C.'; } }

// --- Build Output --- let html = safetyHTML + 'ParameterValue';

html += 'Wire Resistance (' + R_source + ')' + R.toExponential(4) + ' Ω'; html += 'Power Dissipated (P = I²R)' + P.toFixed(4) + ' W';

if (!isNaN(J)) html += 'Current Density (J = I / A)' + J.toFixed(3) + ' A/mm²';

if (!isNaN(R_per_m)) html += 'Resistance per Unit Length' + R_per_m.toFixed(6) + ' Ω/m';

if (timeProvided) { html += 'Heat Energy Generated (Q = P × t)' + Q.toFixed(4) + ' J'; if (massProvided) { html += 'Temperature Rise over ' + t.toFixed(2) + ' s (ΔT = Q / mc)' + deltaT_time.toFixed(3) + ' °C'; html += 'Final Wire Temperature' + T_final.toFixed(2) + ' °C'; } }

if (!isNaN(t_crit)) { html += 'Time to Reach ' + T_max.toFixed(1) + ' °C (tcrit = mc·ΔTmax / P)' + (t_crit '; }

html += '';

if (!massProvided) { html += 'ℹ️ Provide Wire Mass to calculate temperature rise and critical time.

'; } if (!timeProvided) { html += 'ℹ️ Provide Overload Duration to calculate total heat energy and final temperature.

'; }

resultDiv.innerHTML = html; }

#### Formulas Used

Wire Resistance from material properties: R = ρ × L / A

Joule Heating Power (W): P = I² × R

Heat Energy Generated (J): Q = P × t = I² × R × t

Temperature Rise (°C) — adiabatic assumption: ΔT = Q / (m × c) = (I² × R × t) / (m × c)

Time to Reach Critical Temperature (s): tcrit = (m × c × (Tmax − Tamb)) / (I² × R)

Current Density (A/mm²): J = I / A

Where: ρ = resistivity (Ω·m), L = length (m), A = cross-sectional area (m²), I = current (A), R = resistance (Ω), t = time (s), m = mass (kg), c = specific heat capacity (J/kg·K).

#### Assumptions & References

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References

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