# Heat transfer
## Microsim
### Live player
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/QRea-7JU3" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe>
</div>
<div class="microsim-fallback">
<img src="Microsims/thumbs/Heat_transfer.png" alt="Heat_transfer microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;">
<p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/QRea-7JU3">open sketch in the p5.js editor</a></em></p>
</div>
**Editor URL:** https://editor.p5js.org/sciencenibber/sketches/QRea-7JU3
**Description (100 words):**
A vertical cross-section through a gas-tungsten-arc weld decomposes the heat delivered to the workpiece into the three canonical modes: a yellow Stefan-Boltzmann radiation halo around the plasma column, orange Newton's-law convection arrows tracing the cathode jet onto the molten pool, and concentric blue Fourier-law conduction isotherms spreading through the metal. Three sliders control the helium fraction of the [[Shielding_gas|shielding gas]] (0-100 percent), the welding current (50-300 A), and the workpiece thermal conductivity (15-401 W/m K, labelled SS 304 through OFHC Cu). A live gauge stack shows arc [[Voltage|voltage]], plasma temperature, total heat input, the percentage share of each mode, and a penetration proxy that visibly deepens as helium-rich shielding shifts the balance from radiation toward conduction.
```js
// =====================================================================
// Heat_transfer.js -- Wikitube microsim
// Article: Heat transfer en.wikitube.io/wiki/Heat_transfer
// Room: Helium Pattern: C (arc + gas-mix + welding dynamics)
// ---------------------------------------------------------------------
// Idea: a vertical cross-section through a GTAW arc and its workpiece
// that decomposes the heat delivery into the three canonical modes of
// heat transfer -- CONDUCTION, CONVECTION, and RADIATION -- and shows
// how the helium fraction of the shielding gas tilts the balance.
//
// The reader drives three sliders:
// * shielding He fraction fHe (0 - 100 %) -- raises arc voltage
// and plasma temperature, narrows the column, redistributes heat
// from radiation/convection toward conduction
// * welding current I (50 - 300 A) -- scales every mode
// together via the heat-input relation H = eta * V * I / v
// * workpiece thermal conductivity k (15 - 401 W / m K) -- 15 for
// stainless 304, 50 for low-carbon steel, 90 for Inconel 600,
// 237 for pure Al, 401 for OFHC Cu (kept on a labeled tick scale)
//
// Visual overlay (all three modes live on the same cross-section):
// * RADIATION -- a yellow halo around the plasma column whose
// intensity scales as epsilon * sigma * T_plasma^4 (Stefan-
// Boltzmann)
// * CONVECTION -- orange arrows tracing the cathode-jet flow from
// electrode tip down to the weld pool, length proportional to
// h * (T_arc - T_pool)
// * CONDUCTION -- concentric blue isotherms in the workpiece below
// the weld pool, sized by the Rosenthal moving-point-source
// solution T(r) - T_inf = (Q / (2 pi k r)) * exp(-v r / (2 alpha))
// simplified to a sequence of equally-spaced T-rings (the visual
// idiom Energy room Pattern A uses for isothermal lines)
//
// Canonical equations pinned to the bottom-right HUD:
// q_cond = -k * grad(T) Fourier
// q_conv = h * (T_s - T_inf) Newton
// q_rad = e * sigma * T^4 Stefan-Boltzmann
// H = (eta * V * I) / v total weld heat input, J/mm
//
// Physical landmarks reproduced:
// * Fourier (1822, Theorie analytique de la chaleur) -- conduction
// coefficient k as material constant.
// * Newton (1701) -- proportional cooling law, codified into the
// convective heat-transfer coefficient h.
// * Stefan (1879) / Boltzmann (1884) -- T^4 radiation scaling and
// sigma = 5.670 x 10^-8 W / m^2 K^4.
// * Rosenthal (1941, Welding Journal 20) -- moving-point-source
// solution for the 3-D temperature field around an arc weld.
// * AWS Welding Handbook, eta ~ 0.6 for GTAW heat-input efficiency.
// * W3 advmfg cofounder file: He shielding sharpens arc, raises
// T_plasma from ~10 kK (pure Ar) to ~22 kK (pure He), and tilts
// heat delivery toward conduction-dominated penetration -- exactly
// why thick Al and Cu weld better under helium.
//
// Visual layout (720 x 520 canvas):
// * top-left: HUD title + Wikitube subtitle
// * top-right: reader hints + pattern tag
// * left panel: vertical arc + workpiece cross-section with all
// three modes overlaid in their own colors
// * right panel: gauge stack -- T_plasma, V_arc, H_total, q_cond %,
// q_conv %, q_rad %, weld-pool depth proxy
// * bottom: three sliders (left) + canonical equations (right)
//
// Conventions (Wikitube Betterfire Standard v0):
// * single ARTICLE constant at the top, single quotes (validator BF1)
// * p5.disableFriendlyErrors = true to keep the editor console clean
// * non-ASCII (eta, sigma, epsilon, dot, arrow) lives in COMMENTS
// only; every text() string literal is plain ASCII (the editor
// preview mangles non-ASCII inside strings)
// * Energy-room palette (P5_JS_EDITOR section 4) plus plasma extras
// * every createSlider carries .position(x, y).size(w) (FES2 -- no
// floating controls)
// * HUD factored into drawHUD() and called from draw() (BF7)
// =====================================================================
const ARTICLE = 'Heat_transfer';
const TITLE = ARTICLE.replace(/_/g, ' ');
p5.disableFriendlyErrors = true;
// ----- Energy room palette (P5_JS_EDITOR section 4) -------------------
const BG = 18;
const FG = 240;
const DIM = [240, 240, 240, 140];
const HOT = [220, 110, 60]; // warm: convection jet, weld pool
const COLD = [60, 130, 220]; // cool: conduction isotherms
const STRUCT = [120, 130, 150]; // structural grey: electrode, plate
const TRAJ = [240, 220, 80]; // radiation halo (yellow accent)
const GAUGE = [120, 220, 140]; // green: gauges, heat-input bar
// Plasma extras
const PLASMA_CORE = [255, 240, 200]; // white-yellow inner core
const PLASMA_MID = [255, 170, 80]; // orange middle envelope
const PLASMA_EDGE = [140, 90, 220]; // violet ionized halo
const POOL_HOT = [255, 160, 80]; // molten pool surface
// ----- Physical-model constants (matches Pattern C sketches) ---------
const ETA = 0.6; // arc-transfer efficiency, AWS
const V0_BASE = 8.0; // V, baseline arc voltage at I->0
const V_PER_AMP = 0.015; // V/A, V(I) slope for short Ar arc
const V_HE_BONUS = 5.0; // V, full-He voltage bonus
const T_AR_ARC = 10000; // K, pure-Ar plasma temperature
const T_HE_ARC = 22000; // K, pure-He plasma temperature
const SIGMA_SB = 5.670e-8; // Stefan-Boltzmann constant, SI
const EMISS_ARC = 0.45; // effective arc emissivity (band)
const H_CONV0 = 1.8e4; // W / m^2 K, baseline convective
// coefficient under stagnant Ar
const H_CONV_HE_GAIN = 3.5; // x baseline at full He (He cp,
// density combine to ~3-4x h)
const T_POOL = 1700; // K, weld-pool surface temp (Al)
const V_TRAVEL = 4.0; // mm/s, fixed travel for ratio math
// ----- Slider value-ranges (kept here so gauges stay in sync) --------
const HE_DEFAULT = 35;
const I_MIN = 50, I_MAX = 300, I_DEFAULT = 140;
const K_MIN = 15, K_MAX = 401, K_DEFAULT = 237; // W / m K
// ----- Workpiece material tick labels --------------------------------
const K_TICKS = [
{k: 15, label: 'SS 304'},
{k: 50, label: 'mild steel'},
{k: 90, label: 'Inconel 600'},
{k: 237, label: 'pure Al'},
{k: 401, label: 'OFHC Cu'}
];
// ----- Slider handles (set in setup) ---------------------------------
let mixSlider, currentSlider, kSlider;
// ----- Cross-section geometry (set in setup) -------------------------
let panelX, panelY, panelW, panelH;
let plateTopY, plateBottomY;
let electrodeTipY;
// ----- p5 setup -------------------------------------------------------
function setup() {
// Canvas + rendering defaults (Betterfire Standard, P5_JS_EDITOR sec.2)
createCanvas(720, 520);
pixelDensity(2);
textFont('system-ui');
// Left-panel cross-section bounds
panelX = 30;
panelY = 80;
panelW = 380;
panelH = 360;
plateTopY = panelY + 220; // workpiece upper surface
plateBottomY = panelY + 340; // workpiece lower surface
electrodeTipY = panelY + 90; // tungsten tip height
// Sliders -- always .position(x, y).size(w) (validator FES2)
mixSlider = createSlider(0, 100, HE_DEFAULT, 1)
.position( 30, 470).size(160);
currentSlider = createSlider(I_MIN, I_MAX, I_DEFAULT, 5)
.position( 30, 495).size(160);
kSlider = createSlider(K_MIN, K_MAX, K_DEFAULT, 1)
.position( 230, 470).size(160);
}
// ----- Per-frame physics + render ------------------------------------
function draw() {
background(BG);
// Read controls once at the top -- the physics references named locals
const fHe = mixSlider.value() / 100; // 0..1
const I = currentSlider.value(); // A
const k = kSlider.value(); // W / m K
// Arc voltage: short-arc Ar model + linear He bonus
const V = V0_BASE + V_PER_AMP * I + V_HE_BONUS * fHe;
// Plasma temperature: linear blend Ar -> He arc temperature
const Tp = T_AR_ARC + (T_HE_ARC - T_AR_ARC) * fHe;
// Per-mode flux densities, all in W / m^2 (relative scale OK for plot)
const q_rad = EMISS_ARC * SIGMA_SB * Math.pow(Tp, 4);
const h_eff = H_CONV0 * (1 + (H_CONV_HE_GAIN - 1) * fHe);
const q_conv = h_eff * (Tp - T_POOL);
// Conduction "flux into plate" -- use Rosenthal-flavored proxy:
// q_cond ~ k * (T_pool - T_inf) / L_char, with L_char fixed at 1 mm.
const T_INF = 298; // K, ambient
const L_CHAR = 1e-3; // m, characteristic length
const q_cond_raw = k * (T_POOL - T_INF) / L_CHAR;
// Scale q_cond up with arc heating (it cannot exceed what the arc
// delivers). Multiply by (I / 200), so the workpiece "sees" more
// conduction at higher current.
const q_cond = q_cond_raw * (I / 200);
const q_total = q_cond + q_conv + q_rad;
const fCond = q_cond / q_total;
const fConv = q_conv / q_total;
const fRad = q_rad / q_total;
// Total heat input H = eta * V * I / v_travel [J / mm]
// (v_travel in mm/s, V in V, I in A -> J/mm)
const H = (ETA * V * I) / V_TRAVEL;
// ----- LEFT panel: cross-section ----------------------------------
drawCrossSection(fHe, I, Tp, fCond, fConv, fRad);
// ----- RIGHT panel: gauge stack -----------------------------------
drawGaugePanel(I, V, Tp, H, fCond, fConv, fRad, q_total);
// ----- HUD + bottom labels + canonical equations ------------------
drawHUD();
drawSliderLabels(fHe, I, k);
drawEquations();
}
// ----- Cross-section: arc + workpiece + three modes overlaid --------
function drawCrossSection(fHe, I, Tp, fCond, fConv, fRad) {
// Panel frame (subtle)
noFill();
stroke(...DIM);
strokeWeight(1);
rect(panelX, panelY, panelW, panelH);
const cx = panelX + panelW / 2;
// Electrode (tungsten, structural grey)
noStroke();
fill(...STRUCT);
rect(cx - 6, panelY + 20, 12, electrodeTipY - (panelY + 20));
// Tip cone
triangle(cx - 6, electrodeTipY,
cx + 6, electrodeTipY,
cx, electrodeTipY + 14);
// -- RADIATION halo (Stefan-Boltzmann) -- yellow rings around arc
// intensity scales with q_rad share -> alpha
push();
noStroke();
// Arc column width narrows with He fraction (constriction effect)
const arcWidthAr = 36; // px, at fHe = 0
const arcWidthHe = 14; // px, at fHe = 1
const arcW = lerp(arcWidthAr, arcWidthHe, fHe);
const arcHalfTop = arcW * 0.35;
const arcHalfMid = arcW * 0.55;
const arcHalfBottom = arcW * 0.50;
const arcTopY = electrodeTipY + 14;
const arcBotY = plateTopY - 6;
// Radiation halo -- expanding glow, scales with q_rad share
const radAlpha = constrain(50 + 220 * fRad, 30, 220);
for (let r = 6; r > 0; r--) {
fill(TRAJ[0], TRAJ[1], TRAJ[2], radAlpha * (r / 6) * 0.18);
ellipse(cx, (arcTopY + arcBotY) / 2,
arcWidthAr * 2.4 + r * 10,
(arcBotY - arcTopY) * 1.2 + r * 8);
}
// -- Plasma column itself: outer violet edge, mid orange, white core
fill(...PLASMA_EDGE, 130);
quad(cx - arcHalfTop, arcTopY,
cx + arcHalfTop, arcTopY,
cx + arcHalfBottom, arcBotY,
cx - arcHalfBottom, arcBotY);
fill(...PLASMA_MID, 200);
quad(cx - arcHalfTop * 0.7, arcTopY + 2,
cx + arcHalfTop * 0.7, arcTopY + 2,
cx + arcHalfBottom * 0.7, arcBotY - 2,
cx - arcHalfBottom * 0.7, arcBotY - 2);
fill(...PLASMA_CORE, 240);
quad(cx - arcHalfTop * 0.35, arcTopY + 4,
cx + arcHalfTop * 0.35, arcTopY + 4,
cx + arcHalfBottom * 0.35, arcBotY - 4,
cx - arcHalfBottom * 0.35, arcBotY - 4);
pop();
// -- WORKPIECE plate (structural grey)
push();
noStroke();
fill(...STRUCT, 220);
rect(panelX + 20, plateTopY, panelW - 40, plateBottomY - plateTopY);
pop();
// -- WELD POOL (molten Al-style hot spot)
push();
noStroke();
const poolWidth = arcWidthHe * 2 + 60 - 20 * fHe; // narrower with He
const poolDepth = 16 + 24 * fCond + I * 0.08; // deeper w/ cond + I
fill(...POOL_HOT, 230);
ellipse(cx, plateTopY + 4, poolWidth, 18);
fill(...HOT, 200);
ellipse(cx, plateTopY + poolDepth / 2, poolWidth * 0.85, poolDepth);
pop();
// -- CONDUCTION isotherms in the workpiece (Pattern A invariant rings)
// Concentric ellipses scaled by Rosenthal-flavored q_cond share
push();
noFill();
const N_ISO = 6;
for (let i = 1; i <= N_ISO; i++) {
// Outer rings = cooler. Alpha scales with q_cond share.
const alpha = constrain(60 + 200 * fCond * (1 - i / (N_ISO + 1)),
30, 230);
stroke(COLD[0], COLD[1], COLD[2], alpha);
strokeWeight(i === 1 ? 2 : 1);
const w = poolWidth * (1 + 0.6 * i);
const h = poolDepth * (0.7 + 0.6 * i);
ellipse(cx, plateTopY + poolDepth / 2, w, h);
}
pop();
// -- CONVECTION arrows (orange) from arc to pool, along plasma jet
push();
stroke(...HOT, 200 + 30 * fConv);
strokeWeight(2);
fill(...HOT, 220);
const N_ARROW = 5;
for (let i = 0; i < N_ARROW; i++) {
const xOff = (i - (N_ARROW - 1) / 2) * 14;
const aTop = arcBotY - 6;
const aBot = plateTopY - 2;
line(cx + xOff, aTop, cx + xOff * 1.2, aBot);
// Arrowhead
push();
translate(cx + xOff * 1.2, aBot);
noStroke();
triangle(-3, -6, 3, -6, 0, 0);
pop();
}
pop();
// -- Radiation outward arrows (yellow), short ticks pointing outward
// from the column edge, length scales with q_rad share
push();
stroke(...TRAJ, 220);
strokeWeight(1.5);
const radLen = 6 + 22 * fRad;
const arcMidY = (arcTopY + arcBotY) / 2;
const angles = [-1.0, -0.5, 0, 0.5, 1.0];
for (const a of angles) {
const sx = cx + Math.cos(a) * (arcHalfMid + 4);
const sy = arcMidY + Math.sin(a) * 30;
const ex = cx + Math.cos(a) * (arcHalfMid + 4 + radLen);
const ey = arcMidY + Math.sin(a) * (30 + radLen * 0.6);
line(sx, sy, ex, ey);
}
// Mirror on the other side
for (const a of angles) {
const sx = cx - Math.cos(a) * (arcHalfMid + 4);
const sy = arcMidY + Math.sin(a) * 30;
const ex = cx - Math.cos(a) * (arcHalfMid + 4 + radLen);
const ey = arcMidY + Math.sin(a) * (30 + radLen * 0.6);
line(sx, sy, ex, ey);
}
pop();
// -- Mode legend (color-coded) in the panel top-right
push();
noStroke();
textSize(11);
textAlign(LEFT, CENTER);
const lx = panelX + panelW - 130;
fill(...TRAJ); rect(lx, panelY + 12, 10, 10);
fill(FG, 220); text('radiation', lx + 16, panelY + 17);
fill(...HOT); rect(lx, panelY + 30, 10, 10);
fill(FG, 220); text('convection', lx + 16, panelY + 35);
fill(...COLD); rect(lx, panelY + 48, 10, 10);
fill(FG, 220); text('conduction', lx + 16, panelY + 53);
pop();
}
// ----- Right-panel gauge stack ---------------------------------------
function drawGaugePanel(I, V, Tp, H, fCond, fConv, fRad, q_total) {
const gx = 430;
const gy = 80;
const gw = 260;
const gh = 360;
// Panel frame
noFill();
stroke(...DIM);
strokeWeight(1);
rect(gx, gy, gw, gh);
// Gauge label
noStroke();
fill(FG, 220);
textAlign(LEFT, TOP);
textSize(12);
text('Heat-transfer balance', gx + 12, gy + 10);
// Numeric readout block
textSize(11);
fill(FG, 200);
const baseY = gy + 36;
const lineH = 16;
const labels = [
`I = ${I} A`,
`V = ${V.toFixed(2)} V`,
`Tp = ${Tp.toFixed(0)} K`,
`H = ${H.toFixed(0)} J/mm`,
];
for (let i = 0; i < labels.length; i++) {
text(labels[i], gx + 12, baseY + i * lineH);
}
// Three stacked horizontal bars: conduction, convection, radiation
const barX0 = gx + 12;
const barY0 = gy + 130;
const barW = gw - 24;
const barH = 26;
const gap = 14;
drawModeBar(barX0, barY0, barW, barH, fCond,
'conduction', COLD);
drawModeBar(barX0, barY0 + (barH + gap), barW, barH, fConv,
'convection', HOT);
drawModeBar(barX0, barY0 + 2 * (barH + gap), barW, barH, fRad,
'radiation', TRAJ);
// Penetration / depth proxy gauge (lower-right)
push();
noStroke();
fill(FG, 200);
textSize(11);
textAlign(LEFT, TOP);
text('penetration proxy', gx + 12, gy + 260);
const penY = gy + 278;
const penW = gw - 24;
const penH = 16;
// Background
fill(...DIM);
rect(gx + 12, penY, penW, penH);
// Fill -- penetration scales with q_cond share and current
const penFrac = constrain(0.05 + fCond * 0.7 + (I / I_MAX) * 0.25,
0, 1);
fill(...GAUGE);
rect(gx + 12, penY, penW * penFrac, penH);
fill(FG, 220);
textAlign(RIGHT, TOP);
text(`${(penFrac * 100).toFixed(0)} %`,
gx + 12 + penW - 4, penY + 2);
pop();
// Reminder line at panel bottom
push();
noStroke();
fill(FG, 180);
textSize(10);
textAlign(LEFT, TOP);
text('He shifts heat from radiation -> conduction',
gx + 12, gy + gh - 24);
pop();
}
// ----- Single mode bar (label left + filled bar + percentage right) --
function drawModeBar(x, y, w, h, frac, label, color3) {
push();
// Background
noStroke();
fill(...DIM);
rect(x, y, w, h);
// Fill bar
fill(color3[0], color3[1], color3[2], 230);
rect(x, y, w * constrain(frac, 0, 1), h);
// Label and percentage
fill(FG, 230);
textSize(11);
textAlign(LEFT, CENTER);
text(label, x + 6, y + h / 2);
textAlign(RIGHT, CENTER);
text(`${(frac * 100).toFixed(0)} %`, x + w - 6, y + h / 2);
pop();
}
// ----- Header HUD (BF7) ----------------------------------------------
function drawHUD() {
push();
noStroke();
fill(FG);
textAlign(LEFT, TOP);
textSize(22);
text(TITLE, 14, 14);
fill(...DIM);
textSize(12);
text('Wikitube microsim . en.wikitube.io/wiki/' + ARTICLE, 14, 44);
// Top-right pattern + hint
fill(...DIM);
textAlign(RIGHT, TOP);
textSize(11);
text('Pattern C . Helium room', width - 14, 14);
text('drag sliders below', width - 14, 30);
pop();
}
// ----- Bottom slider labels ------------------------------------------
function drawSliderLabels(fHe, I, k) {
push();
noStroke();
fill(FG, 220);
textAlign(LEFT, TOP);
textSize(11);
// Slider value tags
text(`He fraction ${(fHe * 100).toFixed(0)} %`, 195, 472);
text(`current ${I} A`, 195, 497);
// Workpiece material tick
const kVal = k;
let near = K_TICKS[0];
for (const t of K_TICKS) {
if (Math.abs(t.k - kVal) < Math.abs(near.k - kVal)) near = t;
}
text(`k ${kVal} W/mK (${near.label})`, 395, 472);
pop();
}
// ----- Canonical equations in bottom-right ---------------------------
function drawEquations() {
push();
noStroke();
fill(FG, 200);
textAlign(RIGHT, TOP);
textSize(11);
const ex = width - 14;
let ey = 470;
const lh = 14;
text('q_cond = -k * grad(T)', ex, ey); ey += lh;
text('q_conv = h * (T_s - T_inf)', ex, ey); ey += lh;
text('q_rad = e * sigma * T^4', ex, ey); ey += lh;
text('H = (eta * V * I) / v', ex, ey); ey += lh;
pop();
}
```
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Heat_transfer.json (2026-07-30T02:09:12Z) -->
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## From the Real GENERATIVE library
*Heat transfer — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Engineering room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Convection-snapshot.png).*
*Animated: Heat transfer — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Engineering room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Erbe.gif).*
> Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. ([Wikipedia](https://en.wikipedia.org/wiki/Heat_transfer))
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## From the vault media library
!Heat transfer thumb.png
*Heat Transfer — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.*
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## Media (PD/CC)
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!Gif Library/Heat transfer/Erbe.gif
*Erbe.gif · Public domain*
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**Semiotic universals** (the notations and alphabet letters this article speaks — each opens its canonical card): hvac symbols · kanji radicals · temperature heat · energy · flow. Index: the glyph gallery · SEMIOTICS PORTAL.
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> **Room:** [[Helium]] · **Status:** ✅ shipped
## Overview
Heat transfer is the discipline of [[Physics|physics]] and [[Engineering|engineering]] concerned with the generation, exchange, conversion, and use of thermal [[Energy|energy]] between physical systems. It is constrained by the [[Second_law_of_thermodynamics|second law of thermodynamics]], which dictates that heat flows spontaneously from regions of higher temperature toward regions of lower temperature. Three fundamental modes are recognized: conduction, in which energy diffuses through a stationary medium via molecular vibrations and [[Electron|electron]] transport; convection, in which energy is carried by the bulk motion of a fluid; and thermal radiation, in which energy travels as electromagnetic waves and requires no material medium.
The canonical governing relations are Fourier's law of conduction (q = -k grad T), Newton's law of cooling (q = h (T_s - T_inf)), and the Stefan-Boltzmann law for radiation (q = epsilon sigma T^4). Combined with the first-law energy equation, they form the basis of every thermal-systems analysis -- from heat-exchanger design and HVAC to spacecraft thermal control and gas-tungsten-arc welding, where helium's high thermal conductivity (about six times that of argon at arc temperatures) constricts the plasma column, raises peak temperature, and deepens weld-pool penetration in thick aluminum and [[Copper|copper]] sections.
Historical landmarks include Fourier's Theorie analytique de la chaleur (1822), Maxwell's [[Kinetic_theory_of_gases|kinetic theory of gases]], the Buckingham-Pi analysis that produced the Nusselt, Prandtl, and Reynolds numbers, and Planck's blackbody law that resolved the ultraviolet catastrophe. Modern applications span semiconductor cooling, cryogenic propellant management, MRI magnet quench protection, and inertial-confinement fusion targets.
## See also
- Room hub: [[Helium]]
- p5.js Editor conventions: P5 JS EDITOR
- Wiki root: MAIN
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*Scaffolded by `generative-microsim` from row 39 of the Helium sheet on 2026-05-11T23:58:59Z.*
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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*Connected to the Apex Spine:* Heat transfer → [[Fluid_dynamics|Fluid dynamics]] — [[WT!Thury_Hydrodynamics_Compendium|Compendium]] section 1, *Fluid dynamics*.
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**Microsim — three.js (Wikitube framework):** *Heat transfer*
<div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Heat_transfer.html" data-title="Heat transfer"></div>
*Built from `MICROSIM_GUIDE/specs/sims/Heat_transfer.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Heat_transfer) : [Wikitube](https://en.wikitube.io/wiki/Heat_transfer)
## Previous hub tags
Tree parent: [[Helium]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*