Heat transfer — conduction (Fourier's law k), convection, radiation (Stefan-Boltzmann σT⁴)

1.7.6 · Physics › Thermodynamics

Intuition Badi picture

Heat hamesha hot se cold ki taraf flow karta hai (2nd law). Iske travel karne ke exactly teen tarike hain, aur ye aapas mein is baat mein differ karte hain ki energy ko kaun carry karta hai:

Conduction: energy touching atoms ke beech hop karti hai — matter ki koi bulk motion nahi. (chai mein metal ka chammach)
Convection: energy moving fluid ke saath carry ho jaati hai — matter khud flow karta hai. (boiling water, sea breeze)
Radiation: energy electromagnetic waves ke roop mein travel karti hai — iske liye koi medium bilkul nahi chahiye. (space mein sunlight)

YE KYUN important hai: har real object in teeno ke kisi mix se heat lose/gain karta hai. Ye jaanna ki kaun dominant hai batata hai ki ghar ko kaise insulate karein, CPU ko kaise cool karein, ya space mein kaise survive karein.

1. Conduction — Fourier's Law

HUM KYA CHAHTE HAIN: heat flow ki rate $\frac{d Q}{d t}$ (yaani heat current $H$ , units W) ek slab se.

FORMULA KAISE BANATE HAIN (scratch se derivation):

Ek slab socho jisme cross-section $A$ hai, thickness $Δ x$ hai, hot face $T_{1}$ par aur cold face $T_{2}$ par hai ( $T_{1} > T_{2}$ ).

Heat current area $A$ ke saath badhna chahiye — double wall, double flow. Toh $H \propto A$ .
Ye temperature difference $Δ T = T_{1} - T_{2}$ ke saath badhna chahiye — zyada steep drop zyada heat push karta hai. Toh $H \propto Δ T$ .
Ye thickness $Δ x$ ke saath ghattna chahiye — moti wall isko slow karti hai. Toh $H \propto 1/Δ x$ .

Combine karo aur units fix karne ke liye material constant $k$ daalo:

$H = \frac{d Q}{d t} = k A \frac{Δ T}{Δ x}$

Continuous gradient ki limit mein ye proper Fourier's law hai:

2. Convection

Natural convection: sirf buoyancy (density differences) se driven.
Forced convection: fluid ko fan/pump se push kiya jaata hai.

Newton's law of cooling (engineering model): $H = h A (T_{s} - T_{fluid})$ jahan $h$ convection coefficient hai (W m⁻² K⁻¹), $T_{s}$ surface temperature hai.

3. Radiation — Stefan–Boltzmann Law

4th power kyun: Planck's blackbody spectrum ko saare frequencies par integrate karne se total emitted power $\propto T^{4}$ milti hai. Iska key consequence: absolute temperature double karne se radiated power $2^{4} = 16$ guna ho jaati hai.

Figure — Heat transfer — conduction (Fourier's law k), convection, radiation (Stefan-Boltzmann σT⁴)

Common Mistakes (Steel-man + Fix)

Active Recall

#flashcards/physics

Fourier's law of conduction state karo aur har symbol ka matlab batao.

H = - k A d T / d x

;

H

=heat current (W),

k

=thermal conductivity,

A

=area,

d T / d x

=temperature gradient; minus = cold ki taraf flow.

Heat transfer ke teen modes kaun se hain aur unme energy kya carry karta hai?

Conduction (atomic collisions/electrons, koi bulk motion nahi), convection (moving fluid carry karta hai), radiation (EM waves, koi medium nahi chahiye).

Conduction mein matter ki bulk motion kyun nahi hoti lekin convection mein hoti hai?

Conduction = energy fixed/touching molecules ke beech pass hoti hai; convection = hot fluid physically ek nai jagah flow karta hai.

Thermal resistance define karo aur ye series vs parallel mein kaise combine hoti hai.

R = Δ x / (k A)

; series → resistances add hote hain; parallel → conductances (

1/ R

) add hote hain.

Stefan–Boltzmann law state karo aur σ ki value batao.

P = e σ A T^{4}

σ = 5.67 \times 1 0^{- 8}

W m⁻² K⁻⁴,

T

kelvin mein.

Total radiated power

T^{4}

ke proportional kyun hai?

Planck's blackbody spectrum ko saari wavelengths par integrate karne se total power ∝

T^{4}

milti hai.

NET radiation exchange formula likho aur justify karo.

P_{n e t} = e σ A (T^{4} - T_{0}^{4})

; body

e σ A T^{4}

emit karti hai, surroundings se

e σ A T_{0}^{4}

absorb karti hai (Kirchhoff: same

e

Agar absolute temperature teen guna ho jaaye, radiated power kitne factor se badlegi?

3^{4} = 81

guna.

Radiation mein kelvin kyun use karna padta hai lekin Fourier's law °C use kar sakta hai?

T^{4}

absolute hai (T ki power); Fourier sirf difference

Δ T

use karta hai, jo °C aur K mein identical hota hai.

Convection ke liye Newton's law of cooling state karo.

H = h A (T_{s} - T_{f l u i d})

h

=convection coefficient.

Recall Feynman: ek 12-saal ke bacche ko explain karo

Ek hot bowl of soup imagine karo. Conduction aise hai jaise haath pakde bacchon ki ek line hot potato haath se haath pass karti hai — koi hilta nahi, heat hop karte hue jaati hai. Convection aise hai jaise ek baccha hot potato pakadta hai aur daud ke thandi side le jaata hai — carrier khud move karta hai. Radiation aise hai jaise potato itna hot hai ki glow karta hai, aur tum kamre ke doosri taraf se apne chehere par uski garmi feel karte ho — woh garmi invisible light ke roop mein empty air se udke aayi. Glowing wale ki ek chalaak rule hai: ise do guna hot karo (sahi kelvin mein), aur ye solah guna zyada chamkta hai.

Connections

Thermal conductivity k — material property table (metals high, gases low)
Second law of thermodynamics — heat spontaneously flows hot→cold
Black body radiation & Planck's law — $T^{4}$ law ki origin
Wien's displacement law — peak wavelength $T$ ke saath shift hoti hai
Newton's law of cooling — convection se derived exponential cooling
Electrical resistance Ohm's law — thermal resistance ke saath same math
Greenhouse effect — radiation balance application