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Qwestrum Engineering360 · Chemical Engineering · Heat Transfer

Radiation Exchange

Radiative exchange scales with the fourth power of absolute temperature and with emissivity; net transfer between grey surfaces combines their emissivities and the geometric view factor that fixes what fraction of one surface’s radiation reaches the other.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • σ=5.67×10−8Wm2K4\sigma = 5.67 \times 10^{-8} \frac{W}{m^{2}}K^{4}
  • Radiation significant at high T; negligible if ΔT small and low T
  • Blackbody:ε=1;realsurfacesε<1Black body: \varepsilon = 1; real surfaces \varepsilon < 1

Topic details

Introduction

This topic handles heat transfer that needs no medium, dominant in furnaces and high-temperature equipment. You use the Stefan-Boltzmann law for emission, view factors for geometry, and a surface-resistance / space-resistance network (the radiation analogue of the conduction circuit) to find net exchange between grey surfaces.

Key relations & formulas

E=εσT4E = \varepsilon \sigma T^{4}
(emissive power, gray surface)
q=σA1(T14−T24)/(1ε1+(A1A2)(1ε2−1))q = \sigma A_{1} (T_{1}^{4} - T_{2}^{4}) / (\frac{1}{\varepsilon_{1}} + (\frac{A_{1}}{A_{2}})(\frac{1}{\varepsilon_{2}} - 1))
(two gray surfaces, one enclosed)
ΣjFij=1Σ_j F_{ij} = 1
(view-factor summation for an enclosure)

Notation and sign conventions

Relation 1 —
E=εσT4E = \varepsilon \sigma T^{4}
E=εσT4E = \varepsilon \sigma T^{4}
(emissive power, gray surface)
Write this relation with symbols exactly as in Process Heat Transfer — Kern before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
q=σA1q = \sigma A_{1}
q=σA1(T14−T24)/(1ε1+(A1A2)(1ε2−1))q = \sigma A_{1} (T_{1}^{4} - T_{2}^{4}) / (\frac{1}{\varepsilon_{1}} + (\frac{A_{1}}{A_{2}})(\frac{1}{\varepsilon_{2}} - 1))
(two gray surfaces, one enclosed)
Write this relation with symbols exactly as in Process Heat Transfer — Kern before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
ΣjFij=1Σ_j F_{ij} = 1
ΣjFij=1Σ_j F_{ij} = 1
(view-factor summation for an enclosure)
Write this relation with symbols exactly as in Process Heat Transfer — Kern before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Every surface above absolute zero radiates energy proportional to εσT⁴, so radiation becomes decisive at high temperature where the T⁴ term explodes. Two things control net exchange: how well each surface emits and absorbs (emissivity, and for grey surfaces absorptivity equals emissivity) and how much of one surface is “seen” by the other (the view factor, purely geometric and obeying the summation and reciprocity rules). The network method treats the emissivity limitation as a surface resistance and the geometric limitation as a space resistance, letting you solve enclosures like resistor circuits.

Assumptions and validity limits

State assumptions explicitly before using any relation for radiation exchange — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Heat Transfer (Chemical) viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Heat Transfer (Chemical) papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to radiation exchange.
4. Use equation 1:
E=εσT4E = \varepsilon \sigma T^{4}
.
5. Use equation 2:
q=σA1q = \sigma A_{1}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Radiation Exchange appears in heat exchangers and reactors. In Indian chemical curricula this topic is tested because it connects theory to heat exchange in process equipment.
GATE and semester exams often combine radiation exchange with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use radiation exchange?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

The biggest error is using Celsius instead of kelvin in the T⁴ term, which is catastrophic. Others are omitting the emissivity resistances for non-black surfaces, misapplying view-factor reciprocity (A₁F₁₂ = A₂F₂₁), and forgetting that view factors in an enclosure sum to one.

Quick revision checklist

Before attempting radiation exchange problems, confirm you can:
1.
σ=5.67×10−8Wm2K4\sigma = 5.67 \times 10^{-8} \frac{W}{m^{2}}K^{4}

2. Radiation significant at high T; negligible if ΔT small and low T
3.
Blackbody:ε=1;realsurfacesε<1Black body: \varepsilon = 1; real surfaces \varepsilon < 1
Revise the solved examples in Process Heat Transfer — Kern and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Net radiation, small body in large enclosure

Problem

A body at 800 K (ε = 0.8, area 0.5 m²) sits in a large room at 300 K. Find the net radiant loss.

Solution

q = εσA(T₁⁴ − T₂⁴) = 0.8 × 5.67e-8 × 0.5 × (800⁴ − 300⁴) = 0.8 × 5.67e-8 × 0.5 × (4.096e11 − 8.1e9) ≈ 9.1 kW.

Conceptual check — Radiation Exchange

Problem

In a Heat Transfer (Chemical) semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of radiation exchange." What should a complete answer include?

Exams & GATE

View factor algebra: Σ F₁ⱼ = 1 for enclosure.

📖 Standard books (India)

  • Process Heat Transfer — Kern

    Read: Syllabus unit

    Heat exchangers and process heat transfer

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