Back to Heat Transfer

Study notes

LearnExams

Qwestrum Engineering360 · Chemical Engineering · Heat Transfer

Convective Heat Transfer Coefficients

Convective heat transfer is characterised by the coefficient h in Newton’s law of cooling; h is found from dimensionless correlations of the form Nu = C·Re^m·Pr^n after checking whether the flow is laminar or turbulent.
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.

  • Forced vs natural convection — different correlations
  • Pr=μCpk;Re=ρVDμPr = \mu \frac{Cp}{k}; Re = \rho V \frac{D}{\mu}
  • h depends on fluid properties, velocity, and geometry

Topic details

Introduction

This topic teaches you to estimate h — the quantity that dominates most exchanger designs. You compute Reynolds and Prandtl numbers from fluid properties, decide the flow regime, pick the appropriate correlation (Dittus-Boelter for turbulent pipe flow, others for laminar or free convection), and back out h from the Nusselt number.

Key relations & formulas

q=hA(Ts−T∞)q = h A (T_{s} - T_\infty )
(Newton law of cooling)
Nu=hLkNu = h \frac{L}{k}
(Nusselt number)
Nu=CRemPrnNu = C Re^m Pr^n
(Dittus-Boelter: turbulent pipe, heating n=0.4, cooling n=0.3)

Notation and sign conventions

Relation 1 —
q=hAq = h A
q=hA(Ts−T∞)q = h A (T_{s} - T_\infty )
(Newton law of cooling)
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 —
Nu=hLkNu = h \frac{L}{k}
Nu=hLkNu = h \frac{L}{k}
(Nusselt number)
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 —
Nu=CRemPrnNu = C Re^m Pr^n
Nu=CRemPrnNu = C Re^m Pr^n
(Dittus-Boelter: turbulent pipe, heating n=0.4, cooling n=0.3)
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

Convection couples conduction in a thin fluid film to bulk fluid motion. The Nusselt number is the ratio of convective to conductive transport across that film, the Reynolds number decides whether the film is thin and turbulent or thick and laminar, and the Prandtl number tells how the momentum and thermal boundary layers compare in thickness. Because h grows strongly with velocity in turbulent flow (roughly with Re^0.8), pumping harder is an effective but energy-costly way to raise heat transfer. Free convection replaces the Reynolds number with a Grashof number driven by buoyancy.

Assumptions and validity limits

State assumptions explicitly before using any relation for convective heat transfer coefficients — 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 convective heat transfer coefficients.
4. Use equation 1:
q=hAq = h A
.
5. Use equation 2:
Nu=hLkNu = h \frac{L}{k}
.
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

Convective Heat Transfer Coefficients 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 convective heat transfer coefficients with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use convective heat transfer coefficients?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

The dominant error is applying the turbulent Dittus-Boelter correlation to laminar flow (or vice versa) without checking Re. Others include evaluating properties at the wrong temperature, using the wrong exponent n for heating versus cooling, and confusing the Nusselt number with the Biot number.

Quick revision checklist

Before attempting convective heat transfer coefficients problems, confirm you can:
1. Forced vs natural convection — different correlations
2.
Pr=μCpk;Re=ρVDμPr = \mu \frac{Cp}{k}; Re = \rho V \frac{D}{\mu}

3. h depends on fluid properties, velocity, and geometry
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.

h from Nusselt number

Problem

Turbulent water flow in a 25 mm pipe gives Nu = 220. With k_water = 0.6 W/m·K, find h.

Solution

h = Nu·k/D = 220 × 0.6/0.025 = 5280 W/m²·K. The high value is typical of turbulent liquid flow and far exceeds a gas-side coefficient.

Conceptual check — Convective Heat Transfer Coefficients

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 convective heat transfer coefficients." What should a complete answer include?

Exams & GATE

State whether laminar or turbulent before picking correlation.

📖 Standard books (India)

  • Process Heat Transfer — Kern

    Read: Syllabus unit

    Heat exchangers and process heat transfer

Explore related topics

See real chemical engineering careers

After exams and interviews, see how engineers actually built careers — milestones and decisions from people in the field.

Browse Chemical Engineering journeysPlan your path