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Topic Guide

Heat Transfer
GATE CH Guide

Syllabus breakdown, weightage, essential formulas, and a study plan for the Heat Transfer section of GATE Chemical Engineering.

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Overview

Heat Transfer in the GATE Chemical Engineering (CH) syllabus covers how thermal energy moves through solids, fluids, and across phase boundaries, and how engineers size equipment around that movement. It sits under the broader "Fluid Mechanics and Mechanical Operations, Heat Transfer" theme in the official syllabus and is one of the most numerically dense sections of the paper.

The section splits into two halves that build on each other. The first half is the physics: conduction (Fourier's law), convection (dimensionless correlations like Nusselt and Prandtl numbers), radiation (Stefan-Boltzmann law), and unsteady-state conduction (lumped capacitance, Biot number). The second half is applied equipment design: heat exchangers sized with the LMTD or NTU-effectiveness method, plus boiling and condensation, which govern reboilers and condensers in distillation columns.

GATE consistently tests heat exchanger sizing (LMTD, correction factor F, area calculations) as a numerical problem, and pairs it with conceptual questions on the modes of heat transfer, dimensionless groups, and unsteady conduction. ChemeGate's LMTD Calculator covers exactly this, the log mean temperature difference and required heat transfer area, A = Q/(U × LMTD), including the worked GATE 2025 Q51 problem.

Real GATE CH PYQ Frequency (2024–2026)

2024	2025	2026	3-Yr Avg
5	6	4	5

Computed directly from 15 real questions tagged to this topic across our GATE CH 2024–2026 archive, averaging 5 questions/year. Browse the underlying 15 questions for this topic in the PYQ archive, or see the full topic weightage comparison across all topics.

GATE Weightage

Heat Transfer typically contributes 2–4 questions (about 4–8 marks) to the GATE CH paper, most of it concentrated in heat exchanger numericals and conduction/convection theory.

Sub-area	Approx. Marks
Heat exchangers (LMTD, NTU, F-factor)	~3–4
Conduction (steady & unsteady state)	~2–3
Convection & dimensionless correlations	~1–2
Boiling, condensation & radiation	~1–2

Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.

Key Subtopics

Conduction

Fourier's law and steady 1-D conduction through plane walls, cylinders, and spheres. Includes composite-wall thermal resistance networks and the critical radius of insulation for cylindrical/spherical geometries.

Convection fundamentals

Newton's law of cooling, free vs. forced convection, and the boundary-layer concept that connects fluid mechanics to heat transfer.

Dimensionless correlations

Nusselt number correlations (Dittus-Boelter, Sieder-Tate) relate Nu to Re and Pr for forced convection in pipes; Grashof and Rayleigh numbers govern free-convection correlations.

Heat exchangers

The LMTD method for counter-current and co-current flow, the correction factor F for shell-and-tube and cross-flow exchangers, and the NTU-effectiveness method as an alternative sizing approach.

Boiling and condensation

The pool-boiling curve (nucleate, transition, film boiling) and critical heat flux; filmwise vs. dropwise condensation and Nusselt's theory for condensate film thickness.

Radiation

Stefan-Boltzmann law, black-body vs. grey-body emission, emissivity, and view factors for radiative exchange between surfaces.

Unsteady-state conduction

The lumped-capacitance method (valid when the Biot number is small) and transient conduction in solids using Heisler charts for finite Biot numbers.

Extended surfaces (fins)

Temperature distribution along a fin, fin efficiency, and fin effectiveness for enhancing convective heat transfer from a surface.

Essential Formulas

Full formula reference →

$q = -kA\dfrac{dT}{dx}$

Fourier's law of conduction; k = thermal conductivity, A = area normal to flow

$Q = \dfrac{kA(T_1-T_2)}{L}$

Steady conduction through a plane wall of thickness L

$Q = \dfrac{2\pi k L (T_1-T_2)}{\ln(r_2/r_1)}$

Steady radial conduction through a cylindrical wall

$R_{cond} = \dfrac{L}{kA}, \quad R_{conv} = \dfrac{1}{hA}$

Thermal resistances, add in series for composite walls

$q = hA(T_s - T_\infty)$

Newton's law of cooling for convective heat flux

$r_c = \dfrac{k}{h}$

Critical radius of insulation for a cylinder, adding insulation below rc increases heat loss

$Bi = \dfrac{hL_c}{k}$

Biot number, ratio of internal conductive to external convective resistance

$Fo = \dfrac{\alpha t}{L_c^2}$

Fourier number, dimensionless time for unsteady conduction problems

$Nu = \dfrac{hL}{k}$

Nusselt number, ratio of convective to conductive heat transfer

$Nu = 0.023\,Re^{0.8}Pr^{n}$

Dittus-Boelter correlation for turbulent flow in a pipe (n = 0.4 heating, 0.3 cooling)

$\Delta T_{lm} = \dfrac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}$

Log mean temperature difference (LMTD) between hot and cold streams

$A = \dfrac{Q}{U \times \text{LMTD}}$

Required heat transfer area, given duty Q and overall coefficient U, apply an F-factor correction for multi-pass exchangers

$\varepsilon = \dfrac{Q_{actual}}{Q_{max}}, \quad NTU = \dfrac{UA}{C_{min}}$

Effectiveness-NTU method, an alternative to LMTD when outlet temperatures are unknown

$E_b = \sigma T^4$

Stefan-Boltzmann law for black-body emissive power (σ = 5.67×10⁻⁸ W/m²K⁴)

$Q = \varepsilon \sigma A (T_1^4 - T_2^4)$

Radiative heat exchange between a grey surface and its surroundings

Visual Reference

Same 0.1 m thickness, three different k values → three different slopes. The insulation layer (k = 0.04 W/mK) carries 88% of the total ΔT despite being geometrically identical to the other two.

Infrared thermal image of a building at night, showing heat escaping through the envelope in false color — Heat loss made visible — an infrared thermogram, the same conduction/convection physics this guide covers, just imaged directly instead of calculated. Mihai-Cosmin Pascariu, CC BY-SA 4.0, via Wikimedia Commons.

Derivations & Physical Insight

Deriving LMTD from a Differential Energy Balance

LMTD isn't an arbitrary average, it falls out of integrating the heat balance along the length of a counter-current (or co-current) exchanger. Take a differential slice dA of exchanger area. The heat lost by the hot stream equals the heat gained by the cold stream, and both equal the local duty transferred across dA via the overall coefficient U:

Define the local temperature difference ΔT = T_h − T_c. Combining the two energy-balance halves gives dΔT/ΔT as a function of dA alone (the mass-flow and cp terms collapse into constants), so integrating from the inlet end (ΔT₁) to the outlet end (ΔT₂) over the full area A produces a logarithmic, not arithmetic, relationship:

dQ = -\dot m_h c_{p,h}\,dT_h = \pm\dot m_c c_{p,c}\,dT_c = U(T_h - T_c)\,dA

Q = UA \cdot \dfrac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)} = UA \cdot \Delta T_{lm}

Why the Biot Number Decides Whether Lumped Capacitance Applies

The lumped-capacitance method assumes a solid's internal temperature is uniform at every instant during cooling or heating, a huge simplification, since real conduction takes time to propagate through a body. Whether that assumption is safe comes down to comparing two resistances: the internal conductive resistance (L_c/k) that governs how fast heat spreads inside the solid, and the external convective resistance (1/h) that governs how fast heat leaves the surface.

The Biot number Bi = hL_c/k is exactly that ratio. When Bi is small (conventionally < 0.1), the external convective resistance dominates, heat leaves the surface far slower than it can redistribute internally, so the whole solid cools nearly uniformly and a single lumped temperature is a good approximation. When Bi is large, internal conduction is the bottleneck, and real temperature gradients build up inside the solid that a lumped model would miss entirely, requiring Heisler charts or a full PDE solution instead.

Worked Practice Problems

Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.

1-mark · NAT

Biot Number Check for a Quenched Steel Ball

Problem: A steel sphere of radius 1 cm (k = 40 W/m·K) is suddenly quenched in oil with a convective coefficient h = 300 W/m²·K. Determine the Biot number and state whether the lumped-capacitance method is valid.

Given: r = 0.01 m, k = 40 W/m·K, h = 300 W/m²·K. For a sphere, L_c = r/3.

L_c = \dfrac{r}{3} = \dfrac{0.01}{3} = 3.33\times10^{-3}\ \text{m}

Bi = \dfrac{hL_c}{k} = \dfrac{300 \times 3.33\times10^{-3}}{40} = 0.025

Answer: Bi ≈ 0.025 (< 0.1), lumped capacitance is valid.

2-mark · NAT

Counter-Current Exchanger Area from LMTD

Problem: Hot oil enters a counter-current double-pipe exchanger at 150°C and leaves at 90°C, while cooling water enters at 25°C and leaves at 70°C. The duty is 200 kW and U = 450 W/m²·K. Find the required heat transfer area.

Given: T_h,in = 150°C, T_h,out = 90°C, T_c,in = 25°C, T_c,out = 70°C, Q = 200,000 W, U = 450 W/m²·K.

\Delta T_1 = T_{h,in} - T_{c,out} = 150 - 70 = 80\ °C

\Delta T_2 = T_{h,out} - T_{c,in} = 90 - 25 = 65\ °C

\Delta T_{lm} = \dfrac{80-65}{\ln(80/65)} = \dfrac{15}{0.2076} = 72.3\ °C

A = \dfrac{Q}{U \times \Delta T_{lm}} = \dfrac{200{,}000}{450 \times 72.3}

Answer: A ≈ 6.15 m²

Topic-wise PYQ Frequency

High

LMTD & heat exchanger sizing

Almost every GATE CH paper has a numerical here, counter-current vs. co-current comparisons and F-factor problems are favorites.

Medium

Conduction through composite/cylindrical walls

Thermal resistance networks and critical radius of insulation appear regularly as short numericals.

Medium

Unsteady-state conduction (Biot, lumped system)

Frequently tested as conceptual MCQs checking whether the lumped-capacitance assumption is valid.

Medium

Dimensionless correlations (Nu, Pr, Gr)

Usually paired with a convection numerical or asked as a matching/definition question.

Low

Boiling & condensation

Occasional conceptual question on the boiling curve or condensation mode, rarely numerical.

Low

Radiation

Tested less often than conduction/convection; usually a single conceptual or Stefan-Boltzmann numerical.

Low

Fins

Occasionally appears as a short numerical on fin efficiency or effectiveness.

Recommended Study Order

1
1. Conduction & thermal resistance networks
The foundation for every other topic, composite walls, cylinders, and the critical radius of insulation build direct intuition for resistance-in-series thinking.
2
2. Convection fundamentals & dimensionless numbers
Nusselt, Prandtl, and Grashof numbers recur throughout heat exchanger and boiling/condensation problems, so lock these in early.
3
3. LMTD & heat exchangers
The highest-yield GATE topic in this section, practice both counter-current/co-current LMTD and F-factor multi-pass problems until they're automatic.
4
4. NTU-effectiveness method
A natural extension of LMTD, useful when outlet temperatures aren't given directly.
5
5. Unsteady-state conduction
Biot and Fourier numbers are quick to learn once resistance concepts are solid, and show up often as conceptual MCQs.
6
6. Boiling, condensation & radiation
Lower PYQ frequency, cover after the high-yield topics are secure, focusing on the boiling curve and Stefan-Boltzmann law.
7
7. Fins
Lowest frequency; a quick pass over fin efficiency/effectiveness definitions is usually enough.

Common Pitfalls

✗ Mixing up ΔT1/ΔT2 pairing between counter-current and co-current flow when computing LMTD.

✓ Always draw the temperature profile first, for counter-current, pair hot-in with cold-out; for co-current, pair hot-in with cold-in.

✗ Forgetting the F correction factor for shell-and-tube (1-2, 2-4 pass) or cross-flow exchangers.

✓ Only true counter-current or co-current exchangers use LMTD directly. Any multi-pass or cross-flow arrangement needs Q = U·A·F·LMTD with F ≤ 1.

✗ Applying the lumped-capacitance method when Bi > 0.1.

✓ Check the Biot number first, lumped capacitance assumes negligible internal resistance, which only holds for small, highly conductive, or low-h objects.

✗ Treating conduction area as constant for cylindrical or spherical geometries.

✓ Area changes with radius in radial conduction, use the logarithmic mean area (cylinder) or geometric mean area (sphere) instead of a simple arithmetic average.

Put It Into Practice

Work through LMTD and heat-exchanger-area problems interactively, then check your approach against the worked GATE 2025 Q51 solution and other solved previous-year questions.

Open the LMTD Calculator →Take a Practice Test →

Keep Exploring

Heat Transfer
GATE CH Guide

Overview

Real GATE CH PYQ Frequency (2024–2026)

GATE Weightage

Key Subtopics

Essential Formulas

Visual Reference

Derivations & Physical Insight

Deriving LMTD from a Differential Energy Balance

Why the Biot Number Decides Whether Lumped Capacitance Applies

Worked Practice Problems

Biot Number Check for a Quenched Steel Ball

Counter-Current Exchanger Area from LMTD

Topic-wise PYQ Frequency

Recommended Study Order

Common Pitfalls

Put It Into Practice

Related

Fluid Mechanics

Mechanical Operations (Unit Operations)

LMTD Calculator

GATE CH Formula Sheet

GATE Practice Tests by Year

Heat TransferGATE CH Guide

Overview

Real GATE CH PYQ Frequency (2024–2026)

GATE Weightage

Key Subtopics

Essential Formulas

Visual Reference

Derivations & Physical Insight

Deriving LMTD from a Differential Energy Balance

Why the Biot Number Decides Whether Lumped Capacitance Applies

Worked Practice Problems

Biot Number Check for a Quenched Steel Ball

Counter-Current Exchanger Area from LMTD

Topic-wise PYQ Frequency

Recommended Study Order

Common Pitfalls

Put It Into Practice

Related

Fluid Mechanics

Mechanical Operations (Unit Operations)

LMTD Calculator

GATE CH Formula Sheet

GATE Practice Tests by Year

Heat Transfer
GATE CH Guide