Lesson 6.3: Natural & Forced Convection

Convection is the transfer of heat by the motion of fluid. GATE and PSU exams often test convective heat transfer coefficients, dimensionless numbers, and correlations.

🔹 1. Introduction

• Definition: Heat transfer due to bulk fluid motion

• Applications: Heat exchangers, cooling of electronic devices, air conditioning, industrial processes

• Key Concepts:

  1. Velocity of fluid affects convective heat transfer

  2. Temperature difference drives convection

  3. Dimensionless numbers: Grashof, Reynolds, Prandtl, Nusselt

🔹 2. Natural (Free) Convection

• Definition: Fluid motion due to density differences caused by temperature gradients (buoyancy)

• Governing Parameter: Grashof number (Gr)

Gr=gβΔTL3ν2Gr = \frac{g \beta \Delta T L^3}{\nu^2}Gr=ν2gβΔTL3​

Where g = gravity, β = thermal expansion, ΔT = temperature difference, L = characteristic length, ν = kinematic viscosity

• Heat Transfer Coefficient:

Nu=C(Gr⋅Pr)nNu = C (Gr \cdot Pr)^nNu=C(Gr⋅Pr)n

Nu = Nusselt number, Pr = Prandtl number

• Applications: Cooling of vertical plates, chimneys, natural ventilation

🔹 3. Forced Convection

• Definition: Fluid motion imposed by external means like pump, fan, or blower

• Governing Parameters: Reynolds (Re) and Prandtl (Pr) numbers

Nu=CRemPrnNu = C Re^m Pr^nNu=CRemPrn

• Internal Flow (Pipe):

  • Laminar: $Nu=3.66$ (fully developed)

  • Turbulent: Dittus–Boelter correlation: Nu=0.023Re0.8Pr0.4Nu = 0.023 Re^{0.8} Pr^{0.4}Nu=0.023Re0.8Pr0.4

• External Flow (Flat Plate):

  • Laminar: Nux=0.332Rex1/2Pr1/3Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}Nux​=0.332Rex1/2​Pr1/3

  • Turbulent: Nux=0.0296Rex4/5Pr1/3Nu_x = 0.0296 Re_x^{4/5} Pr^{1/3}Nux​=0.0296Rex4/5​Pr1/3

• Applications: Cooling of heat exchangers, fins, turbine blades

🔹 4. Combined Convection

• When both natural and forced convection present:

Nu=(Nuforcedn+Nunaturaln)1/n,n≈3Nu = (Nu_\text{forced}^n + Nu_\text{natural}^n)^{1/n}, \quad n ≈ 3Nu=(Nuforcedn​+Nunaturaln​)1/n,n≈3

• Example: Cooling of electronic device with fan and buoyancy effects

🔹 5. Solved Examples (PYQ Style)

1. Nusselt number and heat transfer coefficient for vertical plate (natural convection)

2. Convective heat transfer in pipe with laminar and turbulent flow

3. Combined convection for electronic cooling

🔹 6. Practice Exercises

1. Calculate Grashof and Reynolds numbers for given system

2. Compute Nu and h for natural and forced convection

3. Apply Dittus–Boelter correlation for turbulent flow in pipe

4. Determine heat transfer rate from vertical plate in air

5. Solve combined convection problems

🔹 7. Summary

• Natural Convection: Driven by buoyancy, characterized by Grashof number

• Forced Convection: Driven by external force, characterized by Reynolds number

• Nusselt Number: Represents convective heat transfer

• Applications: Heat exchangers, cooling of devices, industrial processes