- Asked 2/15
- 2068 Magh · 6 marks
Overall heat transfer coefficient: two-layer plane wall
Short answer
For a two-layer plane wall with convection on both sides, series thermal resistances sum to 1/(h₁A) + L₁/(k₁A) + L₂/(k₂A) + 1/(h₂A). The overall heat transfer coefficient U = 1/(A·R_total) = 1/(1/h₁ + L₁/k₁ + L₂/k₂ + 1/h₂) W/m²·K.
Using thermal resistance derive an expression for overall heat transfer coefficient for composite plane wall consisting of two layers with convection on both sides.
Setup. A plane wall of area A has two layers: thicknesses L₁, L₂ and conductivities k₁, k₂. Hot fluid at T_∞1 touches layer 1 with film coefficient h₁. Cold fluid at T_∞2 touches layer 2 with coefficient h₂. Steady, one-dimensional heat flow.
T_inf1 -[1/h1A]- T_s1 -[L1/k1A]- T_i -[L2/k2A]- T_s2 -[1/h2A]- T_inf2
Resistances in series
R₁ = 1/(h₁A), R₂ = L₁/(k₁A), R₃ = L₂/(k₂A), R₄ = 1/(h₂A)
R_total = 1/(h₁A) + L₁/(k₁A) + L₂/(k₂A) + 1/(h₂A)
Heat flow
The same Q passes through each element, so the temperature drops add:
T_∞1 − T_∞2 = Q (R₁ + R₂ + R₃ + R₄)
Q = (T_∞1 − T_∞2)/R_total
Overall heat transfer coefficient
The overall coefficient U is defined by
Q = U A (T_∞1 − T_∞2)
Comparing the two expressions for Q: U A = 1/R_total, so
U = 1/(A R_total) = 1/[1/h₁ + L₁/k₁ + L₂/k₂ + 1/h₂] (W/m²·K)
For n layers: U = 1/[1/h₁ + Σ L_j/k_j + 1/h₂]. Note that U is smaller than the smallest conductance (h₁, h₂, k_j/L_j) in the series.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Thermal resistance; composite wall with convection · Fundamental of Thermodynamics & Heat Transfer, chapter 7 · asked 2×
- Thermal resistance expressions; three-layer composite wall · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- Heat flow through composite plane wall, three layers · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- Overall heat transfer coefficient of hollow cylinder · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- Thermal resistances: plane wall, cylinder, convection · Fundamental of Thermodynamics & Heat Transfer, chapter 7
- Thermal resistance of composite wall, electric analogy · Fundamental of Thermodynamics & Heat Transfer, chapter 7 · asked 2×
- Insulating layer: minimum outside heat transfer coefficient · Fundamental of Thermodynamics & Heat Transfer, chapter 7 · asked 2×
- Composite furnace wall heat loss · Heat Transfer, chapter 2
- Plane wall with internal heat generation · Heat Transfer, chapter 2
- Thermal performance, transmittance of composite wall · Building Technology, chapter 1
- Stability of gravity wall, two layers · Foundation Engineering, chapter 3
All Fundamental of Thermodynamics & Heat Transfer chapter 7 questions →