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Engineering Calculation Report
Date: 2026-06-13 10:01

Composite Walls with Convection Boundaries

Evaluate overall U-value, thermal resistance profiles, interface temperatures, and room surface condensation risks.

Inside Air T_h Convection h_i Radiation ε_i Layer 1 k₁, L₁ Layer 2 k₂, L₂ Layer 3 k₃, L₃ Outside Air T_c Convection h_o Radiation ε_o Heat Loss / Gain (Q) T_si T_so Area (A)

Calculation Domain Inputs

Specify the properties of the room and environment boundaries:

  • Boundary Fluids ($T_h, T_c$): Air temperatures inside and outside the room.
  • Convection ($h_i, h_o$): Coefficients representing convective boundary layers.
  • Radiation ($\varepsilon_i, \varepsilon_o$): Optional surface thermal emissivity exchanges.
  • Inside Room RH ($RH_{in}$): Inside humidity to assess surface condensation risks ($T_{si} \le T_{dew}$).

Boundary & Wall Setup

Undisturbed 1D Wall Layers

Overall Heat Transfer Coefficient:
$$U = 1 / R_{total}$$ $$R_{total} = R_{si,eff} + \sum (L_i / k_i) + R_{se,eff}$$ • $Q$ = Heat transfer rate [W] $= U A (T_h - T_c)$
• $A$ = Area [m²]
• $R_{total}$ = Total thermal resistance [m²K/W]
• $h_i, h_o$ = Convection coefficients [W/m²K]
• $h_{r,i}, h_{r,o}$ = Radiative heat transfer coefficients [W/m²K]

Results & Visualization

Overall U-Value
--
W/(m²·K)
Total R-Value
--
m²·K/W
Heat Loss/Gain (Q)
--
Watts
Condensation Risk
Safe
Tdew = -- °C

Temperature Profile vs. Dew Point

Thermal Resistance Contribution

Detailed Component Analysis

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Calculation Methodology

Mathematical Model & Theory

Conduction through a composite wall with convection and radiation boundaries is solved using the thermal resistance network. The overall heat transfer coefficient ($U$-value) relates fluid-to-fluid heat exchange:

$$U = \frac{1}{R_{total}}$$ $$R_{total} = R_{si} + \sum_{i=1}^{n} R_i + R_{se}$$

Where the film resistances $R_{si}$ and $R_{se}$ incorporate both convection and radiation:

$$R_{si} = \frac{1}{h_i + h_{r,i}}, \quad R_{se} = \frac{1}{h_o + h_{r,o}}$$

The radiative coefficients are non-linear functions of surface temperatures $T_{si}$ and $T_{so}$:

$$h_{r,i} = \varepsilon_i \sigma (T_{h,K} + T_{si,K})(T_{h,K}^2 + T_{si,K}^2)$$

Magnus-Tetens Dew Point ($T_{dew}$):

The room dew point temperature is calculated to evaluate surface condensation risk. Condensation occurs if $T_{si} \le T_{dew}$:

$$\alpha = \frac{17.625 T_h}{243.04 + T_h} + \ln\left(\frac{RH_{in}}{100}\right)$$ $$T_{dew} = \frac{243.04 \alpha}{17.625 - \alpha}$$

Academic References:

  1. ISO 6946: Building components and building elements — Thermal resistance and thermal transmittance — Calculation methods.
  2. Incropera, F. P. (2011). Fundamentals of Heat and Mass Transfer.

Worked Engineering Example

Problem Statement:
A composite wall has a 100 mm concrete layer ($k = 1.7$ W/m·K) and a 120 mm insulation layer ($k = 0.04$ W/m·K). Inside air is at 20°C ($h_i = 10$ W/m²K) and outside air is at -10°C ($h_o = 25$ W/m²K). Radiation is disabled. Area is 10 m². Find the overall U-value and inner surface temperature.

Step-by-step Solution:
1. Calculate convective surface resistances:
$$R_{si} = \frac{1}{h_i} = 0.1 \text{ m²K/W}$$ $$R_{se} = \frac{1}{h_o} = 0.04 \text{ m²K/W}$$ 2. Calculate solid wall layer conduction resistances:
$$R_{concrete} = \frac{0.100}{1.7} = 0.0588 \text{ m²K/W}$$ $$R_{insulation} = \frac{0.120}{0.04} = 3.0000 \text{ m²K/W}$$ 3. Total thermal resistance:
$$R_{total} = 0.1 + 0.0588 + 3.0 + 0.04 = 3.1988 \text{ m²K/W}$$ 4. Overall heat transfer coefficient (U-value):
$$U = \frac{1}{R_{total}} = \frac{1}{3.1988} = 0.3126 \text{ W/(m²K)}$$ 5. Inner surface temperature ($T_{si}$):
$$q = U(T_h - T_c) = 0.3126 \times (20 - (-10)) = 9.378 \text{ W/m²}$$ $$T_{si} = T_h - q R_{si} = 20 - 9.378 \times 0.1 = 19.06^\circ\text{C}$$
Conclusion: The overall U-value is 0.3126 W/(m²K) and the room face wall surface temperature is 19.06°C.