Overall Heat Transfer Coefficient Calculator
overall heat transfer coefficient calculator U-factor from inside convection hi, wall conductivity k, thickness d, and outside convection ho. Accurate engineering formulas and unit conversions for engineers, students & technicians.
Calculate Overall Heat Transfer Coefficient Calculator
Enter your engineering parameters below to compute verified physical and mathematical metrics.
Calculation Results
Calculated using verified physical methodology: Overall Heat Transfer Coefficient: U = \1 / \frac{1{h_i} + \d / k + \1 / h_o}
Total Thermal Resistance: R_{total} = \1 / U = R_i + R_{wall} + R_o
Quick Summary
The Overall Heat Transfer Coefficient Calculator evaluates the combined composite U-factor ($U = \1 / \frac{1{h_i} + \d / k + \1 / h_o}$) across inside fluid convection, solid wall conduction, and outside fluid convection.
Formula Explanation
Overall Heat Transfer Coefficient: U = \1 / \frac{1{h_i} + \d / k + \1 / h_o}
Total Thermal Resistance: R_{total} = \1 / U = R_i + R_{wall} + R_o
How It Works
The Overall Heat Transfer Coefficient Calculator sums individual thermal resistances in series: inside film resistance ($R_i = 1/h_i$), solid wall conductive resistance ($R_{wall} = d/k$), and outside film resistance ($R_o = 1/h_o$). Taking the reciprocal of total resistance ($R_{total}$) yields the overall U-factor ($U$).
Step-by-Step Worked Example
Practical Problem: Calculate the overall U-factor for a 10 mm steel vessel wall ($k = 50\text{ W/m}\cdot\text{K}$) separating hot water ($h_i = 1,000\text{ W/m}^2\cdot\text{K}$) from ambient air ($h_o = 25\text{ W/m}^2\cdot\text{K}$).
- Step 1: Identify Input Parameters: $h_i = 1,000\text{ W/m}^2\cdot\text{K}$, $k = 50\text{ W/m}\cdot\text{K}$, $d = 0.010\text{ m}$, $h_o = 25\text{ W/m}^2\cdot\text{K}$.
- Step 2: Calculate Individual Thermal Resistances: $R_i = \1 / 1000 = 0.0010\text{ m}^2\cdot\text{K/W}$, $R_{wall} = \0.010 / 50 = 0.0002\text{ m}^2\cdot\text{K/W}$, $R_o = \1 / 25 = 0.0400\text{ m}^2\cdot\text{K/W}$.
- Step 3: Sum Total Series Thermal Resistance: $R_{total} = 0.0010 + 0.0002 + 0.0400 = 0.0412\text{ m}^2\cdot\text{K/W}$.
- Step 4: Execute Reciprocal Division for U-Factor: $U = \1 / R_{total} = \1 / 0.0412 = 24.2718\text{ W/m}^2\cdot\text{K}$.
- Step 5: Convert and Interpret Imperial Metric Outputs: Overall U-Factor $U = 24.27\text{ W/m}^2\cdot\text{K}$. Imperial U-Factor: $24.2718 \times 0.176110 = 4.274\text{ BTU/hr}\cdot\text{ft}^2\cdot^\circ\text{F}$. Imperial R-Value: $R_{total,us} = \1 / 4.274 = 0.234\text{ hr}\cdot\text{ft}^2\cdot^\circ\text{F/BTU}$. Controlling resistance is the outside air convection film ($97.1\%$ of total thermal resistance).
Real-World Calculation Examples
Scenario 1: Water-to-Air Steel Vessel Wall
Parameters: $h_i = 1,000$, $k = 50$, $d = 0.010\text{ m}$, $h_o = 25$
Result: $U = 24.27\text{ W/m}^2\cdot\text{K}$ (4.27 BTU/hr·ft²·°F). Air film controls U-factor.
Scenario 2: Water-to-Water Shell-and-Tube Exchanger
Parameters: $h_i = 3,000$, $k = 400$ (copper), $d = 0.002\text{ m}$, $h_o = 2,500$
Result: $U = 1,353.16\text{ W/m}^2\cdot\text{K}$ (238.30 BTU/hr·ft²·°F). High-efficiency heat exchanger.
Scenario 3: Insulated Building Wall Assembly
Parameters: $h_i = 8.3$, $k = 0.04$ (insulation), $d = 0.100\text{ m}$, $h_o = 25$
Result: $U = 0.376\text{ W/m}^2\cdot\text{K}$ (0.066 BTU/hr·ft²·°F). Building wall thermal U-factor.
Scenario 4: Double-Glazed Glass Window Assembly
Parameters: $h_i = 8.3$, $k = 0.026$ (air gap), $d = 0.012\text{ m}$, $h_o = 25$
Result: $U = 1.608\text{ W/m}^2\cdot\text{K}$ (0.283 BTU/hr·ft²·°F). Double-pane window U-factor.
Key Benefits of Using This Calculator
Heat Exchanger & HVAC Design
Essential tool for sizing shell-and-tube, plate-and-frame, and HVAC hydronic heat exchangers.
Controlling Resistance Breakdown
Identifies which individual layer ($R_i$, $R_{wall}$, $R_o$) controls thermal performance.
SI & Imperial U-Factor & R-Value
Provides readouts in $\text{W/m}^2\cdot\text{K}$, $\text{BTU/hr}\cdot\text{ft}^2\cdot^\circ\text{F}$, SI R-value, and US R-value.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is Overall Heat Transfer Coefficient (U-factor)?
The overall heat transfer coefficient (U) measures overall heat flow rate per unit area per unit temperature difference across composite convective and conductive layers.
What is the formula for overall U-factor across a flat wall?
U = 1 / (1/hi + sum(d_k / k_k) + 1/ho), where 1/hi is inside film resistance, d/k is wall conductive resistance, and 1/ho is outside film resistance.
How does U-factor relate to R-value?
U-factor is reciprocal to total thermal resistance: U = 1 / R_total and R_total = 1 / U.
What is meant by the controlling thermal resistance?
The controlling resistance is the largest individual thermal resistance in series (e.g. gas film h ~ 25 W/m²·K), which limits overall heat transfer regardless of how conductive the metal wall is.
How converts W/m²·K to BTU/hr·ft²·°F?
Multiply W/m²·K by 0.176110 to obtain BTU/hr·ft²·°F (e.g. 24.27 W/m²·K = 4.27 BTU/hr·ft²·°F).
How is fouling factor included in heat exchanger U-factor calculations?
Fouling resistances (Rf,i and Rf,o) are added in series: 1/U = 1/hi + Rf,i + d/k + Rf,o + 1/ho, accounting for scale and rust buildup.
What is the overall heat transfer coefficient for circular pipes?
For cylindrical pipes, Area varies with radius: 1/(U_o * A_o) = 1/(h_i * A_i) + ln(r_o/r_i)/(2 * pi * k * L) + 1/(h_o * A_o).
What typical U-values exist in building insulation codes?
Energy efficient walls: U ~ 0.20 to 0.35 W/m²·K (R-15 to R-25); Energy efficient windows: U ~ 1.2 to 1.8 W/m²·K.
Why does high wall conductivity k have minimal impact when fluid convection h is low?
Because wall resistance d/k is negligible compared to fluid film resistance 1/h (e.g. 0.0002 vs 0.0400 m²·K/W), making fluid boundary layers dominate total resistance.
How is total heat transfer rate calculated from U-factor?
Q = U * A * LMTD, where A is heat transfer area and LMTD is Logarithmic Mean Temperature Difference across the heat exchanger.