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For a single plane layer, U combines inner and outer convection with wall conduction in series.
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Formula
U in W/(m2·K); h in W/(m2·K); L in m; k in W/(m·K)
| Symbol | Meaning | Unit |
|---|---|---|
| Overall heat-transfer coefficient on wall area | W/(m2·K) | |
| hi, ho | Inner and outer convection coefficients | W/(m2·K) |
| Wall thickness | m | |
| Wall thermal conductivity | W/(m·K) |
U=\left(\frac{1}{h_i}+\frac{L}{k}+\frac{1}{h_o}\right)^{-1}The relation adds area-based resistances for inner convection, the plane wall and outer convection. It assumes steady one-dimensional heat flow, a common reference area, constant properties and negligible contact resistance. Add conduction resistances for additional layers; cylindrical walls require logarithmic geometry.
The relation adds area-based resistances for inner convection, the plane wall and outer convection. It assumes steady one-dimensional heat flow, a common reference area, constant properties and negligible contact resistance. Add conduction resistances for additional layers; cylindrical walls require logarithmic geometry.
For a single plane layer, U combines inner and outer convection with wall conduction in series.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Overall heat transfer through a plane wall” and check its unit and magnitude.
For hi=10, ho=25 W/(m2·K), L=0.10 m and k=0.50 W/(m·K), U≈2.94 W/(m2·K).
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: U in W/(m2·K); h in W/(m2·K); L in m; k in W/(m·K).
Formula cluster
For a single plane layer, U combines inner and outer convection with wall conduction in series.
For hi=10, ho=25 W/(m2·K), L=0.10 m and k=0.50 W/(m·K), U≈2.94 W/(m2·K).
Estimate heat loss through walls with convective surface films.
Here is how to work through a typical Overall heat transfer through a plane wall (U = 1/(1/hi + L/k + 1/ho)) task step by step:
Task
Work through the numerical example for “Overall heat transfer through a plane wall” and check its unit and magnitude.
Solution path
For hi=10, ho=25 W/(m2·K), L=0.10 m and k=0.50 W/(m·K), U≈2.94 W/(m2·K).
Steady heat must cross the inner film, wall and outer film in sequence. The same heat rate passes through each; temperature drops add like voltage drops in a series circuit. Thus U is the reciprocal of the sum of area-based resistances. The resistance sum is for steady one-dimensional plane-wall transfer on a consistent area basis. Application: Estimate heat loss through walls with convective surface films. The numerical example For hi=10, ho=25 W/(m2·K), L=0.10 m and k=0.50 W/(m·K), U≈2.94 W/(m2·K) anchors the idea in a concrete measurement case.
Transient conduction, strongly varying properties, multidimensional spreading, radiation or contact resistance require an extended model. In cylindrical walls, area changes with radius and conduction resistance is logarithmic. Check geometry and boundary conditions before using this expression. The resistance sum is for steady one-dimensional plane-wall transfer on a consistent area basis. The corresponding units are U in W/(m2·K); h in W/(m2·K); L in m; k in W/(m·K). For hi=10, ho=25 W/(m2·K), L=0.10 m and k=0.50 W/(m·K), U≈2.94 W/(m2·K). This checks that the reference quantities are compatible.
These coefficients describe transfer between fluid and wall on each side. The smaller h creates the larger film resistance 1/h and may dominate overall transfer. Values depend on fluid, flow, surface and operating state; they are not universal material constants. The resistance sum is for steady one-dimensional plane-wall transfer on a consistent area basis. Scope: The relation adds area-based resistances for inner convection, the plane wall and outer convection. It assumes steady one-dimensional heat flow, a common reference area, constant properties and negligible contact resistance. Add conduction resistances for additional layers; cylindrical walls require logarithmic geometry. A practical application is Estimate heat loss through walls with convective surface films.
Write the quantity and unit from the variable list next to every value: U in W/(m2·K); h in W/(m2·K); L in m; k in W/(m·K). Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For hi=10, ho=25 W/(m2·K), L=0.10 m and k=0.50 W/(m·K), U≈2.94 W/(m2·K). is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The resistance sum is for steady one-dimensional plane-wall transfer on a consistent area basis.
The background states this starting condition: The relation adds area-based resistances for inner convection, the plane wall and outer convection. It assumes steady one-dimensional. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The resistance sum is for steady one-dimensional plane-wall transfer on a consistent area basis.
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