1. Choose what to solve for
2. Boundary conditions
How the model works
This calculator assumes steady-state, one-dimensional heat flow through elements in series. Each element contributes an area-normalized thermal resistance:
Convection film: R'' = 1 / h
Contact resistance: R'' = R''contact
q'' = (TA − TB) / ΣR''
Q = q'' A
For a flowing fluid, velocity alone is not enough to determine h. The convection coefficient depends on geometry, flow regime, fluid properties, and the applicable Nusselt correlation. Enter h directly, or calculate it from a known Nusselt number using h = Nu·k/Lc.
3. Thermal resistance stack
Liquid-water properties reference ↗ · Pure water, 0–99°C at 100 kPa absolute.
Results
Layer-by-layer temperatures
| Location | Element | R'' | Temperature | ΔT across element |
|---|---|---|---|---|
| Calculate to populate the temperature profile. | ||||
Assumptions and limits
- Steady-state, one-dimensional heat transfer with every element in series and the same heat-transfer area.
- Material properties and convection coefficients are treated as constant at the values entered.
- Radiation is not modeled separately. If appropriate, it can be incorporated only through a justified effective heat-transfer coefficient.
- A flowing fluid layer is represented as a boundary-film resistance. This calculator does not model the fluid bulk temperature changing along its flow direction.
- Velocity is optional information only. It is not used unless you independently obtain a Nusselt number or convection coefficient appropriate to your geometry and flow.
- Transient storage, phase change, internal heat generation, multidimensional effects, fins, and parallel heat paths are outside this model.
How to use the thermal-resistance model
Represent the heat path from Side A to Side B as a series of thermal resistances. Add a convection film wherever heat moves between a bulk fluid and a surface, a conduction layer for each solid material, and a contact resistance where two surfaces have a known interface resistance. For a steady one-dimensional series path, the same heat flux passes through every element.
The calculator can solve the overall heat flux and heat rate, either boundary temperature, or one selected layer property. The layer-by-layer table then shows how the total temperature difference is distributed across the resistances.
When to use it
- Flat composite walls, insulation stacks, furnace walls, panels, and similar layered systems.
- Quick estimates that combine internal/external convection with solid conduction.
- Back-solving an effective conductivity, thickness, convection coefficient, or contact resistance from known heat transfer.
- Identifying which layer dominates total thermal resistance.
Key assumptions
- Steady-state, one-dimensional heat transfer.
- Every series element uses the same heat-transfer area.
- Thermal conductivity, convection coefficients, and contact resistance are constant at the entered values.
- No internal heat generation, phase change, transient energy storage, parallel paths, fins, or multidimensional spreading.
- Radiation is omitted unless you deliberately represent it with a justified effective coefficient.
Common mistakes
- Using fluid velocity as though it directly determines h. Velocity is only one input to a convection correlation. Geometry, Reynolds number, Prandtl number, fluid properties, and boundary conditions also matter.
- Confusing conductivity k with convection coefficient h. k has units of W/(m·K); h has units of W/(m²·K).
- Using bulk fluid temperature as a wall-surface temperature. A convection film accounts for the temperature drop between the bulk fluid and the surface.
- Ignoring temperature-dependent properties. For a large temperature span, use representative properties or divide the system into more detailed intervals.
- Using the planar model for a thick cylindrical wall. Radial conduction through pipe or vessel walls has changing area and uses a logarithmic cylindrical resistance.
- Forgetting fouling or contact resistance when it is important. Thin low-conductivity films can dominate otherwise conductive stacks.
Interpreting the temperature profile
The temperature drop across each element is q''R''. A layer with a large fraction of the total resistance will also take a large fraction of the total temperature difference. That makes the interface-temperature table useful for identifying insulation bottlenecks, estimating wall temperatures, and checking whether a material may exceed a temperature limit.
The overall coefficient reported here is U = 1/ΣR'' on the common area basis. In real heat exchangers, inside and outside surface areas may differ, fouling is often added explicitly, and U must be defined on a stated area basis.
Reference background: the U.S. Department of Energy heat-transfer handbook covers conduction, convection, radiation, and thermal-resistance concepts. DOE heat-transfer handbook.
Equation values and input guide
Build the thermal path in order from Side A to Side B. Add fluid films, solids and contact resistances where physically present. Choose the unknown; if solving a layer property, enter known heat flow and select that specific layer.
- TA, TB
- Boundary temperatures. Include a convection film when a boundary is a bulk fluid temperature rather than a solid surface temperature.
- L, k
- Solid layer thickness in m and thermal conductivity in W/(m·K). Use conductivity at a representative material temperature.
- h
- Convection coefficient in W/(m²·K), obtained from a justified correlation or measurement. Velocity alone does not define h.
- Nu, Lc
- Dimensionless Nusselt number and correlation-specific characteristic length (m), used in h = Nu kfluid/Lc. Here kfluid is fluid conductivity, not solid conductivity.
- R″
- Thermal resistance per unit area in m²·K/W. Solid: L/k; fluid film: 1/h; contact: entered area-normalized resistance.
- ΣR″, U
- Sum of the series resistances and overall coefficient U = 1/ΣR″ in W/(m²·K), on the common area basis.
- q″, Q, A
- Heat flux in W/m², total heat rate in W and common transfer area in m². Q = q″A. Positive flux runs from Side A toward Side B.
- Interface temperatures
- Calculated by subtracting q″R″ across each successive resistance. They describe the steady temperature profile through the chosen series path.
Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.