REFERENCES / THERMAL ENGINEERING
Thermal engineering essentials
A practical introduction to heat transfer and the quantities needed before you calculate.
Modes of heat transfer
Heat can be transferred by conduction, convection and radiation. More than one mechanism may occur in an actual device; identify the dominant mechanisms and boundary conditions before calculating.
Conduction
Heat transfer driven by a temperature difference within a medium or between objects in direct contact, such as heat flowing through a wall.
Convection
Heat transfer between a surface and a moving fluid. The rate depends on flow, fluid properties, surface geometry and flow regime.
Radiation
Energy exchange by electromagnetic radiation without a required intervening medium. Net exchange depends on surface temperatures and properties.
Exchanger heat transfer and method selection
Read the heat exchanger engineering guide → for method selection, a worked example and design checks.
For steady single-phase flow with approximately constant specific heat, a fluid’s sensible heat change is Q̇ = ṁcp(Tout − Tin). With negligible heat loss, storage and measurement error, the magnitudes of hot-side heat loss and cold-side heat gain should agree. Use consistent signs and flow bases. Phase change, strong property variation or reactions require another model.
Known terminal temperatures: LMTD
When all four terminal temperatures are known, pair the two terminal differences ΔT₁ and ΔT₂ according to parallel or counterflow and calculate ΔTlm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂). When the differences are equal, use their common value as the limit. For a simple exchanger, Q̇ = U A ΔTlm; U and A must use the same area basis.
The terminal differences must satisfy the positive-approach conditions of the calculator. Check flow direction and temperatures particularly near a pinch or temperature crossing. Multipass and crossflow equipment generally require an appropriate temperature-difference correction; the simple parallel or counterflow result is not a complete equipment design.
Unknown outlets: effectiveness and NTU
When inlet temperatures, flow rates, heat-capacity rates and UA are known but outlet temperatures are unknown, compute C = ṁcp, Cmin and Cmax, then Cr = Cmin/Cmax and NTU = UA/Cmin. Select an effectiveness ε for the flow arrangement. The theoretical maximum heat-transfer rate is Q̇max = Cmin(Th,in − Tc,in), and the actual rate is εQ̇max; Cmin and Cmax must be positive.
The methods describe the same class of heat-transfer problem but suit different known inputs. The site’s ε-NTU tool assumes ideal single-pass parallel or counterflow, constant capacity rates and U, no phase change and negligible external heat loss. Fouling, bypass, axial conduction, flow distribution and pressure drop need separate assessment.
Thermal resistance
Read insulation and thermal resistance basics →
Thermal resistance relates a temperature difference to heat-transfer rate. For a uniform layer in a one-dimensional steady plane wall with constant area, the conduction resistance is:
Here L is thickness (m), k is thermal conductivity (W/(m·K)), and A is the area normal to heat flow (m²). R is measured in K/W. Under these assumptions, conduction resistances of layers in series can be added.
This expression includes conduction through the material only. Add surface convection or contact resistance explicitly when they are relevant to the model.
Dimensionless groups and fins
Re, Pr and Nu
Reynolds number Re = ρvL/μ compares inertia with viscous effects; Prandtl number Pr = cpμ/k compares momentum and thermal diffusivities; Nusselt number Nu = hL/k expresses convection relative to conduction. Density ρ, speed v, dynamic viscosity μ, specific heat cp and fluid conductivity k should refer to the same state. Select characteristic length L as defined for the geometry and correlation.
The site’s Nu calculator computes Nu from a known h. To estimate h using an empirical correlation, separately choose one suited to the geometry, laminar or turbulent regime, thermal boundary conditions and valid Re/Pr ranges. A transition threshold is not universal across geometries.
The Dittus–Boelter tool estimates single-phase, fully developed turbulent convection in smooth straight circular tubes under its stated Re, Pr, length-to-diameter and property-variation limits. It gives a fluid-side estimate, not the overall coefficient of a complete exchanger.
Straight-fin efficiency
Fins increase heat-transfer area, but the fin is generally cooler or warmer than its base. Fin efficiency compares actual heat transfer with the ideal heat transfer if the entire fin were at base temperature. For a uniform straight fin with an adiabatic tip, constant conductivity and convection coefficient, ηf = tanh(mL)/(mL), where m = √(hP/(kAc)). As h approaches zero, efficiency approaches 1.
This model does not automatically account for tip heat loss, radiation, contact resistance, varying cross-section or non-uniform convection. Fin efficiency is distinct from overall efficiency of a finned surface.
Properties and state
Density, heat capacity, viscosity and thermal conductivity vary with substance and state. Identify the temperature, pressure, phase and units of a value before using it for a particular condition.
- Values for the liquid, gas and two-phase states of the same substance are not interchangeable.
- Absolute and gauge pressure have different meanings. Confirm the pressure definition required by the property model.
- Heat capacity, conductivity and viscosity are distinct properties; do not assume that one model covers all of them over the same range.
Choosing a property value
Identify the fluid or material, phase, absolute pressure and temperature range, then select the property needed by the model. Density should match the location at which flow is measured. If temperature varies substantially, choose a representative temperature appropriate to the method, or use segments or a variable-property calculation. Interpolate only within the data and model’s supported range; extrapolation is not a validated value.
Distinguish dynamic from kinematic viscosity and check units such as Pa·s versus mPa·s and J versus kJ. This site’s water and dry-air table covers only its listed states at 101.325 kPa; it is not a steam or saturation table. Other pressures, boiling and two-phase states require appropriate data.
Explore liquid water and dry air property tables →
Single-phase water and superheated steam states · Explore saturated water and steam transport and heat capacity →: discrete saturated-liquid and dry-saturated-steam endpoints; no interpolation.
Explore water and dry-air property plots →: discrete data points at 101.325 kPa absolute; no interpolation.
Steam states and heat calculations →
Explore the saturated water and steam table →: listed discrete states for saturated liquid and dry saturated steam from 5–200 °C; no interpolation.
Material conductivity specimen index →
Building insulation specimen conductivities →
PIR insulation board specimen conductivities →
Spruce-shavings specimen conductivities →
Pipe-insulation specimen conductivities →
Explore authoritative material-conductivity sources →: links to original sources, not an on-site material property table; check material condition, limits and permissions at the source.
Moist air basics
Moist air is a mixture of dry air and water vapour. Humidity ratio normally expresses the mass of water vapour per unit mass of dry air, often in kg/kg dry air.
When mixing air streams, use a consistent dry-air mass basis together with mass and energy balances. Condensation may occur below the dew point; a model that neglects condensate is not applicable in that case.
State, dew point and mixing
Dry-bulb temperature, relative humidity and absolute pressure define the moist-air state in the site’s model. Relative humidity changes with temperature and should not simply be flow-weighted between streams; use a consistent dry-air mass basis for humidity ratio and enthalpy. Dew point is the saturation temperature at the given pressure and humidity ratio.
The site’s mixing tool assumes common pressure, steady adiabatic mixing and no condensation. It does not report a mixed result for supersaturation. Condensation, latent heat, droplets and dehumidification require a model that includes phase change and energy balance.
Indoor thermal comfort basics →
Read about heat stress, wet bulb and WBGT →: the modelled psychrometric wet bulb cannot be used directly as occupational WBGT or a safety assessment.
The moist-air enthalpy split tool separates air-side sensible and moisture enthalpy terms along a chosen virtual path. The terms depend on that path and do not represent the complete equipment duty.
Estimates and tools
Engineering calculations depend on models, data and inputs. These tools support estimates within their stated scope. For final design, review actual operating conditions, reliable data and applicable standards.
For example, steady single-phase flow at 0.1 kg/s, average constant-pressure heat capacity 4200 J/(kg·K) and a 10 K temperature rise has an estimated temperature-related enthalpy-rate increase of 4200 W when pressure effects on enthalpy are negligible. It approximates net heat transfer to the fluid only when shaft work, kinetic and potential energy changes, and other mass flows across the boundary are negligible.
Basic design checks
- Define the purpose, system boundary, design conditions, acceptable uncertainty and input data sources.
- Confirm mass versus volume flow, dynamic versus kinematic viscosity, gauge versus absolute pressure, and temperature and area bases.
- Check energy balance, temperature direction, pinch and order of magnitude against a hand calculation or independent method.
- Assess pressure drop, flow distribution, fouling, material temperature and pressure limits, corrosion and applicable requirements separately; a simple thermal model does not cover them automatically.
- Test sensitivity to uncertain properties, heat-transfer coefficients and operating conditions; use reviewed data and methods for final design.
Related calculators
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Public information sources
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