Unsteady heat transfer

Cooling and Heating Time Calculator

Calculation of changes in the average temperature of a body or a mixed liquid, checking the applicability of the model, taking into account the wall, radiation and variable heat transfer.

Thermal mass Surface Wednesday

What do we expect? Solid body Liquid tank

Solid homogeneous body

Temperatures and environment

Wednesday

Ambient temperature °C Initial temperature °C Required temperature °C Heat transfer coefficient h - can be changed W/(m²K)

The selected environment sets the initial h value. To use a custom value, edit the field above. For natural convection, consider the orientation of the cylinder.

H tip

Select environment and geometry.

Material

Body material Thermal conductivity λ W/(mK) Density ρ kg/m³ Heat capacity c_p J/(kg K)

Thermal diffusivity: —

Geometry

Form

Diameter m

Refine heat transfer

Dependence of h on temperature difference Take into account thermal radiation to an environment of the same temperature

Closed tank with mixed liquid

The internal dimensions determine the volume of liquid.The wall has its own heat capacity;The liquid and wall temperatures are calculated separately using the 2R2C model.

Liquid and temperatures

Liquid Density ρ kg/m³ Heat capacity c_p J/(kg K) Initial temperature °C Required temperature °C

Tank wall

Wall material Thickness m Thermal conductivity λ W/(mK) Density ρ kg/m³ Heat capacity c_p J/(kg K)

Internal geometry

Tank shape

Inner diameter m

Heat exchange

Outdoor environment

Ambient temperature °C External heat transfer h_o - can be changed W/(m²K) Internal heat transfer h_i W/(m²K)

The selected environment sets the initial h_o.Replace it directly with a calculated or manufacturer value.

External hint_o

Select media and tank geometry.

Clarify external heat exchange

Dependency h_o from temperature changes Take into account the radiation of the outer surface

Calculation is performed locally in the browser

What does the calculation take into account?

Model verification

The Biot criterion is calculated based on the maximum heat transfer coefficient at a given temperature range.

Nonlinear heat transfer

Variable heat transfer coefficient and radiation enter directly into the time integration, not just into the graph.

Liquid tank

The heat capacities of the liquid and the wall, internal and external heat transfer, as well as metal resistance are taken into account separately.

Limitations and sources of the technique

The properties of materials are considered constant;phase transitions, evaporation, freezing and internal heat generation are not taken into account.
Reference properties and heat transfer coefficients - starting engineering estimates.For detailed design, use manufacturer’s data and h calculation for specific speed and geometry.
The liquid in the tank is considered to be well mixed, the ambient temperature is constant, contact resistance and pipes are not taken into account.
NASA: lumped heat capacity model and criterion Bi < 0.1.
DOE: conduction, convection and radiation.
NIST CODATA: Stefan-Boltzmann constant.
NIST: Guideline Convective Heat Transfer Coefficient Ranges.
NIST: Natural Convection Correlation Example for a Horizontal Cylinder.