These thermal transfer calculations are designed to inform researchers working on heat generation devices in hydrogen atmospheres. More specifically catalytic thin wire coils mounted in borosilicate or quartz tubes in a hydrogen atmosphere.

***The tables below are interactive.***

Researchers can enter physical parameters in the white, blue and orange cells. The be clear -- the following parameters are inputs and can be changed: Pressure, Emissivity, Length, Wire Diameter, Ambient Temperature, Wire Temperature.

Target or measured temperatures may be entered in the blue and orange cells. Typically the researcher will enter the measured ambient temperature, Ta, in the blue cell. The Wire temperature can then be varied to achieve a target Total Heat Transfer (mauve c ells).

The thermal property parameters for hydrogen are generated from surface plot fits to NIST data for Hydrogen gas. The parameters are fitted to data spanning pressures of 0.1 – 3 bar, and temperatures of 300-1,000K.

The thermal conductivities of Borosilicate and quartz are also fitted to data spanning temperatures of 100 – 1200K.

Links are also provided to relevant information and papers should researchers wish to learn more.

Example calculations and solutions are provided for those researchers interested in replicating the results presented by Francesco Celani at NIWeek and ICCF17 in 2012.

Data and analysis provided by Dr Mark Snoswell, CTO Chava. Inquiries can be directed to This email address is being protected from spambots. You need JavaScript enabled to view it.

Copyright Chava 2012. No copying permitted – refer all links back to this web page.

No comment -- This information is not meant to imply the existence or results of any Chava project and no correspondence will be entered into regarding commercial projects.

No Warranty – This information is provided as is. There is no warranty, real or implied, as to the accuracy or fitness of the information provided for any use.

--------------------------------------------------------------------------- Thermal transfer from wire to Hydrogen calculations --------------------------------------------------------------------------------------------- |
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Hydrogen Properties at Film Temperature | |||||||

Description | Symbol | Value | Units | ||||

Pressure | p | bar | 0.1<p<3 all data ande formulae tested and fitted within this pressure range. | ||||

Film Temperature = (Tc+Ta)/2 | Tf | 298 | ^{o}C |
The average temperature used to look up coefficents. | |||

Specific Heat | Cp | 14373 | J/kg-^{o}C |
The amount of heat per unit mass required to raise thetemperature by one degree Celsius | |||

Coefficient of Thermal Expansion | ß | 0.001751 | 1/K | For ideal gasses the thermal expansion coefficent = the inverse of absolute temperature. | |||

Dynamic Viscosity | µ | 0.00000892 | kg/m-s | Dynamic (absolute) viscosity is a measure of internal resistance to flow. | |||

Density calculated at film temperature Tf | ? | 0.2437 | kg/m3 | ||||

Thermal Conductivity | k | 0.1837 | W/m-^{o}C |
Coefficent of heat transfer without motion. | |||

Emissivity (0-1) | e | None | Reduced Nickel, Copper and Constantan have emissivities 0.05>e>0.15 | ||||

Steffan Boltzman constant | s | 5.67E-08 | kg s^{-3}K^{-4} |
Net energy readiated by a black body relative to black body surroundings. | |||

gravitational accelleration | g | 9.81 | m/s^{2} |
Axcelleration in earths gravitational field. | |||

Wire (cylinder) Dimensions | |||||||

Description | Symbol | Value | Units | ||||

Length | L | Meters | Wire (cylinder) length | ||||

Diameter | D | Meters | Wire (cylinder) diameter | ||||

Ambient Temperature | Ta | ^{o}C |
Ambient temperature measured in Hydrogen atmosphere. | ||||

Wire Temperature | Tc | ^{o}C |
Vary the wire temperature to achieve a match to total heat output - mauve coloured cells. | ||||

Temperate differential = Tc - Ta | Td | 179 | |||||

Results for Horizontal Wire | |||||||

Description | Symbol | Value | Units | ||||

Prandlt Number = Cp*u/ k | Pr | 0.698 | None | Approximating the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivity | |||

Grashof Number = g*B*roh^{2}*(T_{p}-T_{a})D^{3}/u^{2} |
Gr | 0.0192 | None | Correlation of heat and mass transfer due to natural convection at a solid surface in a fluid | |||

Area = PI * D*L | A | 0.00066 | m^{2} |
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Rayleigh Number = Gr*Pr | Ra | 0.0134 | None | A dimensionless term used in the calculation of natural convection | |||

Nusselt = 0.19+0.82*Ra^{0.17} |
Nuv | 0.584 | None | Nusselt number for thin wire coil on vertical axis. | |||

Nusselt = 0.19+0.82*Ra^{0.17} |
Nuh | 0.554 | None | Nusselt number for thin wire coil on horizontal axis. | |||

Av. Heat Transfer Coefficient = Nuv*k/D | hv | 531 | W/m^{2}-C |
Heat transfer for vertical axis coil | |||

Av. Heat Transfer Coefficient = Nuh*k/D | hh | 504 | W/m^{2}-C |
Heat transfer for horizontal axis coil | |||

Convective Heat Transfer = hA*Td | qvconv | 62.79 | W | Convective Heat Transfer for vertical axis coil | |||

Convective Heat Transfer = hA*Td | qhconv | 59.6 | W | Convective Heat Transfer for horizontal axis coil | |||

Radiative Heat Transfer | qrad | 0.5 | W | Radiative heat transfer is not affected by orientation. | |||

Tot. Heat Transfer - vertical = qrad+qvconv | qv | 63.29 | W | Total heat transfer for Vertical axis coil | |||

Tot. Heat Transfer - horiz. = qrad+qhconv | qh | 60.1 | W | Total heat transfer for Horizontal axis coil | |||

--------------------------------------------------------------------------- Thermal transfer through glass tube wall calculations --------------------------------------------------------------------------------------------- |
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Conduction through tube wall | |||||||

Symbol | Value | Units | |||||

Total Heat Transfer | qt | W | |||||

Predicted average wall temperature | Taw | 200 | ^{o}C |
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Thermal Conductivity - Borosilicate | qbCond | 1.15 | W/m.K | Fit from experimental data on Borosilicate glass - temperature dependant | |||

Thermal Conductivity - Quartz | qqCond | 1.57 | W/m.K | Fit from experimental data on Quartz glass - temperature dependant | |||

Wall thickness | thick | m | |||||

diameter | dia | m | |||||

length | len | m | |||||

Area | area | 0.0377 | m^{2} |
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Temperature Differential - Borosilicate | Tdif | 5.5 | ^{o}C |
Temperature differential across the borosilicate glass wall. | |||

Temperature Differential - Quartz | Tdif | 4.1 | ^{o}C |
Temperature differential across the fuzed quartz glass wall. | |||

--------------------------------------------------------------------------- Thermal transfer from glass tube to air calculations --------------------------------------------------------------------------------------------- |
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Air Properties at Film Temperature | |||||||

Description | Symbol | Value | Units | ||||

Pressure | p | bar | 0.1<p<3 all data ande formulae tested and fitted within this pressure range. | ||||

Film Temperature = (Tc+Ta)/2 | Tf | 112.5 | ^{o}C |
The average temperature used to look up coefficents. | |||

Specific Heat | Cp | 1012.55 | J/kg-^{o}C |
The amount of heat per unit mass required to raise thetemperature by one degree Celsius | |||

Coefficient of Thermal Expansion | ß | 0.002594 | 1/K | For ideal gasses the thermal expansion coefficent = the inverse of absolute temperature. | |||

Dynamic Viscosity | µ | 0.00002233 | kg/m-s | Dynamic (absolute) viscosity is a measure of internal resistance to flow. | |||

Density calculated at film temperature Tf | roh | 0.915 | kg/m3 | ||||

Thermal Conductivity | k | 0.0321 | W/m-^{o}C |
Coefficent of heat transfer without motion. | |||

Emissivity (0-1) | e | None | Borosilicate and quartz glass have emissivities 0.85>e>0.95 | ||||

Steffan Boltzman constant | s | 5.67E-08 | kg s^{-3}K^{-4} |
Net energy readiated by a black body relative to black body surroundings. | |||

gravitational accelleration | g | 9.81 | m/s^{2} |
Axcelleration in earths gravitational field. | |||

Glass tube Dimensions | |||||||

Description | Symbol | Value | Units | ||||

Length | L | Meters | Tube length | ||||

Diameter | D | Meters | Tube diameter | ||||

Ambient Temperature | Ta | ^{o}C |
Ambient temperature measured in still air. | ||||

Tube outer wall Temperature | Tc | ^{o}C |
Vary the tube temperature to achieve a match to total heat output - mauve coloured cells. | ||||

Temperate differential = Tc - Ta | Td | 175 | |||||

Results for Horizontal glass tube | |||||||

Description | Symbol | Value | Units | ||||

Prandlt Number = Cp*u/ k | Pr | 0.703897 | None | Approximating the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivity | |||

Grashof Number = g*B*roh^{2}*(T_{p}-T_{a})D^{3}/u^{2} |
Gr | 479075 | None | Correlation of heat and mass transfer due to natural convection at a solid surface in a fluid | |||

Area = PI * D*L | A | 0.022117 | m^{2} |
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Rayleigh Number = Gr*Pr | Ra | 337219 | None | A dimensionless term used in the calculation of natural convection | |||

Nusselt = 0.19+0.82*Ra^{0.17} |
Nuh | 9.3 | None | Nusselt number for horizontal tube in free air. | |||

Av. Heat Transfer Coefficient = Nuh*k/D | hh | 7.47 | W/m^{2}-C |
Heat transfer for horizontal glass tube | |||

Convective Heat Transfer = hA*Td | qhconv | 23.49 | W | Convective Heat Transfer for horizontal glass tube | |||

Radiative Heat Transfer | qrad | 36.52 | W | Radiative heat transfer is not affected by orientation. | |||

Total Heat Transfer = qrad+qhconv | qh | 60.01 | W | Total heat transfer for horizontal glass tube | |||

Description | Symbol | Value | Units |

Ambient Hydrogen atmosphere temp. | aT | 205 | ^{o}C |

Wire temperature | wT | 384 | ^{o}C |

Initial Wire resistance | Ro | 16.8 | Ω/m |

Reistance drop | R/Ro | 0.88 | none |

Opperating resistance | R | 14.78 | Ω/m |

Heating current | I | 1.8 | A |

Heat input | Hi | 47.90 | W/m |

Execss heat measured | FE | 12 | W |

Total heat in wire | qt | 59.90 | W/m |

Total Heat transfer calc. for aT and wT | qc | 60.1 | W/m |

In 2012 at both NIWeek 2012 in Texas, USA and ICCF17 in Seoul, Korea Francesco Celani demonstrated a unit that repeatably delivered 12W of excess power above the 48W heating current required to maintain it's operating temperature. The cell employed a 105cm length of 0.2mm OD NiCu alloy (Isostan) wire that he had prepared via a cyclic thermal/oxidation process.

The question we want to address is what the actual wire temperature was. Celani was only able to indirectly measure the temperature - indicating approximately 200 ^{o}C for the outer borosilicate glass wall with a 3 bar Hydrogen atmosphere inside.

Using the heat flow calculator above and inputting 3 bar pressure and 205 ^{o}C ambient (there is a 5.5 ^{o}C gradient across the tube wall) we find that the predicted wire temperature is 384 ^{o}C to achieve a total heat transfer of 60W. The total heat flow comprises 0.5W radiated heat and 59.6W by natural convection.

Description | Symbol | Value | Units |

Ambient air temperature | aT | 20 | ^{o}C |

Measured glass tube temperature | wT | 200 | ^{o}C |

Diameter of tube | dia | 0.04 | m |

Effective Tube length | len | 0.143 | m |

Convective heat transfer | qc | 23.49 | W |

Radiated heat | qr | 36.52 | W |

Total Heat transfer calc. for aT and wT | qc | 60 | W |

Following on from the first example the next question we want to address is what length of glass tube would rediate the observed 60W into free air.

Using the heat flow calculator above and inputting 1 bar Air at 25 ^{o}C and a tube temperature of 200 ^{o}C we find that the predicted tube dimentions are 14.3cm x 4cm dia to achieve a total heat transfer of 60W. The total heat flow comprises 36.53W radiated heat and 23.49W by natural convection. The 14.3cm is much shorter then the actual tube length of 300cm -- this is expected as most of the heat transfer from the wire inside the tube to the tube is by convection leading to hot spots on the tube wall and effectivly reducing the length of tube at the measured 200 ^{o}C.

Description | Symbol | Value | Units |

Ambient temperature | aT | 400 | ^{o}C |

Wire temperature | wT | 607 | ^{o}C |

Initial Wire resistance | Ro | 15 | Ω/m |

Reistance drop | R/Ro | 0.7 | none |

Opperating resistance | R | 10.5 | Ω/m |

Heating current | I | 2.1 | A |

Heat input | Hi | 46.31 | W/m |

Execss heat measured | FE | 18 | W |

Total heat in wire | qt | 64.31 | W/m |

Total Heat transfer calc. for aT and wT | qc | 64.30 | W/m |

Here we model a wire with 18W/m excess energy at a measured ambient temperature of 400^{o}C in a 0.5 bar hydrogen atmosphere and a heating current of 2.1A -- which is the absolute maximum heating current for the 0.2mm dia wires Celani is producing.

The question we want to address is what the actual wire temperature be?

Using the heat flow calculator above and inputting 0.5 bar pressure and 400 ^{o}C ambient we find that the predicted wire temperature is 607 ^{o}C to achieve a total heat transfer of 64W. The total heat flow comprises 3W radiated heat and 61W by natural convection.

Description | Symbol | Value | Units |

Ambient temperature | aT | 350 | ^{o}C |

Wire temperature | wT | 507 | ^{o}C |

Initial Wire resistance | Ro | 15.0 | Ω/m |

Reistance drop | R/Ro | 0.7 | none |

Opperating resistance | R | 10.5 | Ω/m |

Heating current | I | 1.9 | A |

Heat input | Hi | 37.91 | W/m |

Execss heat measured | FE | 6 | W |

Total heat in wire | qt | 43.91 | W/m |

Total Heat transfer calc. for aT and wT | qc | 43.60 | W/m |

Here we model a wire with 6W/m excess energy at a measured ambient temperature of 350^{o}C in a 0.5 bar hydrogen atmosphere and a heating current of 1.8A -- which is just above the minimum heating current (1.8A) that Celani has observed excess energy emerging.

The question we want to address is what the actual wire temperature be?

Using the heat flow calculator above and inputting 0.5 bar pressure and 350 ^{o}C ambient we find that the predicted wire temperature is 507 ^{o}C to achieve a total heat transfer of 44W. The total heat flow comprises 1.8W radiated heat and 41.7W by natural convection.

Description | Symbol | Value | Units |

Ambient temperature | aT | 559 | ^{o}C |

Wire temperature | wT | 607 | ^{o}C |

Initial Wire resistance | Ro | 15.0 | Ω/m |

Reistance drop | R/Ro | 0.78 | none |

Opperating resistance | R | 11.7 | Ω/m |

Heating current | I | 0 | A |

Heat input | Hi | 0 | W/m |

Execss heat measured | FE | 36 | W |

Total heat in wire | qt | 36.00 | W/m |

Total Heat transfer calc. for aT and wT | qc | 36.39 | W/m |

Here we model a 2m wire with 18W/m excess energy at a target wire temperature of 607 calculated above. In this case we will assume a well insulated vertical vessel that can sustain its own temperature without the need for any additional heater current. The chamber pressure will be 1 bar.

The question we want to address is what the ambient temperature must be? ... this then sets a target for designing suitable insulation to achieve the conditions set.

Using the heat flow calculator above and inputting 1.0 bar pressure and 607 ^{o}C wire temperature we find that the predicted ambient temperature is 559 ^{o}C to achieve a total heat transfer of 36W. The total heat flow comprises 4.5W radiated heat and 31.48W by natural convection.