Thermal Transfer

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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 ---------------------------------------------------------------------------------------------
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 oC The average temperature used to look up coefficents.
Specific Heat Cp 14373 J/kg-oC 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-oC 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-3K-4 Net energy readiated by a black body relative to black body surroundings.
gravitational accelleration g 9.81 m/s2 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 oC Ambient temperature measured in Hydrogen atmosphere.
Wire Temperature Tc oC 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*roh2*(Tp-Ta)D3/u2 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 m2  
Rayleigh Number = Gr*Pr Ra 0.0134 None A dimensionless term used in the calculation of natural convection
Nusselt = 0.19+0.82*Ra0.17 Nuv 0.584 None Nusselt number for thin wire coil on vertical axis. 
Nusselt = 0.19+0.82*Ra0.17 Nuh 0.554 None Nusselt number for thin wire coil on horizontal axis. 
Av. Heat Transfer Coefficient = Nuv*k/D hv 531 W/m2-C Heat transfer for vertical axis coil
Av. Heat Transfer Coefficient = Nuh*k/D hh 504 W/m2-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 ---------------------------------------------------------------------------------------------
Conduction through tube wall
  Symbol Value Units  
Total Heat Transfer qt W  
Predicted average wall temperature Taw 200 oC  
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 m2  
Temperature Differential - Borosilicate Tdif 5.5 oC Temperature differential across the borosilicate glass wall.
Temperature Differential - Quartz Tdif 4.1 oC Temperature differential across the fuzed quartz glass wall.
--------------------------------------------------------------------------- Thermal transfer from glass tube to air calculations ---------------------------------------------------------------------------------------------
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 oC The average temperature used to look up coefficents.
Specific Heat Cp 1012.55 J/kg-oC 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-oC 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-3K-4 Net energy readiated by a black body relative to black body surroundings.
gravitational accelleration g 9.81 m/s2 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 oC Ambient temperature measured in still air.
Tube outer wall Temperature Tc oC 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*roh2*(Tp-Ta)D3/u2 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 m2  
Rayleigh Number = Gr*Pr Ra 337219 None A dimensionless term used in the calculation of natural convection
Nusselt = 0.19+0.82*Ra0.17 Nuh 9.3 None Nusselt number for horizontal tube in free air. 
Av. Heat Transfer Coefficient = Nuh*k/D hh 7.47 W/m2-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
         

 

 

 


Example Calculations - not interactive.

 

 

Description Symbol Value Units
Ambient Hydrogen atmosphere temp. aT 205 oC
Wire temperature wT 384 oC
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 oC 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 oC ambient (there is a 5.5 oC gradient across the tube wall) we find that the predicted wire temperature is 384 oC 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 oC
Measured glass tube temperature wT 200 oC
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 oC and a tube temperature of 200 oC 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 oC.

Description Symbol Value Units
Ambient temperature aT 400 oC
Wire temperature wT 607 oC
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 400oC 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 oC ambient we find that the predicted wire temperature is 607 oC 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 oC
Wire temperature wT 507 oC
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 350oC 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 oC ambient we find that the predicted wire temperature is 507 oC 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 oC
Wire temperature wT 607 oC
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 oC wire temperature we find that the predicted ambient temperature is 559 oC to achieve a total heat transfer of 36W. The total heat flow comprises 4.5W radiated heat and 31.48W by natural convection.