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</o:shapelayout></xml><![endif]--></head><body lang=EN-CA link=blue vlink=purple><div class=WordSection1><p class=MsoPlainText>Dear Aron<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Simple approach:<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>If it is thin metal you can take the conduction rate through the metal to be perfectly efficient or there are worked examples at <a href="http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html">http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html</a> . <o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Assuming you know the gas temperature on the inside of the inner cone, treat the stationary surface gas (boundary layer) to be 0.1mm thick and use air as the heat conduction rate (15 to 20 W/m/°C. That applies to both sides. (I am expecting you want to know the heat transfer rate into the cone as well as out. If not, ignore.)<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>For radiation from the outside of the inner cone, the normal formula is OK: the temperature of the opposing surface and the emitting surface apply. <o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Ԑ(πDL)ơ(T<sup>4</sup><sub>s</sub>-T<sup>4</sup><sub>Sur</sub>)<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Ԑ = 0.9 for corroded steel.<o:p></o:p></p><p class=MsoPlainText>π = 3.14159<o:p></o:p></p><p class=MsoPlainText>ơ = 5.67x10<sup>-8</sup> <o:p></o:p></p><p class=MsoPlainText>T<sup>4</sup><sub>Sur</sub> = (Temperature °K of the radiating surface)<sup>4</sup><o:p></o:p></p><p class=MsoPlainText>T<sup>4</sup><sub>Sur</sub> = (Temperature °K of the receiving surface)<sup>4</sup><o:p></o:p></p><p class=MsoPlainText>L and D = length and diameter in metres, for the radiating surface<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>For convection, treat the cone as a cylinder with a surface area equal to the cone at the same height. If you have to guess, use <i>h</i> = 15 W/m<sup>2</sup></span>·<span style='mso-fareast-language:EN-CA'>K as the free convection heat transfer coefficient.</span> <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>Calculate the heat convecting off the cylinder (<i>H</i><sub>1</sub>)as if it is <i>horizontal</i>. If you need a worked example of that, try problem 1.2, page 11 of Fundamentals of Heat and Mass Transfer by Incropera and DeWitt (a common book).<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>Quantity of heat convected (<i>H</i><sub>1</sub>) = <i>q</i> = Watts = <i>h</i>(</span>π<span style='mso-fareast-language:EN-CA'> DL)(T<sub>s</sub>-T</span><span style='mso-fareast-language:EN-CA'>͚</span><span style='mso-fareast-language:EN-CA'>)<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'><o:p> </o:p></span></p><p class=MsoNormal><i><span style='mso-fareast-language:EN-CA'>h</span></i><span style='mso-fareast-language:EN-CA'> = 15<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>T<sub>s</sub> = Emitting surface temp C or K<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>T</span><span style='mso-fareast-language:EN-CA'>͚</span><span style='mso-fareast-language:EN-CA'> = receiving surface temp C or K (but the same as above)<o:p></o:p></span></p><p class=MsoNormal>L and D = length and diameter in metres<o:p></o:p></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>Then <i>add</i> to the result of the convection calculation (<i>H</i><sub>1</sub>)<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>Sin</span><span style='mso-fareast-language:EN-CA'>Ɵ</span><span style='mso-fareast-language:EN-CA'>(<i>H</i><sub>1</sub>) [1] heat convected from a horizontal cylinder<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>i.e. Sin</span><span style='mso-fareast-language:EN-CA'>Ɵ</span><span style='mso-fareast-language:EN-CA'>(<i>H</i><sub>1</sub>)+ (<i>H</i><sub>1</sub>) = (<i>H</i><sub>2</sub>) [2] heat convected from a cylinder tilted up </span><span style='mso-fareast-language:EN-CA'>Ɵ </span><span style='mso-fareast-language:EN-CA'>degrees<o:p></o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'><o:p> </o:p></span></p><p class=MsoNormal><span style='mso-fareast-language:EN-CA'>where </span><span style='mso-fareast-language:EN-CA'>Ɵ is the wall angle of the cone measured from the horizontal</span><span style='mso-fareast-language:EN-CA'>. The reason for this is that the heat convected from a vertical cylinder is twice that of a horizontal cylinder (because of chimney effect on the outside).<o:p></o:p></span></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>You can ignore conduction from the surface of the cone to the other cone around it. It is a very low value. If it is a forced air system you can usually ignore the radiation too.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Sum the convection and radiation numbers to get the heat transfer off the outer surface of the inner cone.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Fine tuning:<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>You could calculate the total for a cylinder (of the same tilt) for the top diameter and then for the bottom diameter to see if the average is in fact the same as for a cylinder of the average diameter. <o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Cone is D1 and D2 with height H. Side angle elevation Ɵ from horizontal<o:p></o:p></p><p class=MsoPlainText>Calculate the convection heat loss for cylinders:<o:p></o:p></p><p class=MsoPlainText><i>H</i><sub>2</sub>1 (D1+D2)/2, height H, tilt angle ACos((D2-D1)/2H) Degrees. Apply [2] above<o:p></o:p></p><p class=MsoPlainText><i>H</i><sub>2</sub>2 D1, height H, tilt angle = ACos((D2-D1)/2H) Degrees. Apply [2] above<o:p></o:p></p><p class=MsoPlainText><i>H</i><sub>2</sub>3 D2, height H, tilt angle = ACos((D2-D1)/2H) Degrees. Apply [2] above<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Check to see if (<i>H</i><sub>2</sub>2 + <i>H</i><sub>2</sub>3)/2 is the same as <i>H</i><sub>2</sub>1).<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>If you want a ‘real’ answer you can treat it as the sum of a large number of short vertical cylinders tilted at angle Ɵ plus you can engage a CFD expert! The dynamics of the gas flow between two closely spaced cones is probably more of an error than the above approximation.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>The real answer for the vertical flow involves an Eckert and Jackson analysis, an abbreviated worked example of which (applied to vertical walls, not cylinders) can be seen on p 373 of Bejan’s “Convection Heat Transfer” ISBN 0-471-27150-0 (Wiley). You don’t want to go there. Just use bare steam pipe formulae (as above). They are probably close enough in temperatures and surfaces for stove work within expectations.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Regards<o:p></o:p></p><p class=MsoPlainText>Crispin<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>++++++++</p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Can you help me on how to analyse heat tranfer through a cone... Im designing a Biochar stove with coencentric cylinders. In essence its a rocket stove. I want to make the inner cylinder conic so that i can retain more heat in the stove....<o:p></o:p></p><p class=MsoPlainText>The books i have read dont show me how to analyse conduction and convection in a cone...<o:p></o:p></p><p class=MsoPlainText>Will need a reply as soon as possible, if your able to help.<o:p></o:p></p><p class=MsoPlainText>Thank you in advance...<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>On 8/10/12, Erin Rasmussen <<a href="mailto:erin@trmiles.com"><span style='color:windowtext;text-decoration:none'>erin@trmiles.com</span></a>> wrote:<o:p></o:p></p><p class=MsoPlainText>> Hi Aron,<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> We have the TLUD Handbook is on our web site here:<o:p></o:p></p><p class=MsoPlainText>> <a href="http://stoves.bioenergylists.org/tludhandbookdraft-1"><span style='color:windowtext;text-decoration:none'>http://stoves.bioenergylists.org/tludhandbookdraft-1</span></a><o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> a shorter link directly to the handbook pdf file is <o:p></o:p></p><p class=MsoPlainText>> <a href="http://bit.ly/NhrZWX"><span style='color:windowtext;text-decoration:none'>http://bit.ly/NhrZWX</span></a><o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Plans for the Anila stove are here: <o:p></o:p></p><p class=MsoPlainText>> <a href="http://stoves.bioenergylists.org/anila"><span style='color:windowtext;text-decoration:none'>http://stoves.bioenergylists.org/anila</span></a><o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> I hope that helps, let me know if I can be of any assitance.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Kind regards,<o:p></o:p></p><p class=MsoPlainText>> Erin Rasmussen<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> TR Miles Technical Consultants Inc. <a href="http://www.trmiles.com/"><span style='color:windowtext;text-decoration:none'>http://www.trmiles.com/</span></a><o:p></o:p></p><p class=MsoPlainText>> and BioEnergy Discussion Lists <a href="http://www.bioenergylists.org/"><span style='color:windowtext;text-decoration:none'>http://www.bioenergylists.org/</span></a><o:p></o:p></p><p class=MsoPlainText>> <a href="mailto:erin@trmiles.com"><span style='color:windowtext;text-decoration:none'>erin@trmiles.com</span></a><o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> -----Original Message-----<o:p></o:p></p><p class=MsoPlainText>> From: Aron Tjihumino <a href="mailto:[mailto:atjihumino@gmail.com]"><span style='color:windowtext;text-decoration:none'>[mailto:atjihumino@gmail.com]</span></a><o:p></o:p></p><p class=MsoPlainText>> Sent: Wednesday, August 01, 2012 9:59 AM<o:p></o:p></p><p class=MsoPlainText>> To: <a href="mailto:Erin@trmiles.com"><span style='color:windowtext;text-decoration:none'>Erin@trmiles.com</span></a><o:p></o:p></p><p class=MsoPlainText>> Subject: Need designs<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Afternoon...<o:p></o:p></p><p class=MsoPlainText>> I'm Aron Tjihumino, a final year Bachelor of Engineering: Mechanical <o:p></o:p></p><p class=MsoPlainText>> Engineering Student at the Polytechnic of Namibia, Namibia<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> I am desgining a biochar and i need plans from where to start.<o:p></o:p></p><p class=MsoPlainText>> Can you please email me plans for Anila And Anderson TLUD biochar <o:p></o:p></p><p class=MsoPlainText>> stove, please Look forward to hearing from you soon.<o:p></o:p></p><p class=MsoPlainText>> kind regards<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Aron Tjihumino<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>_______________________________________________<o:p></o:p></p><p class=MsoPlainText>Stoves mailing list<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>to Send a Message to the list, use the email address <a href="mailto:stoves@lists.bioenergylists.org"><span style='color:windowtext;text-decoration:none'>stoves@lists.bioenergylists.org</span></a><o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>to UNSUBSCRIBE or Change your List Settings use the web page <a 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