上海交通大学：《生物传热学教与学 Bioheat Transfer》课程教学资源（电子讲义）lecture 12&13 Bioheat transfer Equations

Riview: Radiation Exchange between Surfaces ·The view factor Radiosity J Emissive Power(E) Reflective Power (Gret) Radiosity.J 4i→j Incident Radiation AJ G F4=A F A fraction of the total seen by Aj

Riview: Radiation Exchange between Surfaces • The view factor Radiosity , i j i j i i q F A J → = i J Emissive Power (E) Reflective Power (Gref) Fi, j Ai = AjFj,i A fraction of the total seen by Aj ρG E G

Blackbody Radiation Exchange qii=FiAJ q=FAJ If A &A are blackbody,no reflection, J=E=OT4 Net radiation heat transfer between the surfaces △q=FA,oI-FAoI, △9=FA,(T4-T)

• Blackbody Radiation Exchange i j i j i i q F A J → = , 4 J = Eb =σT j i j i j j q F A J → = , If Ai &Aj are blackbody, no reflection, Net radiation heat transfer between the surfaces 4 , 4 ij Fi, j Ai Ti Fj iAj Tj Δq = σ − σ ( ) 4 4 ij Fi, j Ai Ti Tj Δq = −

Electrical Resistance Analogy and network analysis enclosure 4 1 91 Eb 1/A Fi2 E62y92 1 W 2 3 42FG 9, Ep4 1/A4F3 Ev3 9 Fig.10.11

Electrical Resistance Analogy and network analysis

Lecture 12-13 Bioheat transfer Equations

Lecture 12-13 Bioheat transfer Equations

The Pennes Equation a)Experimental study-Temp mapping in the Human Forearm Subjects:Bare forearms of normotensive males (Neurological Institute) Environmental conditions: Room Temperature 25-27C Relative Humidity: 中。=62% Air:Free convection Measurement: T-type thermocouples J.A.P Vol.1No.2p.93-122,1948 H.H.Pennes Surface temp. Blood temp

The Pennes Equation a) Experimental study-Temp mapping in the Human Forearm Subjects: Bare forearms of normotensive males (Neurological Institute) Environmental conditions: Room Temperature 25-27 ℃ Relative Humidity: Air: Free convection Measurement: T-type thermocouples J.A.P Vol. 1 No.2 p.93-122, 1948 H.H.Pennes Surface temp. Blood temp. φ ∞ = 62%

Radius Uina Uine NtA Fig.3a.ExPERIMENTAL POSITION OF THE RICHT ARM (superior surface).The pronated forearm was centered between the 2 vertical supports of the wire controller shown in figure 4. The elbow was supported by a soft rubber disc with a central opening just wide enough to receive the medial malleolus of the humerus.The palm of hand was supported on a fat surface of linen twels extended from the head of the metacarpals to the finger tips.Forearm and distal half of upper arm were completely in the air.Inferior aspect of the forearm 5.o cm.above base of the ire controller(fig.4).Horizontal line indicates the plane of passage of the needle;lineI indicates.the level of figure 3c.;line I/indicates the distal plane around the circumference of which temnverature

vE AND DLUUD IEMFEKATURES The experimental subjects were all normotensive males in the b state drawn from the ward population of the Neurological Institute.N of these patients had subjective,clinical or laboratory evidence of dis of the neuromuscular system of the upper extremities.Experiments v begun between 8:oo-9:oo A.M.and lasted four to six hours.The exp mental period covered May-August 1947.On entering the laboratory fi the wards,subjects stripped immediately and lay on an ordinary hosp Fig.t.Top.26-GAUGE STAINLESS STEEL NEEDLE used for introduction of Y-model therm couple.Needle contains steel wire coated with varnish and baked in place.Loop at end of wi receives lead wire of thermocouple which is knotted in place.This needle is shown in place the forearm in figure sa.Bottom. Brachial artery thermocouple,built in a 24-gauge hypoderm eedle with insulated junction in bevel of needle.Preliminary puncture of artery performed wit togauge needle with to cc.syringe attached;on appearance of arterial blood,syringe is di connected and the 24-gauge needle slipped into the ro-gauge needle,the two bevels lying flusl Between readings of arterial blood temperatures,the inner needle is routinely removed lon enough to show arterial spurting from the ro-gauge needle.No anesthesia used in punctures. bed with a small sheet draped over the hips and with two pillows under heac and shoulders.Air and wall temperatures in the laboratory were identical

DISTAL FOREARM.CIRCULATION OCCLUSION OCCLUSION CIRCULATION UPPER ARM c 36.03 HeDersuam hend LeLateral toc He Dorsum hand MeMedial 350- L+Lalaral surfoce.foreerm,plone MaMediol 340- 530 320- 03040040700060020304 04000170401900020 h城evT TIME IN MINUTE等 40 360 D 330 340 320 Fig.13.CoMPARISON or EFPECrs of occlusion of circulation at distal forearm and at upper arm,in same subject,on skin temperature of the proximal forearm and hand.Note only minor changes in surface temperature distribution between A and B at conclusion of period of occlusion

3700 3600 3500 藏00 ppwiwywm。f 3100 +4000000a0903040 80 60-040302040000010400 阅T利码 5700 00 400 00 5200 3100 utubot d 04000010000和3040.00 D帆例城 Fig.15.Tissug TEMPERATURE-DEPru coxvEs in 9 subjects;plane I,transverse axis of

b)Theoretical analysis -Assumptions 1.Steady-state 1-D tissue conduction in the Cylindrical Coordinate 2.Effect of bones not clearly observed in exp. uniform tissue thermal conductivity K,.(w/m2K) 3.Uniform Volumetric heating rate: 9=9m+96

• b) Theoretical analysis – Assumptions 1. Steady-state 1-D tissue conduction in the Cylindrical Coordinate 2. Effect of bones not clearly observed in exp. - uniform tissue thermal conductivity Kt. (w/m2K) 3.Uniform Volumetric heating rate: m b qq q   = +