The Analysis of Convection Experiment

Transcription

1 Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 5) The Analyss of Convecton Experment Zlong Zhang School of North Chna Electrc Power Unversty, Baodng 7, Chna Keywords: convecton; numercal method; the lumped parameter method. Abstract. The paper manly dscusses the temperature dstrbuton n eggs from the heatng process. For eggs' heatng process, the paper would explore the temperature change rules from the analyss, the lumped parameter method, numercal method of three aspects. Based on each methods, dagrams would be drawn, the features of temperature s gong to analyze and the errors would be calculated.. Problem Analyss Heatng an egg and puttng t nto the bolng water at, then the analyss objectve s the varaton of temperature n the center of the egg. It s assume that egg densty s kg/m 3, the specfc heat of egg s 33J/(kg*k) and durng the heatng process, the surface heat transfer coeffcents for h equals W/(m *k). The paper uses lumped parameter method, numercal analyss method and conducts two-dmensonal mathematcal smulaton.. Heatng Process The arranged recordng data of experment s shown n Appendx. The real heatng curve can be obtaned by data fttng usng Matlab. Table The arranged recordng data of experment Analyss calculaton s performed frst, then the lumped parameter method s used. The process of heatng eggs belongs to unsteady heat conducton. The eggs can be seen as hgh thermal conductve objects and t also can be consdered as a whole sothermal egg. The egg temperature of lumped-parameter equaton can be wrtten. Calculatng nternal egg temperature changes over tme, the temperature dstrbuton mappng can fnally obtaned. The use of numercal method s to dscrete the regon frst and dvde egg nto regons and then the forward and mplct dfference equatons can be dsplayed respectvely and usng teratve method to solve forward dfference equaton, t can obtan temperature change results and fnally 5. The authors - Publshed by Atlants Press 94

2 the comparson of temperature dstrbuton ss made. 3. Model Assumpton It s assumed that egg s a sphere wth 5cm dameter. In the heatng process, the convectve heat transfer coeffcent remans unchanged. In the lumped parameter method, egg s assumed to be a sphere wth unform temperature. 4. Symbol Illustraton : Inte eror thermal conductvty of egg; ; :egg surface heatt conducton coeffcent; r :thee sphere radus of egg; :egg den nsty; c :eggg specfc heat; h :eggg surface heat transfer coeffcent; :tme; u :egg temperature; M :node locaton 5. Model Buldng and Soluton 5. Heatng process analyss Makng fttng of data, the real temperature varaton over tme can c be obtaned. Fg. real temperaturee varaton Usng the analyss method, t s calculated that when the temperature n the center of egg comes to 8, t needs 635s. B hr, B * Hurstwood:.77.7 a ; a Coeffcent of volume expanson: c 33*.45* 7 It s assumed that when the center temperature of eggs reaches8 degrees, t comes nto the formal stage (Fg. ). Transcendental equatons characterstc root: u n cotun B, n..... m 8 sn u u cos u u ; ; u cosu sn u 943

3 Fg. formal stage In the center of egg: r sn x. ;lm ; sn(3.9 )exp( 3.9 Fo).exp(3.3 Fo). l x x 3.9* * the root s: 7 at.5* F.4 ; F 635; R. 5. heatng process lumped parameter method In the heatng process, t s seen that nternal thermal conductvty of the eggs s much larger than the convectve heat transfer coeffcent of the egg surface, so t can be concluded that the temperatures nsde the egg are bascally consstent. Boundary condton:, t t ; ha t exp t t t Averagee temperature changes over tme: cv Throughh the calculated result, t can obtan that (Fg. 3): Fg. 3 the temperatures nsde the eggg It can be concluded that the mage obtaned by lumped parameter method has great errorr comparng wth the actual value, so t can tt be selected as the mathematcall model of heatng the eggs. 5.3 Numercal method of heatng process Frst, the regonal dscrete nsde the egg s made and the number of dscrete regons are whch can be seen n Fg. 4. t a t ( ( r The mathematcal model s : r r r )) t,t t ; r, ; r r3, Boundary condton: r t h( t t ); r.5 / M r Forward dfferencee format equatons (onee node): 944

4 4 c r ( 3 t t ) 4 ( r t t ) 3 r r a Fo r tm tm c {[( m ) r] [( m ) r] } 3 tm tm tm t 4[( m ) r] 4 [( m ) r] Mnodes: r r 8m F 4m Convergence condton: tm tm c {( mr) [ ( m ) r] } 3 tm tm 4 [( m ) r] h4m r ( t t m ) Eleven nodes: r m Fg. 4 the regonal dscretee nsde the egg Becausee the regonn s dvdedd nto nodes, t gets the Fo=.53 whch meets the convergencee crtera, therefore, thee teraton result r can be obtaned by wrtng MATLAB program as shown n Table. Table rror between the mages of numercal method and the real one Node Temperature Plottng the curves: From the results, there s stlll great errorr between the mages of o numercal method and the real one. And at the begnnng, there s a temperature change delay n the t numercal mage. Through the analyss of heat conducton model, t concludes that because t s assumed that the coeffcent of convectvee heat transfer of bolng water ss a constant, whle the actual convectve heat transferr coeffcent may be a change n value, and the egg s assumed as a pure thermal conductvty model but actually t exstss two states: convecton heat transfer of egg whte and conducton after soldfcaton of eggs. 945

5 6. Concluson Substances n eggs s complex, thermal conductvty, surface emssvty, naccuracy can cause errors. Analyss error comes from the whole egg assumpton and thermocouple movement wthn the egg. References [] ZHAO Shu, ZHU Huren, GUO Tao, et al. Numercal Predctons of Flow and Heat Transfer for Rotatng Internal Coolng Channels wth Rb Turbulators [J].Journal of X an Jaotong Unversty. 4,48(); [] CHEN Jnglng, ZHU Xuhong, WANG Qan, et al. Study on the Heat Convecton between Tomato Frutage and Ar [J]. Acta Agrculturae boreal-snca.,7(6). 946