鸡蛋冷却实验.docx

1、鸡蛋冷却实验鸡蛋冷却实验问题研究 1.鸡蛋冷却实验研究背景：将一个已经煮熟的鸡蛋放置于空气中进行对流冷却的研究。主要的研究方向为随着时间的变化鸡蛋温度的变化情况。在此问题中，我们将鸡蛋简化为一个球体，并根据实际情况将鸡蛋的直径记为d=0.04m。将鸡蛋的密度设为1000kg/m3。鸡蛋的比热记为3310J/(kg*k)。鸡蛋的导热系数记为0.5W/（m*k）。2.鸡蛋冷却实验问题分析：因为我们已经将鸡蛋简化为了一个球体，所以在球坐标下，可以将此问题认为为无内热源的一维非稳态导热问题（将该问题的导热系数假设为常数）取温度差为10摄氏度，将对流换热系数看做不变(例如在8070摄氏度的温度区间内，将

2、对流换热系数取为温度为75摄氏度时候空气的对流换热系数）。研究在一维方向上温度随着径向方向的变化，并且画出鸡蛋的温度随着时间的变化图像，和理论温度进行比较，并且对最后形成的差异做出一定的理论分析。3.对问题进行数值求解：（1）利用集总参数法将8030之间的温度分为5个区间，并且认为每个区间内的对流换热系数视为不变（例如：8070区间内，取温度为75时候的对流换热系数）根据等温球体表面的自然对流传热可知，其特征式关联式可用下式进行计算：其中球的特征长度为直径D,其中特征温度为Tm=,然后根据特征温度查附录5可以得到空气的各种物性参数。又因为：得到利用公式=-可得到下表，如图所示：温度区间特征温度

3、t1vG温差膨胀系数80-70501.798*10(-5)9.8500.00309597570-60451.750*10(-5)9.8400.00314465460-50401.702*10(-5)9.8300.00319488850-40351.665*10(-5)9.8200.00324675340-30301.608*10(-5)9.8100.00330033GrPrNu空气导热系数h时间300326.85 0.722810.00101570.027356.838194484646.37257610.06290.72419.7061362170.026996.549215413847.1

4、3207521.86190.72559.3069714380.026626.1937894921197.86146911.85860.72688.7078535430.026255.7145288881948.6880055.529130.72827.7682101540.025885.0260319747369376.04根据上表可以做出理论上鸡蛋表面的温度随着时间的变化曲线由实验数据，可以得到鸡蛋表面的温度变化曲线理论温度随着时间的变化：图表实际测得的鸡蛋中心点的温度随着时间的变化情况：实际测量所得数据时间温度072.13062.35056.67052.110047.212044.7150

5、41.7170402003822036.825035.327034.430033.335031.840030.645029.650028.755028图表（2）研究一维径向上温度随着X的变化 简化的鸡蛋问题对其列数学描述：边界方程为：（在此分析中，鸡蛋中心只有导热，没有对流）(边界上时，只有对流，没有辐射换热）将鸡蛋分为0,1，2,3,4共5个节点，分别对其列节点方程对于节点0：化简得：收敛条件：对于内部节点1，2，3；由于函数是一个单调递增的函数（m0），得出71.71对于边界点4，节点方程为：收敛条件为：，得出12.3。4.对鸡蛋问题进行数值分析：利用Excel进行迭代前三十次的迭代图如下

6、：时间i节点编号01234072.172.172.172.172.1172.172.172.172.171.85736094272.172.172.172.0980235471.61874231372.172.172.0999817372.0941276871.38405673472.172.0999997772.0999276772.0883679971.15321885572.0999999972.0999988772.0998210472.080798670.92614535672.0999999572.0999966472.0996457772.0714722170.702754827

7、72.0999998372.0999922472.0993864872.0604401570.48296779872.0999995672.0999846572.0990284472.0477524170.26670662972.0999990272.0999726872.0985575872.0334576770.05389551072.0999980672.0999549672.0979604572.0176033369.844460361172.099996572.0999372.0972241972.0002355569.63832891272.0999940972.099896157

8、2.0963365571.9813992769.435430451372.0999905472.0998516372.0952858171.9611382869.235696031472.0999855172.0997945572.0940608371.9394951969.039058241572.0999785972.0997228972.0926509771.916511568.845451241672.0999693272.0996345372.0910461171.8922276368.654810731772.0999571972.0995272672.0892366471.866

9、6829368.467073891872.0999416172.0993987772.087213471.839915768.282179361972.0999219372.0992466672.0849677171.8119632568.100067212072.0998974672.0990684872.0824913471.782861967.920678872172.0998674272.0988616872.0797764771.7526470167.743957152272.0998309772.0986236772.0768157171.7213530167.5698461423

10、72.0997872272.0983517872.0736020771.6890134267.398291272472.099735272.098043372.0701289671.6556608767.229239182572.0996738872.0976954972.0663901571.6213271367.062637772672.0996021972.0973055372.0623797771.5860431466.898436112772.0995189672.096870672.0580923371.5498389966.736584472872.0994229872.0963

11、878372.0535226471.51274466.577034222972.0993129972.0958543472.0486658671.4747867166.419737893072.0991876472.095267272.0435174571.4359948866.26464905最后的迭代情况如下:959432.0747254632.07472332.0747158932.0747051532.07469228959532.0747253732.0747229132.0747158132.0747050932.07469224959632.0747252932.07472283

12、32.0747157432.0747050332.0746922959732.074725232.0747227432.0747156632.0747049732.07469216959832.0747251132.0747226632.0747155932.0747049132.07469212959932.0747250232.0747225732.0747155132.0747048532.07469207960032.0747249332.0747224932.0747154432.0747047932.07469203960132.0747248432.074722432.07471

13、53632.0747047332.07469199960232.0747247532.0747223232.0747152932.0747046732.07469195960332.0747246732.0747222332.0747152132.0747046132.07469191960432.0747245832.0747221532.0747151432.0747045532.07469187960532.0747244932.0747220632.0747150632.074704532.07469183960632.074724432.0747219832.0747149932.0

14、747044432.07469178960732.0747243132.0747218932.0747149232.0747043832.07469174960832.0747242332.0747218132.0747148432.0747043232.0746917960932.0747241432.0747217332.0747147732.0747042632.07469166961032.0747240532.0747216432.0747146932.074704232.07469162961132.0747239632.0747215632.0747146232.07470414

15、32.07469158961232.0747238832.0747214832.0747145532.0747040832.07469154961332.0747237932.0747213932.0747144732.0747040232.0746915961432.074723732.0747213132.074714432.0747039632.07469146961532.0747236232.0747212232.0747143232.0747039132.07469142961632.0747235332.0747211432.0747142532.0747038532.07469

16、138961732.0747234432.0747210632.0747141832.0747037932.07469134961832.0747233632.0747209832.074714132.0747037332.0746913961932.0747232732.0747208932.0747140332.0747036732.07469126962032.0747231832.0747208132.0747139632.0747036232.07469121962132.074723132.0747207332.0747138932.0747035632.0746911796223

17、2.0747230132.0747206432.0747138132.074703532.07469113962332.0747229332.0747205632.0747137432.0747034432.07469109962432.0747228432.0747204832.0747136732.0747033832.07469105962532.0747227532.074720432.074713632.0747033332.07469101鸡蛋内部各节点随时间变化情况图表5.结果误差分析本次实验把鸡蛋简化为一个球体探究一维径向温度分布随着时间变化的思想，极大地简化了对鸡蛋内部温度温

18、度分布的分析与探究，但是由于理论数据和实际数据有很大的误差，现将可能导致误差的原因分析如下：1）由于该问题中的Bi=0.1所以在采用集总参数法进行计算时会存在较大的误差；2）集总参数的问题是考虑鸡蛋平均的温度变化，并不能直观的反映鸡蛋内部温度的分布情况；3）由于理论上我们只考虑了鸡蛋表面的对流换热，没有考虑鸡蛋与周围环境之间的辐射换热的影响，4）我们查表所得到的是干空气的物性参数，并没有考虑空气的浓度，湿度，室内空气的流速对物性参数的影响，5）我们在划分温度是=10，沿鸡蛋径向分布所取的步长=0.005m,所取间隔较大，导致较大的误差；6）我们所取的对流换热系数在每个时间段内为定值，而在实际情况中对流换热系数随着温度的变化而不断地变化，这与我们的假设所不符，从而导致一定的误差。