建模的影响内部对流传热系数的液体食品

Sajid阿里¹,拉希德·阿里²
机械工程系助理教授,ACN,阿里格尔,U。P, India1
客人教员、机械工程系、ZHCET阿姆河,阿里格尔,U。2 P,印度

文摘

内部对流冷却过程中产生的影响从表面对流传热系数的容器,这些对流可能增加表面膜电导的有效值(h)。因此,在这种情况下Nu-Re相关性,通常用来预测h-values,可能不会产生现实的结果。在目前的工作,这种效应被使用实证调查相关开发通过温度测量液体食品容器的中心冷却期间,主要关注目前的工作是关于考虑传热行为对液体食品的圆柱形容器形状的铜金属,在本工作利用短暂的时间——温度关系计算对流传热系数的值(h)为每个测量温度的核心筒(ρ= 0)。之后绘制图形之间„ha和„Tah和T之间的表达式,这是美联储在项目开发的帮助下获得的时间——温度变化的有限差分法。实验过程是用来确定表面膜电导的圆柱形容器,苹果和橙汁时计算的温度与实验结果相比表面膜电导测量被用来解决瞬态热传导方程在圆柱坐标。一个持续观察基本一致。

关键字

对流,对流传热系数,表面膜电导、液体食物

介绍

传热分析中冷却的液态食品容器非常复杂的现象。保护易腐商品尤其是食品在固体或液体形式是最常见的一种使用机械制冷。食品必须保持在保存条件在瞬态和随后的存储,直到他们终于消耗。许多食品,特别是水果和蔬菜,含水固体,是季节性的,因为它们仅在特定的季节里。他们必须存储和保存,如果可以。表面传热系数可以确定实验稳定和非稳定态的方法。在目前的实验设计和制造工作。装置由一个制冷系统使用有门路,用r12制冷剂和冷却管。空气是流动冷却线圈冷却过程中。冷却空气通过导管流传。 A cylindrical container filled with fruit juice sealed with rubber cork at both ends was hanged with the help of thread in the duct and blast of cooled air is allowed to pass over its outer surface. Thermocouple was inserted in the cylindrical container to note down the temperature of fruit juice for different time intervals and temperature was recorded by suitable arrangements at desired locations (i.e. at the centre) in the cylindrical container. Experimental procedure was used to determine surface film conductance of cylindrical Apple and Orange, juice container. Kopelman etÃ¢ÂÂ al [1] have used the classical method of Carslaw and Jaegar to solve the transient heat conduction equations for simple product geometry. Charan [2] has described a method which avoids the use of surface temperature and which determine the heat transfer coefficient from the time-temperatures measurements at the centre of an ice block, which was immersed in the freezing medium. Ramsey etÃ¢ÂÂ al [3] have used a conduction model to calculate the surface heat transfer coefficient of fresh cut, sweet potato flesh from experimental temperature measurements. The temperature variations were measured at an interior point in the potato and calculations were made to find the surface temperature, heat flux, and heat transfer coefficient. The empirical correlations reported by Ansari and his co-workers [4, 5, 6, 7] were found to predict effective values of surface film conductance for regular shaped bodies through transient time-temperature measurements. The reliability of the method was tested statically, and it was found to give satisfactory results. Dyer etÃ¢ÂÂ al [8] assumed the humidity transfer from the food product to the circulating air, which was considered as unsaturated. Their model yielded a cooling rate, which was faster than the measured cooling rate in the initial stages of cooling, and it becomes slower than the measured cooling rate during the later stages. On the other hand the analytical method developed by Badri Narayan [9] and Krishnamurthy and co-workers [10, 11, 12] used for unsaturated air-stream, yielded an overall faster cooling rate compared to the actual one. In the initial stages of cooling the difference between the measured and calculated was small but it becomes more pronounced during the later stages.

二世的数学公式

一般形式的非稳态或瞬态热传导的三维非齐次(各向异性的)和selfinternal热代材料,在缺乏外部力场和内部质量扩散,可能会写成[11]。

(1)

简化的假设

1。产品是同质的,

2。一代被忽视和内部热量

3所示。传热在径向方向。

(2)

结合以上方程可以写在下列广义形式;

(3)

板,m = 0, 1缸,2 r =距离范围的点考虑的中心轴气缸或球体的中心。初始和边界条件在冷却前初始条件下面的方程

(4)

中心的边界条件

(5)

表面边界条件如果只考虑对流换热产品表面,定义的边界条件将方程

(6)

如果水分含量的影响也考虑表面边界条件将被修改成包括呼吸和潜热将定义的方程

(7)

这就完成了预冷时瞬态传热的数学公式。非维传热方程:为了开发一个通用的数学模型有必要non-dimensionalize上述方程。无量纲的数据用于此目的最常用的是那些食品专家和作为

(8)

(9)

(10)

(11)

冷却介质温度(T厘米)取决于实际的物理过程的情况。能量转移的同时传热传质:当从产品表面通过对流以及干燥的最低温度在这种情况下,可以达到冷却空气的湿球温度T厘米= T wb。考虑到上述事实而应用上面的无量纲参数。替换的方程分别减少以下方程的方程。

(12)

(13)

(14)

(15)

以下相关开发和报道,安萨里埃塔¢al(5、6)圆柱的身体:

(16)

在哪里

(17)

与已知的温度历史ro和k,„公顷的价值¢可以计算从方程(16)。Nu-Re表面膜电导的相关性:实验的时间——温度测量,安萨里[13]不同的水果和蔬菜是用来确定使用的热扩散系数方程所需的值的表面膜电导计算Nu-Re气流速度的关系可用的文学和表我[6]中给出。

(18)

三世的结果和讨论

在目前的工作中,„公顷的变化¢与产生温度被认为是。对于每个样本„hA¢值、温度数据已经安装和温度相关的二次方程„hA¢已经出现。这些二次最佳匹配块表面膜电导与温度及其对应的方程,如图1所示,每个生产了2、3和4。这些方程被用来计算变量„公顷¢在每个计算时间步使用温度在考虑时间步前的一个节点。纯对流边界条件是使用这种有效的„hA¢值和预测方程解决瞬态温度其他重要参数、热物理特性和测量温度历史的橙、苹果样本选择从文献[14]。计算温度与时间已经绘制如图5、6、7和8。这些数字还包括5 - 8测量温度的预测和实际值进行比较。为建立和方案的有效性和真实性的计算时间特性的计算也与文献中可用的数学模型。与纯对流模型表面边界条件方程[7]是前面定义的使用。其他属性和参数是一样的使用模型。 The plots of the time-temperature calculated by this scheme are also indicated in the figures 5 to 8 a look at these plots shows that the rate of cooling by this model consistently slower compared to its actual rate. This means a higher cooling time shall be predicted by mathematical model. It is observed from the temperature-time plots that the present scheme of calculation yields much improved results as compared to the other scheme available in the literature and commonly used. The time-temperature plots by the schemes of the present author results into a consistently remarkable agreement between the computed and experimentally measured temperatures. The agreement is particularly excellent at the later stages of cooling. Incidentally the later stages of cooling are improved from the point of view of calculation of precooling or processing time.

橘色在给定的情节1和2首样的橙色和第二个样本的橙汁,同样的苹果汁。

4结论

在目前的工作,表面薄膜电导计算从瞬态温度记录圆柱形容器的中心的苹果和橙汁。这被发现非常高的开始后期,它随温度降低。变化是由非线性近似方程。温度估计是首先假定常数„hA¢Nu-Re值的关系。然后重复通过变量„hA¢值计算在目前的工作。这两个估计温度绘制在同一图。温度产生的变量„公顷¢值被发现一直在更好的协议与测量值相比产生了由常数„公顷¢值。这证实本方法使用变量„公顷¢值提高液体食物和更可靠。

命名法

面积(平方米)

Bi毕奥数(无量纲)

Cp比热容(焦每千克K)

h对流传热系数(W / m2 K)

导热系数k (W / m k)

公里的传质系数(Kg / m2 s)

L潜伏的熔化热卷的基础上(J / m3)

质量(千克)

νNustle数量(无量纲)

(N / P压力m2)

公关普朗特数(无量纲)

问热流率(W)

问单位面积上的热流率(W / m2)

再保险雷诺数(无量纲)

T温度(K)

t时间(年代)

你无量纲温度

V体积(立方米)

W特定的湿度比

w含水量由质量(%)

R无因次空间坐标(= R / ro)

r空间坐标

ro特征半径(米)

希腊字母:

α热扩散率(m2 /秒)

θimplicit-explicit方案的考虑因素

φ相对湿度(%)

ρ质量密度(公斤/立方米)

τ傅里叶数无量纲(=αt / ro 2)

下标和标:

一个空气

c连续相

厘米的冷却介质

d分散相

db干球

e有效

我空间点(在时空网)

在最初的

j时间点(在时空网)

L潜伏

m潮湿

年代饱和

se明智的

科幻小说系统最终

如果系统初始

v蒸汽

t总

表乍一看

表1

数据乍一看


图1	图2	图3	图4	图5


图1	图2	图3

引用

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Srinivasamurthy年代。,Krishnamurthy M. V. and Ramachandran A., Trans ASAE, Vol. 17, pp.769, 1974.
安萨里f。,“heat and mass transfer analysis in cold preservation of food products” Ph.D. Thesis, University of Roorkee India 1984.
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