Study of the Fastest Rate of Freezing Saline Solution Using Factorial Design Method

An engineer needed the ability to design an experiment research to be effective and efficient to obtain optimal results. The purpose of this experiment is to determine the fastest rate of freezing saline solution. The research process begins with determining the independent variables as much as possible and determines the three independent variables to be tested. After determine variables, and then create table factorial design to determine the research steps as much as 8 times. Then determine the most influential variables using Yates's algorithm was then tested again using response surface methodology (RSM), but for this study only uses two steps of the three step RSM. So it can be concluded that the lower temperature and salinity the faster the rate of freezing for both type of salt, Krosok and salt.


Introduction
An engineer needed the ability to design an experiment research to be effective and efficient to obtain optimal result. These experiments use factorial design methods to make it easier for researchers to get effective and efficient results.
Factorial design is a method for determining the influence of several independent variables on the response. Basically an experiment is designed to determine one variable in one response. Therefore, factorial design can make it easier to experiment with more than one independent variable. Another use of factorial design is that it can reduce the number of experiments we have to do by studying several factors simultaneously.
The purpose of this experiment is to determine the fastest rate of freezing saline solution. The output to be produce of this study is a graph and the most influential variable as a result. In this study the output will be obtained by using factorial design and least square and response surface methodology.

Factorial Design
Factorial design is an important method to determine the effects of multiple variables on a response/output. Traditionally, experiments are designed to determine the effect of one variable upon one response/output. There are advantages by combining the study of multiple variables in the same factorial experiment. Factorial design can reduce the number of experiments one has to perform by studying multiple factors simultaneously. Additionally, it can be used to find both main effects (from each independent factor) and interaction effects (when both factors must be used to explain the outcome).
Factorial design is a useful method to design experiments in both laboratory and industrial settings. Because factorial design can lead to a large number of trials, which can become expensive and time-consuming, factorial design is best used for a small number of variables with few states (1 to 3).

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Study of the Fastest Rate of Freezing Saline Solution Using Factorial Design Method

Least Square
The method of least squares is a standard approach to the approximate solution of over determined systems, i.e., sets of equations in which there are more equations than unknowns.
Least square means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. The most important application is in data fitting.
In this equation the β's are unknown constants to be estimated and the x have known values. One common example is where x 1 , x 2 ,... are the levels of k factors, say temperature x 1 , line speed x 2 , concentration x 3 , and so on, and y is a measured response such as yield. Table 1 shows a small illustrative set of data from an experiment to determine how the initial rate of formation of an undesirable impurity y depended on two factors: A) the concentration x o of monomer and B) the concentration of dimer x 1 . The mean rate of formation y was zero when both components x 0 and x 1 were zero. Over the relevant ranges of x 0 and x 1 the relationship was expected to be approximated by  Table 1, if 0 = 1 and 1 = 7, would get: Thus in principle could obtain the minimum value of S by repeated calculation for a grid of trial values. It would eventually be able to construct Figure 2, a 3D plot of the sum of squares surface of S( ) versus 0 and 1 . The coordinates of the minimum value of this surface are the desired least square estimates Table 1. Initial Rate of Impurity Investigation

3) Factorial Design Method
This experiment used the 2 3 factorial design methods with two quantitative factors, temperature and salinity and one qualitative factor, the type of salt.

Results and Discussion
1) The experiment was carried out in 8x according to the design factorial table that was made before. 2) The Most Influential Variables The next step after getting the results from the experiment is to determine the most influential variables. Determine the most influential variable using the Yates Algorithm method. Yates algorithms table above shows that the most influential variable is the salinity. To find the value of b0 and b1 use the Matrix, so that it is obtained: b0 = -3.6976 b1 = -3.24341

3) Result of Least Square Method
So the equation obtained is: FR = -3.697 T -3.243 S

Conclusions
In both types of salt cannot carry out RSM experiments for the first order secondary steps. This is caused by the following [3,4,5]: a. The results show that the value continues to decrease with a maximum freezing rate of 50 g/hour and constant for Krosok and 48 g/hour and continues to decrease to 50 g/hour constant for salt. b. Change in the percentage of salinity is limited because if the water adds more salt, it will become saturated so that it cannot dissolve completely. c. The freezer temperature changes are limited according to the specifications of the refrigerator.
On the graph of the Krosok, the freezing rate tends to the bottom left at an angle of 15.25 o . On the graph of the salt, the freezing rate tends to the upper left with an angle of 1.74 o . This indicates that the salinity is more influential than the temperature of the freezer.
The results obtained for both types of salt are, the lower the salt content, the faster the freezing rate. As for the type of salt, the fastest freezing rate according to the results of the data obtained is salt.