^{1}

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This study investigated the effect of air-conditioning system on the tem-perature and speed of automobile engine before and after the air-conditioning system was put to use, while the vehicle was at static position. A 16-valve Nissan engine was used for this study, the engine was first run for 20 minutes before the data are collected. In the first case, the temperatures (℃) of the engine were taken in the interval o f 10 minutes before and after the air-conditioning system is run and in the second case, the speeds of the engine were taken under the same conditions. The research hypothesis was formulated for 20 observations to argue that neither temperature nor speed of the engine changes when the air-conditioning system is put on and Paired t-Test statistics were used. The obtained result of t-statistics analysis for temperature and speed were -4.0329 and -5.51832 respectively. These results when compared to their critical values at 5 percent significant level, t-Statcritical < -1.73 for temperature and speed, were discovered to be at the rejection region which indicates that the null hypothesis (Ht0 and Hs0) in each case is rejected and accept that the air-conditioning system changes the temperature of the engine. Also, changes in speed requirements of the engine are not immediate and it could be as a result of an increase in fuel consump-tion due to more load on the engine. The regression correlation coefficients of 0.999996066 and 0.999653453 were obtained for the temperatures and speeds respectively with their R2 values, 0.999992132 and 0.999307027. The coefficients in the analysis were used to formulate the regression equations; T2 = 135.640 1.025t 0.496T1 and N2 = 634.005 3.824t 0.270N1 which can be used to forecast the temperatures and speeds of the engine during air-conditioning usage giving the initial parameters.

Automobile engineering is one of the main branches of engineering that deals with the various types of automobiles, their mechanism of transmission systems, cooling system, subsystems (such as air conditioning) and its applications. Almost all of the vehicle which is automobiles work on the fundamental of internal combustion processes and are called internal combustion engines (ICE). Therefore, the distinct types of fuels are burnt inside the cylinders at enhanced temperatures to get the transmission motion in the vehicles. Apart from the mechanisms that propel the wheels of the vehicles to get them into motion, it has also become equally important to maintain the comfortability in the vehicles while in motion or stationary [

Javotkova and Pavelek [_{2} as its working medium. Meanwhile, the assessment did not reflect the effect of air-conditioning system on the internal combustion engines using any methods. Another study by Kiatsiriroat and Euakit [

In another literature by ariazone automotive training handbook [

The equipment used are:

1) digital multimeter (Voltcraft, AT-200) with K-Type thermocouple sensors. The range specifications were 20˚C to 760˚C and the accuracy of ±3% for temperature measurement; and

2) digital laser photo tachometer, Hard shell ABS plastic digital non-contact with range 2.5 to 100,000 (RPM) for speed measurement. Calibrated in revolutions per minute (RPM) at the speed range of 600 to 4000 (RPM) and the accuracy of ±2% Output of ≤1 MW; Mirror length of L50 by W25 mm overall size of L130 by W65 mm and Scan diameter of 20 mm. Mirror length of L50 by W25 mm.

The temperature measurements were taken when the switch of the K-type thermo-sensors meter was set to the temperature position in degree celsius within the range of 20˚C to 760˚C. The probes of the meter were connected into the sockets 6 and 7 and the readings of the temperatures were taken from the engine at an idle speed in the intervals of ten minutes. The same procedure was repeated when the A/C of the vehicle was on. To measure the speed, a reflective mark (a reflective tape) was created on the power belt that transmitted power from the engine to both alternator and compressor. The belt is used because it is running at the same speed as the engine. The beam of the laser tachometer was carefully aimed at the belt within the distance of 20 mm while rotating during when the engine is running, each time the reflective point passes the beam of the tachometer, some light is allowed back towards the tachometer, this light is picked up by the tachometer sensor while at the same time count the number of times the light is triggered in a given time to measure the speed of the engine. The same process was repeated when the A/C system was put on.

The set of data for temperatures and speeds of the engine were collected at the condition when the A/C was not running and later when running. The engine was first to run for some 20 minutes so that it can reach the required thermal condition. The temperatures of the engine were then taken and recorded in the interval of 10 minutes when the A/C system was off, the A/C system was later put on and the temperatures were measured and recorded again in the interval of 10 minutes. The same procedures were done for the measurement of the speeds of the engine with photo tachometer. The data collected were analyzed with paired t-test to compare the effect of the air-condition on the temperature and speed of the engine at a 5% significance level using excel data analysis package. More analyses were done to also know the relationship between the variables considered and their effects on the engine over the period of time.

The purpose of this study was to test if the air-conditioning unit has an effect on the temperature of the engine using the twin cam 16 valve Nissan engine at 5% significance level, from the problem statement in Equations (1) and (2), it can be deduced that the:

H t 0 : D t = 0 (1)

H t a > 0 ; o r μ t 1 < μ t 2 (2)

where μ t 1 is the mean temperature before the A/C is run and μ t 2 is the mean temperature after A/C is run.

The hypothesis indicates that the test is one-tailed test of the greater type.

H_{t}_{0} represents the null hypothesis. If this is found true, it would mean that the A/C system does not have any effect on the condition of an internal combustion engine.

H_{ta} represents the alternative hypothesis. If this is found true, it would mean that the A/C system increases the temperature of the condition of an internal combustion engine.

D_{t} represents the difference between the temperatures before and after the A/C system is run.

The t-statistics (t_{T}) was first calculated using Equation (3) and the components of the equation were gotten from Equations (4) and (5). The pair t-test was used because of the related samples and small sample size in line with the literature [

t T = D ¯ − 0 σ d i f f / n (3)

D ¯ t = ∑ D t n (4)

( σ d i f f ) 2 = ∑ D t 2 − ( D ¯ t ) 2 ⋅ n n − 1 (5)

This was used to test if the air-conditioning unit has an effect on the speed of the engine using the twin cam 16 valve Nissan engine at 5% significance level, from the problem statement in Equations (6) and (7), it can be deduced that the:

H s 0 : D s = 0 (6)

H s a > 0 ; o r μ s 1 < μ s 2 (7)

where μ s 1 and μ s 2 are the mean speeds before and after the A/C is run on the engine.

The hypothesis indicates that the test is a one-tailed test.

H_{s}_{0} represents the null hypothesis for the speed. If this is found true, it would mean that the A/C system does not increase the speed of the internal combustion engine

H_{sa} represents the alternative hypothesis. If this is found true, it would mean that the A/C system increases the speed of the internal combustion engine.

D_{s} represents the difference between the speeds before and after A/C system is run. The test statistics for the speed was also calculated in a similar way to the temperature as expressed in Equations (8) to (10)

t s = D ¯ s − 0 σ d i f f / n (8)

D ¯ s = ∑ D s n (9)

( σ d i f f ) 2 = ∑ D t 2 − ( D ¯ s ) 2 ⋅ n n − 1 (10)

The data analysis was carried out using the regression tool package on Microsoft Excel Data software. This was done to investigate effects of the A/C on the temperature and speed of the engine through a set of regression models in each case.

The results presented in

The data were generated by the paired t-test in data analysis solver on the Microsoft Excel software. The result of the temperature and speed statistics are shown in

S/N | Time (mins) | Temperature (˚C) | Speed (rpm) | ||
---|---|---|---|---|---|

T_{1} | T_{2} | N_{1} | N_{2} | ||

1 | 10.00 | 133.50 | 213.00 | 1260.00 | 1004.00 |

2 | 20.00 | 170.10 | 239.00 | 894.00 | 979.00 |

3 | 30.00 | 218.00 | 275.00 | 809.00 | 940.50 |

4 | 40.00 | 219.00 | 285.50 | 515.00 | 935.00 |

5 | 50.00 | 261.25 | 316.50 | 379.50 | 927.53 |

6 | 60.00 | 291.69 | 341.85 | 255.50 | 932.17 |

7 | 70.00 | 322.13 | 367.20 | 167.50 | 946.56 |

8 | 80.00 | 352.57 | 392.55 | 115.50 | 970.68 |

9 | 90.00 | 383.01 | 417.90 | 99.50 | 1004.55 |

10 | 100.00 | 413.45 | 443.25 | 119.50 | 1048.15 |

11 | 110.00 | 443.89 | 468.60 | 175.50 | 1101.50 |

12 | 120.00 | 474.33 | 493.95 | 267.50 | 1164.58 |

13 | 130.00 | 504.77 | 519.30 | 395.50 | 1237.41 |

14 | 140.00 | 535.21 | 544.65 | 559.50 | 1319.97 |

15 | 150.00 | 565.65 | 570.00 | 759.50 | 1412.28 |

16 | 160.00 | 596.09 | 595.35 | 995.50 | 1514.32 |

17 | 170.00 | 626.53 | 620.70 | 1267.50 | 1626.11 |

18 | 180.00 | 656.97 | 646.05 | 1575.50 | 1747.63 |

19 | 190.00 | 687.41 | 671.40 | 1919.50 | 1878.90 |

20 | 200.00 | 717.85 | 696.75 | 2299.50 | 2019.90 |

Parameters | T_{1} | T_{2} |
---|---|---|

Mean | 428.67 | 455.925 |

Variance | 32,456.37 | 22,498.27 |

Observations | 20 | 20 |

df | 19 | |

t Stat | −4.0329 | |

P (T ≤ t) one-tail | 0.000355 | |

t Critical one-tail | 1.729133 | |

P (T ≤ t) two-tail | 0.000711 | |

t Critical two-tail | 2.093024 |

Parameters | N_{1} | N_{2} | |
---|---|---|---|

Mean | 741.5 | 1235.535 | |

Variance | 409,767.8 | 121,517.5 | |

Observations | 20 | 20 | |

df | 19 | ||

t Stat | −5.51832 | ||

P (T ≤ t) one-tail | 1.27E−05 | ||

t Critical one-tail | 1.729133 | ||

P (T ≤ t) two-tail | 2.53E−05 | ||

t Critical two-tail | 2.093024 | ||

As stated in _{t0} is one-sided, the analysis has applied a one-tailed test (in the left tail because H_{t0} is of less than type, μ t 1 < μ t 2 ) for determining the rejection region at 5 percent level of significance. Therefore, the critical value in _{critical} < −1.73. The observed value of t is ≈ −4.0329 which falls in the rejection region and thus, we reject H_{t0} at 5 percent level and conclude that the A/C has an effect of increasing the temperature of the engine over a meaningful period of hours.

This was also stated in _{s0} is one-sided and the analysis has applied a one-tailed test (in the left tail because H_{s0} is of less than type, μ s 1 < μ s 2 ) for determining the rejection region at 5 percent level of significance. The critical value in _{critical} < −1.73 while the observed value of t is ≈ −5.518. This falls in the rejection region and thus, we reject H_{s0} at 5 percent level and conclude that the A/C has an effect of increasing the speed of the engine over a significant number of hours

Multiple regression analyses were performed between the variables to determine their relationships. In the first instance, the analysis of the correlation between the temperature of the engine (T_{1}), before the A/C is run; the temperature of the engine (T_{2}) after A/C is run and the time is estimated. The second case was the analysis of the speed of the engine before (N_{1}) and after (N_{2}) A/C is run respectively. The correlation summaries among variables are shown in

In the first case, from the result of the multiple correlation coefficient which has the value of 0.999992132 in _{1} and time (t) and a dependent variable, T_{2} is positive. Considering the second case, the value is 0.999653453 which also shows a similar relationship between the independent variables, N_{1} and time (t), and dependent variable N_{2}. The R-Square (R^{2}) is called the coefficient of determination; this value measures the percentage of variation in the dependent variable that can be explained by the independent variables. Using the values in ^{2} values. The high percentage reveals accuracy of the proposed models is good at forecasting the independent variables in each of the two cases, i.e. T_{2} and N_{2}. The standard error of regression is an appraisal of the fluctuations in each of the dependent variables about the regression line.

The results of the regression models in each case include the independent variables that are statistically significant in explaining the variations in the final parameters of the engine considered, final temperature (T_{2}) and final speed (N_{2}) respectively. The values of these models were validated in each case by Regression P-Value statistics, which is the probability of observing a test statistic more extreme than what we observed. If the p-value of each coefficient in the regression analysis is less than the value of significant level (0.05% or 5%) then there would be the acceptability that the values of the independent variables can be used to predict the dependent variable or the dependent variable in each case varies in line with their respective independent variables. The Regression model outputs generated by the Microsoft Excel data Analysis are shown in _{2}) and final speed (N_{2}) of the engine.

Regression Statistics | |
---|---|

Multiple R | 0.999996066 |

R Square | 0.999992132 |

Adjusted R Square | 0.999991206 |

Standard Error | 0.444806048 |

Observations | 20 |

Regression Statistics | |
---|---|

Multiple R | 0.999653453 |

R Square | 0.999307027 |

Adjusted R Square | 0.9992255 |

Standard Error | 9.701301718 |

Observations | 20 |

Independent Variables | Coefficients | Standard Error | P-value |
---|---|---|---|

Intercept | 135.64 | 2.21 | 2.12 × 10^{−21} |

Time (t) | 1.02 | 0.06 | 5.69 × 10^{−22} |

T_{1 } | 0.50 | 0.02 | 9.93 × 10^{−22} |

Independent Variables | Coefficients | Standard Error | P-value |
---|---|---|---|

Intercept | 634.00 | 4.55 | 1.93 × 10^{−27} |

Time (t) | 3.82 | 0.04 | 5.78 × 10^{−24} |

N_{1 } | 0.27 | 0.00 | 5.62 × 10^{−22} |

The model equations generated from the analysis of the regression coefficients in

T 2 = 135.640 + 1.025 t + 0.496 T 1 (11)

N 2 = 634.005 + 3.824 t + 0.270 N 1 (12)

_{2} increases with time which is an indication that the temperature of the engine is increased over the specific time of using the A/C system. Also, between the ranges of 540˚C to 570˚C, at around 170 minutes, what was observed is the intersection of T_{1} and T_{2}, at this equilibrium point, it can be inferred that these two conditions of the engine temperature are the same. In _{2}, was observed to be less than the initial speed (N_{1}). Later, the decline in the initial speed of the engine was observed while the N_{2} maintained. The increase in fuel consumption of the engine may be accounted for the speed requirement after the A/C system is put to use. The relationship between the T_{1} and T_{2} according to

_{1} and T_{2}) and the speeds (N_{1} and N_{2}) before and after the AC system is being used.

Analyses have been carried out to investigate the temperature and speed of the engine before and after A/C usage; the paired t-test analysis, at 5% significant level showed that the air-conditioning system has effect of increasing the temperature and speed of the twin cam 16-valve Nissan engine but the regression analyses predicted that the temperature and the speed of the engine could drop

over a significant amount of time even while air-conditioning is in usage. The correlation and R-Squared values showed that the data obtained had good correlations and the analysis is accurate in predicting the temperatures and speeds of the engine before and after air-conditioning system usage.

Authors hereby acknowledge the Head of Department of Mechanical Engineering of Federal University of Technology Akure, Nigeria; for the release of workshop tools and equipment required for this study.

The authors declare no conflicts of interest regarding the publication of this paper.

Bamisaye, O.S., Oyerinde, A.Y. and Essien, U.A. (2019) Investigation of the Effects of Air- Conditioning System on the Temperature and Speed of Automobile Engine Using Paired T-Test and Regression Analysis. Open Access Library Journal, 6: e5090 https://doi.org/10.4236/oalib.1105090

A/C = Air-conditioning

T_{1} = Temperature (˚C) of the engine before Air Conditioning is put to use

T_{2} = Temperature (˚C) of the engine after Air Conditioning is put to use

N_{1} = Speed (rpm) of the engine before Air Conditioning is put to use

N_{2} = Speed (rpm) of the engine after Air Conditioning is put to use

t = Time (minutes)

H_{t0} = Null hypothesis for the temperature

H_{s0} = Null hypothesis for the speed

R^{2} = Coefficient of determination

˚C = Degree Celsius

RPM = Revolution per minute

MW = Mega Watts

mm = Millimetres

RPM = Revolutions per minute (speed)