Mathematical Model for Design Conditions for Cooling Load Calculations

1981 ◽  
Vol 103 (2) ◽  
pp. 328-334 ◽  
Author(s):  
D. Kohli
Keyword(s):  
Mathematical Model ◽  
Numerical Procedure ◽  
Barometric Pressure ◽  
Daily Temperature ◽  
Temperature Deviation ◽  
Average Value ◽  
Hourly Temperature ◽  
Temperature Ranges ◽  
Maximum Temperatures ◽  
T Distribution

A numerical procedure using Newton-Raphson technique is used for finding wet bulb temperature from observed dry bulb temperature relative humidity and barometric pressure. Assuming maximum temperatures and daily temperature ranges of the day as random variables, maximum temperatures and daily ranges are estimated from samples of ten years data by t-distribution for various confidence limits. A parameter called “Average Hourly Temperature Deviation” is defined and its effect on Equivalent temperature differential is demonstrated. A mathematical model for finding out optimum daily temperature distribution has been developed. An average value of the “Average Hourly Temperature Deviation” is chosen as the optimality criterion. The procedures are demonstrated by numerical examples and the design conditions for 20 major cities of India are provided in tabular form.

scholarly journals Estimation of seasonal boundaries using temperature data: a case of northwest part of Bangladesh

2020 ◽  
Vol 6 (1) ◽  
pp. 50-62
Author(s):  
Syed Mustafizur Rahman ◽  
Syed Mahbubur Rahman ◽  
Md. Shuzon Ali ◽  
Md. Abdullah Al Mamun ◽  
Md. Nezam Uddin
Keyword(s):  
Spectral Analysis ◽  
Crop Productivity ◽  
Temperature Data ◽  
Daily Temperature ◽  
Temperature Cycle ◽  
Local Climate ◽  
Higher Power ◽  
Cycle Plays ◽  
Maximum Temperatures ◽  
Harmonic Analyses

Abstract Seasons are the divisions of the year into months or days according to the changes in weather, ecology and the intensity of sunlight in a given region. The temperature cycle plays a major role in defining the meteorological seasons of the year. This study aims at investigating seasonal boundaries applying harmonic analysis in daily temperature for the duration of 30 years, recorded at six stations from 1988 to 2017, in northwest part of Bangladesh. Year by year harmonic analyses of daily temperature data in each station have been carried out to observe temporal and spatial variations in seasonal lengths. Periodic nature of daily temperature has been investigated employing spectral analysis, and it has been found that the estimated periodicities have higher power densities of the frequencies at 0.0027 and 0.0053 cycles/day. Some other minor periodic natures have also been observed in the analyses. Using the frequencies between 0.0027 to 0.0278 cycles/day, the observed periodicities in spectral analysis, harmonic analyses of minimum and maximum temperatures have found four seasonal boundaries every year in each of the stations. The estimated seasonal boundaries for the region fall between 19-25 February, 19-23 May, 18-20 August and 17-22 November. Since seasonal variability results in imbalance in water, moisture and heat, it has the potential to significantly affect agricultural production. Hence, the seasons and seasonal lengths presented in this research may help the concerned authorities take measures to reduce the risks for crop productivity to face the challenges arise from changing climate. Moreover, the results obtained are likely to contribute in introducing local climate calendar.

scholarly journals Tail-Actuator Propulsion Device for Aquatic Robot

2006 ◽  
Vol 18 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Andrea Manuello Bertetto ◽  
◽  
Maurizio Ruggiu
Keyword(s):  
Mathematical Model ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Operating Principle ◽  
The Other ◽  
Kinematics And Dynamics ◽  
Experimental Characterization ◽  
Fish Propulsion ◽  
Geometrical Dimensions ◽  
Simplified Mathematical Model

In this paper an aquatic device inspired to the fish propulsion is proposed. At the first, the operating principle of the fluidic actuator and its experimental characterization are presented. Then, the results of numerous tests carried out on the integrated tail-actuator device are shown either in terms of thrust exerted or as biomorphism of its kinematics. The tests were run at several driven frequencies with different fins depending on their geometrical dimensions and compliances. On the other hand, a simplified mathematical model of the propulsion system, based on the calculation of the instantaneous tail kinematics and dynamics by means of a numerical procedure, is proposed with the aim of simulating performances either in terms of thrust exerted or kinematics behavior. Finally a discussion about the results obtained and a comparison between experimental and numerical data are presented.

Distribution Characteristics of Multivariate Financial Assets Return based on Mathematical Model

2021 ◽  
Vol 7 (5) ◽  
pp. 2244-2259
Author(s):  
Han Wang
Keyword(s):  
Mathematical Model ◽  
Stock Return ◽  
Time Variability ◽  
Financial Assets ◽  
Return Distribution ◽  
Proposed Model ◽  
Dynamic Portfolio ◽  
T Distribution ◽  
Dynamic Portfolio Optimization ◽  
Fluctuation Model

For the non-normality and time variability of the distribution of multivariate financial assets return, a dynamic model of the distribution of multivariate financial assets return based on mathematical model is constructed in this paper. AR(1)-DCC(1,1)-GARCH(1,1) model reflects dynamic characteristics of conditional expectation and conditional variance of multivariate financial assets return. It solves the problem that restricts the in-depth research on high order dynamic portfolio optimization, which is the estimation of conditional coskewness matrix and conditional cokurtosis matrix. By constructing a multi-dimensional fluctuation model with biased t distribution, conditional asymmetric parameter and conditional free degree parameter, the distribution of multivariate financial assets return is researched. Experimental results show that the proposed model can reasonably reflect the time-varying characteristics of the multivariate stock return distribution in China’s stock market.

Relationship between temperature and flowering in almond: effect of location

1987 ◽  
Vol 27 (6) ◽  
pp. 905 ◽  
Author(s):  
K Rattigan ◽  
SJ Hill
Keyword(s):  
Continuous Function ◽  
Threshold Temperature ◽  
Chilling Requirement ◽  
Flowering Date ◽  
Hourly Temperature ◽  
Single Location ◽  
Growing Degree Hours ◽  
Chill Unit ◽  
Maximum Temperatures ◽  
Different Climates

A model for the prediction of flowering date in almond requires estimates of the chilling and heat sum requirements. We estimated hourly temperatures from daily minimum and maximum temperatures. A continuous function relating hourly temperature to rate of chilling was used to calculate daily chill unit accumulations. Heat sums were measured as growing-degree-hours: the linear accumulation of hourly temperatures above a threshold temperature. Our model was tested with estimates derived from data obtained at 1 French and 2 Australian locations. The results indicate that estimates derived from data at a single location can be successfully used for other locations with different climates. The accuracy of flowering date prediction generally improves as the number of locations and years of data on which it is based increase. The predictions for the cultivars Mission and Nonpareil were within 5 days of the observed dates in 73 and 88% respectively of the locations-years examined. We concluded that the chilling requirement in almond is (mean � s.e.) 284 � 33 chill units and 3 groups of cultivars can be identified with respect to heat sum requirement in the ranges 5300-6300; 6800-7700 and 8200-8900 degree hours above 4.5�C.

A Comparison of Daily Temperature-Averaging Methods: Spatial Variability and Recent Change for the CONUS

2018 ◽  
Vol 31 (3) ◽  
pp. 979-996 ◽  
Author(s):  
Jase Bernhardt ◽  
Andrew M. Carleton ◽  
Chris LaMagna
Keyword(s):  
Spatial Variability ◽  
Daily Temperature ◽  
Maximum Temperature ◽  
Underlying Assumption ◽  
First Order ◽  
Daily Average ◽  
Hourly Temperature ◽  
Significant Difference ◽  
Weather Stations

Abstract Traditionally, the daily average air temperature at a weather station is computed by taking the mean of two values, the maximum temperature (Tmax) and the minimum temperature (Tmin), over a 24-h period. These values form the basis for numerous studies of long-term climatologies (e.g., 30-yr normals) and recent temperature trends and changes. However, many first-order weather stations—such as those at airports—also record hourly temperature data. Using an average of the 24 hourly temperature readings to compute daily average temperature has been shown to provide a more precise and representative estimate of a given day’s temperature. This study assesses the spatial variability of the differences in these two methods of daily temperature averaging [i.e., (Tmax + Tmin)/2; average of 24 hourly temperature values] for 215 first-order weather stations across the conterminous United States (CONUS) over the 30-yr period 1981–2010. A statistically significant difference is shown between the two methods, as well as consistent overestimation of temperature by the traditional method [(Tmax + Tmin)/2], particularly in southern and coastal portions of the CONUS. The explanation for the long-term difference between the two methods is the underlying assumption for the twice-daily method that the diurnal curve of temperature is symmetrical. Moreover, this paper demonstrates a spatially coherent pattern in the difference compared to the most recent part of the temperature record (2001–15). The spatial and temporal differences shown have implications for assessments of the physical factors influencing the diurnal temperature curve, as well as the exact magnitude of contemporary climate change.

Mathematical Modelling and Field Measurements of Nitrogen Oxides in Metropolitan Areas

1992 ◽  
Vol 3 (2) ◽  
pp. 133-147
Author(s):  
M.M. Elkotb ◽  
O.M.F. Elbahar ◽  
T.A. Abdou Ahmed ◽  
T.W. Abou-Arab
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Field Measurements ◽  
Mass Conservation ◽  
Eddy Diffusivity ◽  
Solution Procedure ◽  
Pollutant Emissions ◽  
Motor Vehicles

A mathematical model for the prediction of pollutant emissions from motor vehicles is presented. The model is based on the numerical solution of the three-dimensional equation representing the mass conservation of dilute diffusing species. The variation of wind speed and eddy diffusivity with height is taken into consideration. The three-dimensional diffusion equation is solved numerically. The numerical procedure involves the discretization of the partial differential equation using the finite volume approach. The resulting set of discretization equation is solved iteratively using a fully implicit solution procedure. Furthermore, field measurements of the concentrations of nitrogen oxide in the downtown area of Cairo were conducted. For this purpose, a mobile air pollution laboratory fitted with gas analyzers, particulate matter sampler and equipment for the measurement of wind speed and direction has been used. This laboratory is also fitted with data recording and monitoring facility. The mathematical model is tested by comparing the computed pollutant concentrations with the experimental data obtained from the field measurements in the Cairo Metropolitan Area.

Performance Evaluation of Hybrid Photovoltaic Thermal Thermoelectric Collector Using Grasshopper Optimization Algorithm With Simulated Annealing

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Anmol Gupta ◽  
Sanjay Agrawal ◽  
Yash Pal
Keyword(s):  
Mathematical Model ◽  
Performance Evaluation ◽  
Simulated Annealing ◽  
Optimization Algorithm ◽  
Single Channel ◽  
Electrical Energy ◽  
Average Value ◽  
Grasshopper Optimization Algorithm ◽  
Mass Flowrate ◽  
Grasshopper Optimization

Abstract In this paper, a mathematical model of a single-channel photovoltaic thermal (PVT) air collector incorporated with a thermoelectric (TE) module has been presented. The overall electrical energy obtained from the photovoltaic thermal-thermoelectric (PVT-TE) collector is 5.78% higher than the PVT collector. Further, the grasshopper optimization algorithm (GOA) and hybrid grasshopper optimization algorithm with simulated annealing (GOA-SA) have been proposed and implemented to optimize the parameters of opaque PVT-TE collector. Although there are different parameters that influence the performance of PVT-TE system, yet in this study only four parameters, viz., length of the channel (L), width of the channel (b), mass flowrate of air in the channel (mair), and temperature of air at the inlet of channel (Tair,i) are considered for optimization. The simulation result demonstrates that the hybrid GOA-SA algorithm turned out to be an exceptionally effective method for optimal tuning of the parameters of the PVT-TE system. The result explicitly shows that the average value of overall electrical efficiency and exergy gain are 15.27% and 27.0565 W, respectively, when the parameters are optimized by the suggested GOA-SA algorithm which is way ahead with respect to the outcomes obtained with that of the calculated values or using GOA algorithm alone.

Computational analysis of temperature distribution in microwave-heated potatoes

2020 ◽  
Vol 26 (6) ◽  
pp. 465-474
Author(s):  
Deepak Singh ◽  
Dhananjay Singh ◽  
Sattar Husain
Keyword(s):  
Mathematical Model ◽  
Temperature Distribution ◽  
Computational Analysis ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Maximum Temperature ◽  
Bacterial Inactivation ◽  
Food Material ◽  
Drying Time ◽  
Temperature Ranges

This research article reports the computational analysis of temperature distribution in microwave-heated convenience food such as potato. The detailed study of temperature (because temperature is a function of bacterial inactivation) and microwave powers along with drying time for the preservation of food material has been presented. Therefore, a mathematical model for potato sample is developed to predict the behavior of temperature distribution at each possible point and different shapes (slab, cylindrical, and spherical) of food material. The developed mathematical model is programmed by MATLAB software. Another parameter, microwave power is also a function of temperature. The ranging values of various microwave powers (125 W, 375 W, 625 W, 875 W, and 1250 W) along with different values of drying time (0 to 10 minutes) have been used for computation. The obtained results show the uniformity of temperature distribution throughout the whole product in the form of a three-dimensional structure. The model provides the minimum and maximum temperature ranges in specimens without performing an experiment which depicts the condition of bacterial inactivation.

scholarly journals Numerical simulation of concentrating solar collector P2CC with a small concentrating ratio

2012 ◽  
Vol 16 (suppl. 2) ◽  
pp. 471-482 ◽  
Author(s):  
Velimir Stefanovic ◽  
Sasa Pavlovic ◽  
Marko Ilic ◽  
Nenad Apostolovic ◽  
Dragan Kustrimovic
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Solar Radiation ◽  
Solar Energy ◽  
Radiation Intensity ◽  
Solar Collector ◽  
Numerical Procedure ◽  
Working Fluid ◽  
Flow Rates ◽  
Solar Radiation Intensity

Solar energy may be practically utilized directly through transformation into heat, electrical or chemical energy. A physical and mathematical model is presented, as well as a numerical procedure for predicting thermal performances of the P2CC solar concentrator. The demonstrated prototype has the reception angle of 110? at concentration ratio CR = 1.38, with the significant reception of diffuse radiation. The solar collector P2CC is designed for the area of middle temperature conversion of solar radiation into heat. The working fluid is water with laminar flow through a copper pipe surrounded by an evacuated glass layer. Based on the physical model, a mathematical model is introduced, which consists of energy balance equations for four collector components. In this paper, water temperatures in flow directions are numerically predicted, as well as temperatures of relevant P2CC collector components for various values of input temperatures and mass flow rates of the working fluid, and also for various values of direct sunlight radiation and for different collector lengths. The device which is used to transform solar energy to heat is referred to as solar collector. This paper gives numerical estimated changes of temperature in the direction of fluid flow for different flow rates, different solar radiation intensity and different inlet fluid temperatures. The increase in fluid flow reduces output temperature, while the increase in solar radiation intensity and inlet water temperature increases output temperature of water. Furthermore, the dependence on fluid output temperature is determined, along with the current efficiency by the number of nodes in the numerical calculation.

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