Pub Date : 2023-01-28DOI: 10.26782/jmcms.2023.01.00002
B. C. Bag
In this paper, the framework of polyp image segmentation is developed using a Deep neural network (DNN). Here Unet Mobile NetV2 is considered to evaluate the performance of the image from the CVC-612 dataset for the segmentation method. The proposed model outperformed earlier results. To compare our results two parameters, normally Dice co-efficient and Intersection over Union (IoU) are considered. The proposed model may be used for accurate computer-aided polyp detection and segmentation during colonoscopy examinations to find out abnormal tissue and thereby decrease the chances of polyps growing into cancer. MobileNetV2 significantly outperforms U-Net and MobileNetV2, two key state-of-the-art deep learning architectures, by achieving high evaluation scores with a dice coefficient of 89.71%, and an IoU of 81.64%.
本文提出了一种基于深度神经网络的息肉图像分割框架。这里考虑Unet Mobile NetV2来评估CVC-612数据集图像的分割方法的性能。所提出的模型优于先前的结果。为了比较我们的结果，考虑了两个参数，通常是骰子系数和交联(IoU)。该模型可用于结肠镜检查时计算机辅助息肉的准确检测和分割，以发现异常组织，从而减少息肉长成癌的机会。MobileNetV2通过获得89.71%的骰子系数和81.64%的IoU的高评估分数，显著优于U-Net和MobileNetV2这两个最先进的关键深度学习架构。
{"title":"UNET MOBILENETV2: MEDICAL IMAGE SEGMENTATION USING DEEP NEURAL NETWORK (DNN)","authors":"B. C. Bag","doi":"10.26782/jmcms.2023.01.00002","DOIUrl":"https://doi.org/10.26782/jmcms.2023.01.00002","url":null,"abstract":"In this paper, the framework of polyp image segmentation is developed using a Deep neural network (DNN). Here Unet Mobile NetV2 is considered to evaluate the performance of the image from the CVC-612 dataset for the segmentation method. The proposed model outperformed earlier results. To compare our results two parameters, normally Dice co-efficient and Intersection over Union (IoU) are considered. The proposed model may be used for accurate computer-aided polyp detection and segmentation during colonoscopy examinations to find out abnormal tissue and thereby decrease the chances of polyps growing into cancer. MobileNetV2 significantly outperforms U-Net and MobileNetV2, two key state-of-the-art deep learning architectures, by achieving high evaluation scores with a dice coefficient of 89.71%, and an IoU of 81.64%.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"207 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132822653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-27DOI: 10.26782/jmcms.2022.11.00001
P. Bhattacharyya
In this paper, the author has opened a new horizon in the theory of quadratic equations. The author proved that the value of x which satisfies the quadratic equation cannot be the only criteria to designate as the root or roots of an equation. The author has developed a new mathematical concept of the dimension of a number. By introducing the concept of the dimension of number the author structured the general form of a quadratic equation into two forms: 1) Pure quadratic equation and 2) Pseudo quadratic equation. First of all the author defined the pure and pseudo quadratic equations. In the case of pure quadratic equation ax^2+bx+c=0 , the root of the equation will be a two-dimensional number having one root only while in the case of pseudo quadratic equation ax^2+bx+c=0, the root of the equation will be a one-dimensional number having two roots only. The author proved that all pseudo quadratic equation is factorizable but all factorizable quadratic equation is not a pseudo quadratic equation. The author begs to differ from the conventional theorem: “A quadratic equation has two and only two roots.” By introducing the concept that any quadratic surd is a two-dimensional number, the author developed a new theorem: “In a quadratic equation with rational coefficients, irrational roots cannot occur in conjugate pairs” and proved it. Any form of quadratic equation ax^2+bx+c=0, can be solved by the application of the ‘Theory of Dynamics of Numbers’ even if the discriminant b^2-4ac<0 in real number only without introducing the concept of an imaginary number. Therefore, the question of imaginary roots does not arise in the method of solution of any quadratic equation
{"title":"AN OPENING OF A NEW HORIZON IN THE THEORY OF QUADRATIC EQUATION : PURE AND PSEUDO QUADRATIC EQUATION – A NEW CONCEPT","authors":"P. Bhattacharyya","doi":"10.26782/jmcms.2022.11.00001","DOIUrl":"https://doi.org/10.26782/jmcms.2022.11.00001","url":null,"abstract":"In this paper, the author has opened a new horizon in the theory of quadratic equations. The author proved that the value of x which satisfies the quadratic equation cannot be the only criteria to designate as the root or roots of an equation. The author has developed a new mathematical concept of the dimension of a number. By introducing the concept of the dimension of number the author structured the general form of a quadratic equation into two forms: 1) Pure quadratic equation and 2) Pseudo quadratic equation. First of all the author defined the pure and pseudo quadratic equations. In the case of pure quadratic equation ax^2+bx+c=0 , the root of the equation will be a two-dimensional number having one root only while in the case of pseudo quadratic equation ax^2+bx+c=0, the root of the equation will be a one-dimensional number having two roots only. The author proved that all pseudo quadratic equation is factorizable but all factorizable quadratic equation is not a pseudo quadratic equation. The author begs to differ from the conventional theorem: “A quadratic equation has two and only two roots.” By introducing the concept that any quadratic surd is a two-dimensional number, the author developed a new theorem: “In a quadratic equation with rational coefficients, irrational roots cannot occur in conjugate pairs” and proved it. Any form of quadratic equation ax^2+bx+c=0, can be solved by the application of the ‘Theory of Dynamics of Numbers’ even if the discriminant b^2-4ac<0 in real number only without introducing the concept of an imaginary number. Therefore, the question of imaginary roots does not arise in the method of solution of any quadratic equation","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132467133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-27DOI: 10.26782/jmcms.2022.11.00002
Md. Rakibul Islam
Breast cancer is a serious trouble and one of the greatest causes of death for women throughout the world. Computer-aided diagnosis (CAD) techniques can help the doctor make more credible decisions. We have determined the possibility of knowledge transfer from natural to histopathological [IX][XII] images by employing a pre-trained network ResNet-50.This pre-trained network has been utilized as a feature generator and extracted features are used to train support vector machine (SVM), random forest, decision tree, and K nearest neighbor(KNN) classifiers[X]. We altered the softmax layer to support the vector machine classifier, random forest classifier, decision tree classifier, and k-nearest neighbor classifier, to evaluate the classifier performance of each algorithm. These approaches are applied for breast cancer classification and evaluate the performance and behavior of different classifiers on a publicly available dataset named Bttheeak-HIS dataset. In order to increase the efficiency of the ResNet[III] model, we preprocessed the data before feeding it to the network. Here we have applied to sharpen filter and data augmentation techniques, which are very popular and effective image pre-processing techniques used in deep models.
{"title":"BREAST CANCER HISTOLOGICAL IMAGES CLASSIFICATION AND PERFORMANCE EVALUATION OF DIFFERENT CLASSIFIERS","authors":"Md. Rakibul Islam","doi":"10.26782/jmcms.2022.11.00002","DOIUrl":"https://doi.org/10.26782/jmcms.2022.11.00002","url":null,"abstract":"Breast cancer is a serious trouble and one of the greatest causes of death for women throughout the world. Computer-aided diagnosis (CAD) techniques can help the doctor make more credible decisions. We have determined the possibility of knowledge transfer from natural to histopathological [IX][XII] images by employing a pre-trained network ResNet-50.This pre-trained network has been utilized as a feature generator and extracted features are used to train support vector machine (SVM), random forest, decision tree, and K nearest neighbor(KNN) classifiers[X]. We altered the softmax layer to support the vector machine classifier, random forest classifier, decision tree classifier, and k-nearest neighbor classifier, to evaluate the classifier performance of each algorithm. These approaches are applied for breast cancer classification and evaluate the performance and behavior of different classifiers on a publicly available dataset named Bttheeak-HIS dataset. In order to increase the efficiency of the ResNet[III] model, we preprocessed the data before feeding it to the network. Here we have applied to sharpen filter and data augmentation techniques, which are very popular and effective image pre-processing techniques used in deep models.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124798733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-27DOI: 10.26782/jmcms.2022.11.00003
Mehria Nawaz
{"title":"ONLINE SKILL TEST PLATFORM","authors":"Mehria Nawaz","doi":"10.26782/jmcms.2022.11.00003","DOIUrl":"https://doi.org/10.26782/jmcms.2022.11.00003","url":null,"abstract":"","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131640439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-27DOI: 10.26782/jmcms.2022.11.00004
Hafeezullah Channa
In this paper, we take into account the system of differential equations with boundary conditions of a fixed elastic beam model (EBM). Instead of finding a solution of EBM for a particularly specified load, which is the usual practice, we derive the general analytical solution of the model using techniques of integrations. The proposed general analytical solutions are not load-specific but can be used for any load without having to integrate successively again and again. We have considered load in a general polynomial form and obtained a general analytical solution for the deflection and slope parameters of EBM. Direct solutions have been determined under two types of loads: uniformly distributed load and linearly varying load. The formulation derived has been validated on the known cases of uniformly distributed load as appears frequently in the literature.
{"title":"GENERAL ANALYTICAL SOLUTION OF AN ELASTIC BEAM UNDER VARYING LOADS WITH VALIDATION","authors":"Hafeezullah Channa","doi":"10.26782/jmcms.2022.11.00004","DOIUrl":"https://doi.org/10.26782/jmcms.2022.11.00004","url":null,"abstract":"In this paper, we take into account the system of differential equations with boundary conditions of a fixed elastic beam model (EBM). Instead of finding a solution of EBM for a particularly specified load, which is the usual practice, we derive the general analytical solution of the model using techniques of integrations. The proposed general analytical solutions are not load-specific but can be used for any load without having to integrate successively again and again. We have considered load in a general polynomial form and obtained a general analytical solution for the deflection and slope parameters of EBM. Direct solutions have been determined under two types of loads: uniformly distributed load and linearly varying load. The formulation derived has been validated on the known cases of uniformly distributed load as appears frequently in the literature.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130026977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.26782/jmcms.2022.06.00003
Arshad Ullah Khan
Fire is an unwanted event that could carry a high loss of social wealth and human life. To stop such losses, different alarm systems such as smoke detectors, and temperature sensor-based systems have been developed. Our proposed system is aimed to design and develop a fire detection system that detects fire without any heat or temperature sensor. The primary objective of the fire detection system is to detect a fire early and warn authorities when a fire takes place. The Machine Learning Algorithm has been used to detect the accurate image of fire because it has a prior pattern of fire images already fed into it. On occurring the fire, the camera will send this pattern to Raspberry pi which has already predefined patterns of fire written in the form of an algorithm and afterward will compare it with the new existing fire pattern. When both the pattern matches system will do processing based on the image processing technique. Finally, the system generates a warning message which will be sent on the LCD screen for display, and thereafter the buzzer starts working. The key benefit of this system is it will decrease the risk of losses which occurs mainly due to failure in controlling the fire. The experimental results showed that the designed system can efficiently extract and keep trace of fire pixels in the form of patterns and is worthwhile in providing better output results. This system has compact circuitry and functionality like it is easily implanted in public and commercial places for security and surveillance
{"title":"A PROPOSED FIRE DETECTION SURVELLIANCE THROUGH MACHINE LEARNING BASED ON HAAR CASCADE CLASSIFIER","authors":"Arshad Ullah Khan","doi":"10.26782/jmcms.2022.06.00003","DOIUrl":"https://doi.org/10.26782/jmcms.2022.06.00003","url":null,"abstract":"Fire is an unwanted event that could carry a high loss of social wealth and human life. To stop such losses, different alarm systems such as smoke detectors, and temperature sensor-based systems have been developed. Our proposed system is aimed to design and develop a fire detection system that detects fire without any heat or temperature sensor. The primary objective of the fire detection system is to detect a fire early and warn authorities when a fire takes place. The Machine Learning Algorithm has been used to detect the accurate image of fire because it has a prior pattern of fire images already fed into it. On occurring the fire, the camera will send this pattern to Raspberry pi which has already predefined patterns of fire written in the form of an algorithm and afterward will compare it with the new existing fire pattern. When both the pattern matches system will do processing based on the image processing technique. Finally, the system generates a warning message which will be sent on the LCD screen for display, and thereafter the buzzer starts working. The key benefit of this system is it will decrease the risk of losses which occurs mainly due to failure in controlling the fire. The experimental results showed that the designed system can efficiently extract and keep trace of fire pixels in the form of patterns and is worthwhile in providing better output results. This system has compact circuitry and functionality like it is easily implanted in public and commercial places for security and surveillance","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131680045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.26782/jmcms.2022.06.00002
Raju Kundu
The flow of dusty visco-elastic fluid between two parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane is considered because of its growing importance in various technical problems in modern applied science. In this paper, we would like to consider the laminar flow of visco-elastic fluid containing uniformly small solid particles between two infinitely extended parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane. The analytical expressions for velocity fields of fluid and dust particles are obtained which are in elegant forms. The effects of elastic elements in the fluid, the mass concentration, and the relaxation time of dust particles on the velocity profiles are studied in detail. The skin friction at the lower plate wall and the total volume flow in between the plates are also obtained.
{"title":"THE FLOW OF DUSTY VISCO-ELASTIC FLUID BETWEEN TWO PARALLEL FLAT PLATES.","authors":"Raju Kundu","doi":"10.26782/jmcms.2022.06.00002","DOIUrl":"https://doi.org/10.26782/jmcms.2022.06.00002","url":null,"abstract":"The flow of dusty visco-elastic fluid between two parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane is considered because of its growing importance in various technical problems in modern applied science. In this paper, we would like to consider the laminar flow of visco-elastic fluid containing uniformly small solid particles between two infinitely extended parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane. The analytical expressions for velocity fields of fluid and dust particles are obtained which are in elegant forms. The effects of elastic elements in the fluid, the mass concentration, and the relaxation time of dust particles on the velocity profiles are studied in detail. The skin friction at the lower plate wall and the total volume flow in between the plates are also obtained.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122887767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.26782/jmcms.2022.06.00001
M. A. Khan
This paper presents the effective utilization of industrial waste steel mill scale in concrete. Tests were performed on concrete specimens incorporating 10%, 20%, 30%, and 40% steel mill scale by weight of sand and a control specimen. Results were assessed in terms of workability, compressive strength, flexural strength, and durability. The compressive and flexural strength of concrete incorporating a 20% steel mill scale was recorded higher as opposed to control and other percent replacement specimens. It was also observed that the durability and resistance against sulphate attack of concrete enhanced as the replacement proportion of mill scale were increased. Furthermore, the higher specific gravity of mill scale waste makes it a suitable material for heavyweight concrete members and radiation shield structures.
{"title":"A STUDY OF CONCRETE INCORPORATING STEEL MILL SCALE WASTE","authors":"M. A. Khan","doi":"10.26782/jmcms.2022.06.00001","DOIUrl":"https://doi.org/10.26782/jmcms.2022.06.00001","url":null,"abstract":"This paper presents the effective utilization of industrial waste steel mill scale in concrete. Tests were performed on concrete specimens incorporating 10%, 20%, 30%, and 40% steel mill scale by weight of sand and a control specimen. Results were assessed in terms of workability, compressive strength, flexural strength, and durability. The compressive and flexural strength of concrete incorporating a 20% steel mill scale was recorded higher as opposed to control and other percent replacement specimens. It was also observed that the durability and resistance against sulphate attack of concrete enhanced as the replacement proportion of mill scale were increased. Furthermore, the higher specific gravity of mill scale waste makes it a suitable material for heavyweight concrete members and radiation shield structures.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115655727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.26782/jmcms.2022.06.00004
P. Bhattacharyya
The concept of the circle has been known to human beings since before the beginning of recorded history. With the advent of the wheel, the study of the circle in detail played an important role in the field of science and technology. According to the author, there are three types of circles, 1) Countup circle, 2) Countdown circle, and 3) Point circle instead of two types of circles as defined by René Descartes in real plane coordinate geometry and Euler in the complex plane. The author has been successful to solve the equations of three types of circles in the real plane by using three fundamental recent (2021 – 2022) inventions, 1) Theory of Dynamics of Numbers, 2) Rectangular Bhattacharyya’s Co-ordinate System, 3) The novel Concept of Quadratic Equation where the author becomes successful to solve the quadratic equation of x2 + 1 = 0 in real number instead of an imaginary number. In the present paper, the author solved successfully the problem where radius if g2 + f2 < c, c the constant term of the general form of the equation of a circle x2 + y2 + 2gx + 2fy + c = 0 by using Bhattacharyya’s Coordinate system without any help from the complex plane where Euler solved it by using a complex plane. According to Bhattacharyya’s Co-ordinate System, the equation of the countdown circle is as follows : where, the coordinates of the moving point P are (x, y) with Centre C (a, b) and radius = – r The concept of a countdown circle is very much interesting and it exists really in nature. We may consider that the rotational motion of the Earth around the Sun is a countdown rotational motion.
{"title":"A NOVEL METHOD TO FIND THE EQUATION OF CIRCLES","authors":"P. Bhattacharyya","doi":"10.26782/jmcms.2022.06.00004","DOIUrl":"https://doi.org/10.26782/jmcms.2022.06.00004","url":null,"abstract":"The concept of the circle has been known to human beings since before the beginning of recorded history. With the advent of the wheel, the study of the circle in detail played an important role in the field of science and technology. According to the author, there are three types of circles, 1) Countup circle, 2) Countdown circle, and 3) Point circle instead of two types of circles as defined by René Descartes in real plane coordinate geometry and Euler in the complex plane. The author has been successful to solve the equations of three types of circles in the real plane by using three fundamental recent (2021 – 2022) inventions, 1) Theory of Dynamics of Numbers, 2) Rectangular Bhattacharyya’s Co-ordinate System, 3) The novel Concept of Quadratic Equation where the author becomes successful to solve the quadratic equation of x2 + 1 = 0 in real number instead of an imaginary number. In the present paper, the author solved successfully the problem where radius if g2 + f2 < c, c the constant term of the general form of the equation of a circle x2 + y2 + 2gx + 2fy + c = 0 by using Bhattacharyya’s Coordinate system without any help from the complex plane where Euler solved it by using a complex plane. According to Bhattacharyya’s Co-ordinate System, the equation of the countdown circle is as follows : where, the coordinates of the moving point P are (x, y) with Centre C (a, b) and radius = – r The concept of a countdown circle is very much interesting and it exists really in nature. We may consider that the rotational motion of the Earth around the Sun is a countdown rotational motion.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116170668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-26DOI: 10.26782/jmcms.2022.05.00003
Akter Hossain
In this article, the effect of temperature-dependent viscosity (TVD) on the unsteady laminar flow and heat transfer (HT) of a viscous incompressible fluid due to a rotating disc (RD) has been investigated numerically by exploiting an in-house numerical code. A set of time-dependent, axisymmetric, and non-linear partial differential equations which govern the fluid flows and heat transfer are reduced to non-linear local non-similarity ordinary differential equations by introducing a newly developed group of transformations for different time regimes. Three different solution methods, such as, (i) perturbation solution method for small t, (ii) asymptotic solution method for large t, and (iii) implicit finite difference method for the entire t regime, have been applied to solve the resulting equations treating t as the time-dependent rotating parameter. The local radial skin friction, tangential skin friction and the heat transfer are computed at the surface of the disc for different numerical parameters, such as, Prandtl number, Pr and the viscosity-variation parameter, e. Besides, the key dimensionless quantities such as velocity and temperature profiles, which are inherently linked with the boundary layer thickness, are presented graphically for different values of e while Pr = 0.72. It is found that the dimensionless radial, tangential and axial velocity profiles decrease as e increases, and consequently, the momentum boundary layer thickness is decreased. On the other hand, the non-dimensional temperature profiles are increased owing to the increasing values of e, and this effect eventually leads to a small increment in the thermal boundary layer thickness.
{"title":"NUMERICAL STUDY OF THE INFLUENCE OF TEMPERATURE-DEPENDENT VISCOSITY ON THE UNSTEADY LAMINAR FLOW AND HEAT TRANSFER OF A VISCOUS INCOMPRESSIBLE FLUID DUE TO A ROTATING DISC","authors":"Akter Hossain","doi":"10.26782/jmcms.2022.05.00003","DOIUrl":"https://doi.org/10.26782/jmcms.2022.05.00003","url":null,"abstract":"In this article, the effect of temperature-dependent viscosity (TVD) on the unsteady laminar flow and heat transfer (HT) of a viscous incompressible fluid due to a rotating disc (RD) has been investigated numerically by exploiting an in-house numerical code. A set of time-dependent, axisymmetric, and non-linear partial differential equations which govern the fluid flows and heat transfer are reduced to non-linear local non-similarity ordinary differential equations by introducing a newly developed group of transformations for different time regimes. Three different solution methods, such as, (i) perturbation solution method for small t, (ii) asymptotic solution method for large t, and (iii) implicit finite difference method for the entire t regime, have been applied to solve the resulting equations treating t as the time-dependent rotating parameter. The local radial skin friction, tangential skin friction and the heat transfer are computed at the surface of the disc for different numerical parameters, such as, Prandtl number, Pr and the viscosity-variation parameter, e. Besides, the key dimensionless quantities such as velocity and temperature profiles, which are inherently linked with the boundary layer thickness, are presented graphically for different values of e while Pr = 0.72. It is found that the dimensionless radial, tangential and axial velocity profiles decrease as e increases, and consequently, the momentum boundary layer thickness is decreased. On the other hand, the non-dimensional temperature profiles are increased owing to the increasing values of e, and this effect eventually leads to a small increment in the thermal boundary layer thickness.","PeriodicalId":254600,"journal":{"name":"JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123732066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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