scholarly journals Evento contextualizado: uma proposta para o ensino e a aprendizagem de equações diferenciais ordinárias na engenharia civil

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
RIEUSE LOPES PINTO ◽  
GABRIEL LOUREIRO DE LIMA
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Teaching And Learning ◽  
Civil Engineering ◽  
Masonry Wall ◽  
Fourier Law ◽  
Laboratory Practice ◽  
Doctoral Research ◽  
Engineering Mathematics ◽  
Para Determinar

ResumoEste artigo é um recorte de uma pesquisa de doutorado que está sendo desenvolvida sobre o ensino e a aprendizagem de Equações Diferenciais Ordinárias (EDO). Apresentamos a questão que norteia essa pesquisa, os objetivos, o referencial teórico-metodológico adotado (A Matemática no Contexto das Ciências), e parte de uma organização didática que compõe o evento contextualizado. Esse evento foi elaborado a partir de um problema integrando disciplinas matemáticas com não matemáticas da Engenharia Civil, e engloba uma série de conceitos matemáticos e físicos relacionados aos conceitos da Termodinâmica e à transferência de calor. A organização didática, construída a partir da análise do comportamento térmico de três configurações de paredes em alvenaria durante uma prática laboratorial, tem como finalidade possibilitar ao estudante a utilização da Lei de Fourier, que é uma EDO, para determinar o fluxo térmico, ou seja, a taxa de transferência de calor por unidade de área. Palavras-chave: Sequência Didática; Equações Diferenciais; Engenharia Civil; Matemática no Contexto das Ciências.AbstractThis article is an excerpt from a doctoral research that is being developed on the teaching and learning of Ordinary Differential Equations (EDO). We show the issues that guides this research, the objectives, the theoretical-methodological framework adopted (Mathematics in the Context of Science), and part of a didactic organization that makes up the contextualized event. This event was elaborated from a problem integrating mathematical disciplines with non-mathematical Civil Engineering and encompasses a series of mathematical and physical concepts related to the concepts of Thermodynamics and heat transfer. The didactic organization, built from the analysis of the thermal behavior of three masonry wall configurations during a laboratory practice, aims to enable the student to use the Fourier Law, which is an EDO, to determine the thermal flow, in other words, the rate of heat transfer per unit area.Keywords: Didactic Sequence; Differential Equations; Civil Engineering; Mathematics in the Context of Science.   

Use of Computer Algebra Systems in Teaching and Learning of Ordinary Differential Equations among Engineering Technology Students

2012 ◽  
pp. 207-220
Author(s):  
Siti Mistima Maat ◽  
Effandi Zakaria
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Undergraduate Students ◽  
Teaching And Learning ◽  
Traditional Approach ◽  
Engineering Technology ◽  
Mathematics Problems ◽  
Technology Students ◽  
Engineering Mathematics ◽  
And Robotics

This chapter describes the computer algebraic system, Maple, used to enhance engineering technology students’ understanding in learning ordinary differential equations (ODE). Ten undergraduate students studying industrial automation and robotics technology were selected to be the participants. They were required to enroll in engineering mathematics as the prerequisite for control system and robotics subject. Engineering mathematics is commonly taught using the traditional approach but the lecturer as a researcher introduced Maple as an alternative teaching approach to engage students in the learning of differential equations. The students were interviewed after using Maple for solving mathematics problems. It was found that these students managed to visualize the solutions of the given mathematics problems. The learning of differential equations has become meaningful in such a way that they could see the relationship between mathematics and its application in the real world.

scholarly journals Uma proposta de ensino de equação diferencial no curso de Engenharia Civil à luz da teoria matemática no contexto das ciências

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
ALESSANDRO ROSA SILVA ◽  
GABRIEL LOUREIRO DE LIMA
Keyword(s):  
Higher Education ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Teaching And Learning ◽  
Civil Engineering ◽  
Teaching Sequence ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Doctoral Work

ResumoApresentamos por meio deste artigo o trabalho de doutorado que estamos desenvolvendo com o objetivo de discutir o ensino e a aprendizagem de Equações Diferenciais Ordinárias lineares de 1ª e 2ª ordens em um curso de Engenharia Civil, sob à luz da Matemática no Contexto das Ciências. A pesquisa encontra-se atualmente na fase da análise de livros textos utilizados como referências principais nas disciplinas não matemáticas do curso citado, guiada pela etapa central da metodologia Dipcing, inserida em uma das fases da MCC, a curricular. Identificaremos, a partir desta análise, situações-problemas do contexto da Engenharia Civil que mobilizam EDO lineares de 1ª e 2ª ordens. Tais situações nos servirão de base para a construção de uma sequência de ensino contextualizando as EDO na Engenharia Civil. Os problemas propostos serão trabalhados em sala de aula e posteriormente analisaremos os resultados, em termos de aprendizagem, obtidos por meio da sequência de ensino desenvolvida. Palavras-Chave: Ensino Superior; Engenharia; Equações Diferenciais Ordinárias; Matemática no Contexto das Ciências.AbstractWe present, by means of this article, the doctoral work we are developing with the objective of discussing the teaching and learning of 1st and 2nd order linear Ordinary Differential Equations in a Civil Engineering course under the light of Mathematics in the Context of Sciences. The research is currently in the phase of the analysis of textbooks used as main references in the non-mathematical disciplines of the mentioned course, guided by the central stage of the methodology Dipcing, inserted in one of the phases of the MCC, the curricular. We will identify, from this analysis, situations-problems of the Civil Engineering context that mobilize linear ORDs of 1st and 2nd orders. Such situations will serve as a basis for the construction of a teaching sequence contextualizing the ODE in Civil Engineering. The problems proposed will be worked in the classroom and later we will analyze the results, in terms of learning, obtained through the developed teaching sequence.Keywords: Higher Education; Engineering; Ordinary Differential Equations; Mathematics in the Context of Science. 

scholarly journals Performance-based comparison of Yamada–Ota and Hamilton–Crosser hybrid nanofluid flow models with magnetic dipole impact past a stretched surface

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Hina Gul ◽  
Muhammad Ramzan ◽  
Kottakkaran Sooppy Nisar ◽  
Roshan Noor Mohamed ◽  
Hassan Ali S. Ghazwani
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Magnetic Dipole ◽  
Hydrodynamic Interaction ◽  
Flow Model ◽  
Fluid Model ◽  
Vital Role ◽  
Hybrid Nanofluid ◽  
Fourier Law ◽  
Excessive Heat

AbstractThe nanofluid flows play a vital role in many engineering processes owing to their notable industrial usage and excessive heat transfer abilities. Lately, an advanced form of nanofluids namely “hybrid nanofluids” has swapped the usual nanofluid flows to further augment the heat transfer capabilities. The objective of this envisaged model is to compare the performance of two renowned hybrid nanofluid models namely Hamilton–Crosser and Yamada–Ota. The hybrid nanoliquid (TiO2-SiC/DO) flow model is comprised of Titanium oxide (TiO2) and Silicon carbide (SiC) nanoparticles submerged into Diathermic oil (DO). The subject flow is considered over a stretched surface and is influenced by the magnetic dipole. The uniqueness of the fluid model is augmented by considering the modified Fourier law instead of the traditional Fourier law and slip conditions at the boundary. By applying the suitable similarity transformations, the system of ordinary differential equations obtained from the leading partial differential equations is handled by the MATLAB solver bvp4c package to determine the numerical solution. It is divulged that the Yamada–Ota model performs considerably better than the Hamilton–Crosser flow model as far as heat transfer capabilities are concerned. Further, the velocity reduces on increasing hydrodynamic interaction and slip parameters. It is also noted that both temperature profiles increase for higher hydrodynamic interaction and viscous dissipation parameters. The envisioned model is authenticated when compared with an already published result in a limiting case.

scholarly journals O estudo de um problema da engenharia civil à luz da teoria a matemática no contexto das ciências

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
ALESSANDRO ROSA SILVA ◽  
GABRIEL LOUREIRO DE LIMA
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Teaching And Learning ◽  
Civil Engineering ◽  
A Priori ◽  
Linear Ordinary Differential Equations ◽  
Classic Problem ◽  
Teaching Situation ◽  
Doctoral Work ◽  
Mathematics In Context

ResumoApresentamos por meio deste artigo um recorte do trabalho de doutorado que estamos desenvolvendo com o objetivo de discutir o ensino e a aprendizagem de Equações Diferenciais Ordinárias lineares (EDO) em um curso de Engenharia Civil. Como embasamento teórico, adotamos pressupostos da Matemática no Contexto das Ciências (MCC) e do modelo didático associado a tal referencial, o Modelo Didático da Matemática em Contexto (MoDiMaCo). Por meio de um livro texto utilizado como referência principal na disciplina não matemáticas do curso citado, guiada pela etapa central da metodologia Dipcing, inserida em uma das fases da MCC, a curricular, foi identificado, a partir desta análise, uma situação com potencial para gerar um evento contextualizado a partir de um problema clássico dessa habilitação de Engenharia. A proposta deste artigo é apresentar tal evento, bem como trazer uma análise a priori da situação de ensino, com o intuito de introduzir o conceito de equações diferenciais separáveis. Tais situações nos servirão de base para a construção de uma sequência de ensino contextualizando as EDO a ser desenvolvida em aulas para alunos dependência no curso de Engenharia Civil. Palavras-chave: Educação Matemática; Engenharia; Equações Diferenciais Ordinárias; Matemática no Contexto da Ciência..AbstractThis article presents a bibliographic research that aims to present an overview of the Through this article we present an excerpt of the doctoral work that we are developing with the objective of discussing the teaching and learning of linear Ordinary Differential Equations (EDO) in a Civil Engineering course. As a theoretical basis, we adopted assumptions of Mathematics in the Context of Sciences (MCC) and the didactic model associated with such reference, the Didactic Model of Mathematics in Context (MoDiMaCo). Through a textbook used as the main reference in the non-mathematical discipline of the mentioned course, guided by the central stage of the Dipcing methodology, inserted in one of the phases of the MCC, the curriculum, a situation with potential for generate a contextualized event from a classic problem of this Engineering qualification. The purpose of this article is to present such an event, as well as to bring an a priori analysis of the teaching situation, in order to introduce the concept of separable differential equations. Such situations will serve as a basis for the construction of a teaching sequence contextualizing the ODE to be developed in classes for dependency students in the Civil Engineering course.Keywords: Mathematics Education; Engineering; Ordinary Differential Equations; Mathematics in the Context of Science. 

Modifikasi Sistem Asistensi dan Responsi Kelas Kecil pada Praktikum Parasitologi Blok Digestif dan Hematoimunologi Fakultas Kedokteran Universitas Riau

2017 ◽  
Vol 8 (1) ◽  
pp. 46
Author(s):  
Suri Dwi Lesmana ◽  
Esy Maryanti
Keyword(s):  
Large Class ◽  
Teaching And Learning ◽  
Learning Activities ◽  
Small Class ◽  
Laboratory Practice ◽  
Large Classes ◽  
Average Value ◽  
Competency Based

Faculty of Medicine University of Riau has been implementing Competency Based Curriculum (KBK) with theProblem Based Learning (PBL) since 2007 with the implementation of teaching and learning activities of the systemconsists of a tutorial activities, skillab, expert lectures, independent and practical. However, there are still manyproblems in the implementation of the KBK on preclinic degree. One part of the block that is identified to be one ofthe causes of low graduation exam block is less efective coaching laboratory practice. Parasitology is one part of thetask is to provide laboratory practice in several blocks on the stage of preclinic especially digestive and hematoimunologyblock. This study aimed to compare the results of the evaluation of parasitology laboratory practice in hematoimunologyand digestive assistance and posttest in large classes with small class. Assistance and posttest in large class performedon the digestive block implementation and hematoimunologi in 2011 while assisting and posttest of small classes ona block implementation in 2012. Average value of small class digestive laboratory practice was not significantlylower than the large class but the proportion of the value of quality B and C more many in small classes. The meanvalue of the block hematoimunologi laboratory practice significantly higher on small class assistance and posttest aswell as the proportion of the value of quality A, B and C was higher in small classes than large classes.

scholarly journals Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 138
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Base Fluid ◽  
Research Work ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Analytical Analysis ◽  
Transfer Ratio ◽  
The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

Entropy generation and heat transfer analysis for ferrofluid flow between two rotating disks with variable conductivity

2021 ◽  
pp. 095440622199118
Author(s):  
Anupam Bhandari
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Differential Equations ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Entropy Generation Rate ◽  
Geometrical Parameters ◽  
Rotating Disks ◽  
Coupled Differential Equations ◽  
Lower Disk

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

scholarly journals Investigation of binary chemical reaction in magnetohydrodynamic nanofluid flow with double stratification

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110162
Author(s):  
Aisha Anjum ◽  
Sadaf Masood ◽  
Muhammad Farooq ◽  
Naila Rafiq ◽  
Muhammad Yousaf Malik
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Hartmann Number ◽  
Concentration Field ◽  
Double Stratification ◽  
Nanofluid Flow ◽  
Homotopy Analysis ◽  
Flow Heat ◽  
Chemically Reactive Species ◽  
Physical Features

This article addresses MHD nanofluid flow induced by stretched surface. Heat transport features are elaborated by implementing double diffusive stratification. Chemically reactive species is implemented in order to explore the properties of nanofluid through Brownian motion and thermophoresis. Activation energy concept is utilized for nano liquid. Further zero mass flux is assumed at the sheet’s surface for better and high accuracy of the out-turn. Trasnformations are used to reconstruct the partial differential equations into ordinary differential equations. Homotopy analysis method is utilized to obtain the solution. Physical features like flow, heat and mass are elaborated through graphs. Thermal stratified parameter reduces the temperature as well as concentration profile. Also decay in concentration field is noticed for larger reaction rate parameter. Both temperature and concentration grows for Thermophoresis parameter. To check the heat transfer rate, graphical exposition of Nusselt number are also discussed and interpret. It is noticed that amount of heat transfer decreases with the increment in Hartmann number. Numerical results shows that drag force increased for enlarged Hartmann number.

Effects of Suction and Freestream Velocity on a Hydromagnetic Stagnation-Point Flow and Heat Transport in a Newtonian Fluid Toward a Stretching Sheet

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
P. G. Siddheshwar ◽  
N. Meenakshi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Transport ◽  
Newtonian Fluid ◽  
Stretching Sheet ◽  
Forced Flow ◽  
Stream Velocity ◽  
Freestream Velocity ◽  
Exponential Order ◽  
Order Surface

Forced flow of an electrically conducting Newtonian fluid due to an exponentially stretching sheet is studied numerically. Free stream velocity is present and so is suction at the sheet. The governing coupled, nonlinear, partial differential equations of flow and heat transfer are converted into coupled, nonlinear, ordinary differential equations by similarity transformation and are solved numerically using shooting method, and curve fitting on the data is done by differential transform method together with Padé approximation. Prescribed exponential order surface temperature (PEST) and prescribed exponential order surface heat flux are considered for investigation of heat transfer related quantities. The influence of Chandrasekhar number, suction/injection parameter, and freestream parameter on heat transport is presented and discussed. Coefficient of friction and heat transport is also evaluated in the study. The results are of interest in extrusions and such other processes.

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