The study of the calculation of energy consumption load for heating and cooling in building using the Laplace Transform solution

( Kyu Il Han ) 한국어업기술학회 2014 수산해양기술연구 Vol.50 No.3

The Laplace Transform solution is used as a mathematical model to analyse the thermal performance of the building constructed using different wall materials. The solution obtained from Laplace Transform is an analytical solution of an one dimensional, linear, partial differential equation for wall temperature profiles and room air temperatures. The main purpose of the study is showing the detail of obtaining solution process of the Laplace Transform. This study is conducted using weather data from two different locations in Korea: Seoul, Busan for both winter and summer conditions. A comparison is made for the cases of an onoff controller and a proportional controller. The weather data are processed to yield hourly average monthly values. Energy consumption load is well calculated from the solution. The result shows that there is an effect of mass on the thermal performance of heavily constructed house in mild weather conditions such as Busan. Building using proportional control experience a higher comfort level in a comparison of building using on-off control.

A Boundary Integral Equation Formulation for an Unsteady Anisotropic-Diffusion Convection Equation of Exponentially Variable Coefficients and Compressible Flow

Mohammad Ivan Azis 경북대학교 자연과학대학 수학과 2022 Kyungpook mathematical journal Vol.62 No.3

The anisotropic-diffusion convection equation with exponentially variable co efficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coeffi cients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace transformed equation is consequently written as a boundary integral equation which in volves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

A TYPE OF FRACTIONAL KINETIC EQUATIONS ASSOCIATED WITH THE (p,q)-EXTENDED τ-HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

Owais Khan,Nabiullah Khan,Junesang Choi,Kottakkaran Sooppy Nisar 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the $(p,q)$-extended $\tau$-hypergeometric function and the $(p,q)$-extended $\tau$-confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations areLaplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, $P_\chi$-transform, and an alternative method.

The study of the calculation of energy consumption load for heating and cooling in building using the Laplace Transform solution

한규일 한국수산해양기술학회 2014 수산해양기술연구 Vol.50 No.3

The Laplace Transform solution is used as a mathematical model to analyse the thermal performance of the building constructed using different wall materials. The solution obtained from Laplace Transform is an analytical solution of an one dimensional, linear, partial differential equation for wall temperature profiles and room air temperatures. The main purpose of the study is showing the detail of obtaining solution process of the Laplace Transform. This study is conducted using weather data from two different locations in Korea: Seoul, Busan for both winter and summer conditions. A Comparison is made for the cases of an on-off controller and a proportional controller. The weather data are processed to yield hourly average monthly values. Energy consumption load is well calculated from the solution. The result shows that there is an effect of mass on the thermal performance of heavily constructed house in mild weather conditions such as Busan. Building using proportional control experience a higher comfort level in a comparison of building using on-off control.

The study of the calculation of energy consumption load for heating and cooling in building using the Laplace Transform solution

Han, Kyu-Il The Korean Society of Fisheries and Ocean Technolo 2014 수산해양기술연구 Vol.50 No.3

The Laplace Transform solution is used as a mathematical model to analyse the thermal performance of the building constructed using different wall materials. The solution obtained from Laplace Transform is an analytical solution of an one dimensional, linear, partial differential equation for wall temperature profiles and room air temperatures. The main purpose of the study is showing the detail of obtaining solution process of the Laplace Transform. This study is conducted using weather data from two different locations in Korea: Seoul, Busan for both winter and summer conditions. A comparison is made for the cases of an on-off controller and a proportional controller. The weather data are processed to yield hourly average monthly values. Energy consumption load is well calculated from the solution. The result shows that there is an effect of mass on the thermal performance of heavily constructed house in mild weather conditions such as Busan. Building using proportional control experience a higher comfort level in a comparison of building using on-off control.

SOME INTEGRAL TRANSFORMS INVOLVING EXTENDED GENERALIZED GAUSS HYPERGEOMETRIC FUNCTIONS

Choi, Junesang,Kachhia, Krunal B.,Prajapati, Jyotindra C.,Purohit, Sunil Dutt Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4

Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

THE DOUBLE FUZZY ELZAKI TRANSFORM FOR SOLVING FUZZY PARTIAL DIFFERENTIAL EQUATIONS

Kishor A. Kshirsagar,V. R. Nikam,S. B. Gaikwad,S. A. Tarate 충청수학회 2022 충청수학회지 Vol.35 No.2

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the $n^{th}$ order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

(p; q)-LAPLACE TRANSFORM

김영록,유천성 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5

In this paper we dene a (p; q)-Laplace transform. By using this denition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the dierential equation using the (p; q)-Laplace transform.

(p, q)-LAPLACE TRANSFORM

KIM, YOUNG ROK,RYOO, CHEON SEOUNG The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.5

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

유리차수 미분을 이용한 위치제어기 구현

강정욱(Jung-Yoog Kang),전용호(Yong-Ho Jeon) 한국전자통신학회 2019 한국전자통신학회 논문지 Vol.14 No.1

본 연구는 유리차수 미분의 수학적인 방법을 시스템의 응답을 제어하는 제어기에 적용하고자 한다. 일반적인 PID제어기의 라플라스 변환은 의 정수지수를 갖게 된다. 유리차수의 미분은 라플라스 변환에서 에 대한 유리수 지수를 갖게 된다. 따라서 이를 제어기로 구성하기 위해서는 유리수 지수에 대한 설계가 적절하지 않아 이산시간으로 변환하여 설계하는 방법을 제안한다. 이를 표준 2차 시스템에 적용하여 성능을 살펴보고, 산업현장에서 많이 사용되는 솔레노이드밸브에 적용한다. 외란 상태의 추정이 가능하도록 루엔버거 관측기를 설계하고 관측된 상태에 대하여 유리차수 제어기를 적용하여 균일하며 정밀한 제어성능을 얻을 수 있었다. 정상상태의 위치오차가 0.1 [%]이내이고, 기동시간이 약 0.3 [s]이내의 정밀하며 균일한 위치제어성능 가짐을 확인할 수 있었다. This study aims to apply the mathematical method of fractional order derivatives to the controller that controls the system response. In general, the Laplace transform of the PID controller has an exponent of the integer order of s. The derivative of the fractional order has a fractional exponent of s when it is transformed by Laplace transform. Therefore, this controller proposes a design method with the result of discrete time conversion. Because controllers with fractional exponents of s are not easy to design. This controller is applied to a standard secondary system and its performance is examined. Then, it applies to solenoid valve which is widely used in industrial field. A Luenberger‘s observer was designed to estimate the disturbance state and the observed state was applied to the fractional order controller. As a result, uniform and precise control performance was obtained. It was confirmed that the position error of the steady state is within 0.1 [%] and the rising time is within about 0.03 [s].