APPLICATION OF HOMOTOPY PERTURBATION METHOD TO THE MATHEMATICAL MODELLING OF TEMPERATURE RISE DURING MICROWAVE HYPERTHERMIA

2021 ◽  
Vol 5 (2) ◽  
pp. 273-282
Author(s):  
Erinle-Ibrahim L. Morenikeji ◽  
Ayeni O. Babatunde ◽  
Idowu K Oluwatobi
Keyword(s):  
Thermal Conductivity ◽  
Cancer Therapy ◽  
Perturbation Method ◽  
Microwave Heating ◽  
Homotopy Perturbation Method ◽  
Blood Perfusion ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Maximum Rise ◽  
Microwave Hyperthermia

We study a one dimensional non-linear model of multi-layered human skin exposed to microwave heating during cancer therapy. The model is analyzed using homotopy perturbation method and the fact that there are variations in specific heat, thermal conductivity and blood perfusion from one individual to another were considered. The purpose of this study was to investigate the effect of variable blood perfusion, microwave heating and thermal conductivity on the temperature field during microwave hyperthermia. By varying the parameters, we were able to determine maximum rise of temperature as an individual undergoes cancer therapy. The results were presented in graphs and it was discovered that the temperature of the tumor increases with increase in the microwave heating index while the blood perfusion remain constant.

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

scholarly journals Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 111-115 ◽  
Author(s):  
Domiri Ganji ◽  
Ziabkhsh Ganji ◽  
Domiri Ganji
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Variable Thermal Conductivity ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

In this paper, homotopy perturbation method has been used to evaluate the temperature distribution of annular fin with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. This method is useful and practical for solving the nonlinear heat transfer equation, which is associated with variable thermal conductivity condition. The homotopy perturbation method provides an approximate analytical solution in the form of an infinite power series. The annular fin heat transfer rate with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity

Heat Transfer From Solids With Variable Thermal Conductivity and Uniform Internal Heat Generation Using Homotopy Perturbation Method

2008 ◽  
Author(s):  
Rahim Gul ◽  
Zafar H. Khan ◽  
Waqar A. Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Perturbation Method ◽  
Heat Generation ◽  
Homotopy Perturbation Method ◽  
Outer Boundary ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Dimensionless Temperature ◽  
Homotopy Perturbation

Homotopy perturbation method (HPM) is employed to investigate the effects of temperature dependent thermal conductivity and internal heat generation on the dimensionless temperature distribution and heat transfer from solids of arbitrary shapes (rectangular, cylindrical and spherical). Dirichlet and Robin boundary conditions are applied at the outer boundary of the solids.

Homotopy Perturbation Method for the Analysis of Heat Transfer in an Annular Fin With Temperature-Dependent Thermal Conductivity

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Rishi Roy ◽  
Sujit Ghosal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Base Temperature ◽  
Temperature Dependent ◽  
Homotopy Perturbation ◽  
Annular Fin ◽  
Temperature Dependent Thermal Conductivity

A recent mathematical technique of homotopy perturbation method (HPM) for solving nonlinear differential equations has been applied in this paper for the analysis of steady-state heat transfer in an annular fin with temperature-dependent thermal conductivity and with the variation of thermogeometric fin parameters. Excellent benchmark agreement indicates that this method is a very simple but powerful technique and practical for solving nonlinear heat transfer equations and does not require large memory space that arises out of discretization of equations in numerical computations, particularly for multidimensional problems. Three conditions of heat transfer, namely, convection, radiation, and combined convection and radiation, are considered. Dimensionless parameters pertinent to design optimization are identified and their effects on fin heat transfer and efficiency are studied. Results indicate that the heat dissipation under combined mode from the fin surface is a convection-dominant phenomenon. However, it is also found that, at relatively high base temperature, radiation heat transfer becomes comparable to pure convection. It is worth noting that, for pure radiation condition, the dimensionless parameter of aspect ratio (AR) of a fin is a more desirable controlling parameter compared to other parameters in augmenting heat transfer rate without much compromise on fin efficiency.

NUMERICAL SOLUTIONS OF WAVE EQUATIONS SUBJECT TO AN INTEGRAL CONSERVATION CONDITION BY HE'S HOMOTOPY PERTURBATION METHOD

2011 ◽  
Vol 25 (32) ◽  
pp. 4457-4469 ◽  
Author(s):  
AHMET YILDIRIM ◽  
YAǦMUR GÜLKANAT
Keyword(s):  
Perturbation Method ◽  
Wave Equations ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Conservation Condition ◽  
Direct Problems

The aim of this paper is to solve one-dimensional wave equations that combine classical and integral boundary conditions using the homotopy perturbation method (HPM). The studied equations are changed into direct problems easy to be handled by the homotopy perturbation method. Several examples are given and the results are compared with exact solutions, revealing effectiveness and simplicity of the method.

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