The method of images for solving the equations of heat conduction in layered media

Gaponenko, N. P.; Zaks, D. I.

doi:10.1007/bf00827829

Cited by 2 publications

(2 citation statements)

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“…The total solution of the diffusion equation (1) with the boundary conditions at the interfaces can be expressed as a superposition of two functions in Laplace domain [16]:…”

Section: System Modelmentioning

confidence: 99%

Modelling of multilayer biological medium under molecular communication paradigm

Al-Zu'bi

2017

2017 IEEE Life Sciences Conference (LSC)

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Abstract-Molecular communication is an emerging paradigm that enables both the biological and synthetic nanomachines to communicate with each other within an aqueous biological environment such as the communication between living cells. Prediction of the number of drug molecules near a target site, e.g., tumor cells, is very important for determining the required drug dosages to increase positive therapeutic outcomes. In this paper, we derive an analytical expression for the received molecular signal in a multilayer biological environment. We also present development of particle-based simulator and the analytical results for threelayer biological medium compared well with the simulation results. The effect of the diffusion coefficient and the separation distance between the transmitter and the receiver (e.g., targeted cells) are examined.

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“…The total solution of the diffusion equation (1) with the boundary conditions at the interfaces can be expressed as a superposition of two functions in Laplace domain [16]:…”

Section: System Modelmentioning

confidence: 99%

Modelling of multilayer biological medium under molecular communication paradigm

Al-Zu'bi

2017

2017 IEEE Life Sciences Conference (LSC)

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“…Using the method of images in the plane, Gaponenko and Zaks [22] obtained the temperature field generated by an instanta neous point source in the layer. The "image method" is a method of solving the bounded heat conductor prob lem.…”

Section: Journal Of Manufacturing Science and Engineeringmentioning

confidence: 99%

A Predictive Model for Temperature Rise of Spindle–Bearing Integrated System

Deng

Zhang

2015

Journal of Manufacturing Science and Engineering

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A P re d ic tiv e M o d e l fo r T e m p e ra tu re R is e of S p in d le -B e a rin g In te g ra te d S ystemIn order to obtain the thermal characteristics o f the spindle-bearing integrated system of the computer numerical control (CNC) machine tools effectively, a mathematical model is established by employing the heat source method (HSM). The thermal characteristics of spindle-bearing system are identified by using the derived mathematical formula, and the presented model is validated by the finite element method (FEM) under four types of conditions corresponding to different heat intensities, heat transfer coefficients, geometri cal model sizes, and heat source positions. Compared with the FEM, the presented model has better computational efficiency. The temperature fields of the two spindle systems o f a CNC machine tool are predicted by using the present model. The predicted temperature field is compared with the measured data and results show that the maximum relative errors for the two systems are 0.41% and 8.38%, respectively. The proposed model has a potential to be applied in calculating temperature field and thermal deformation or other related engineering area.

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The method of images for solving the equations of heat conduction in layered media

Cited by 2 publications

References 1 publication

Modelling of multilayer biological medium under molecular communication paradigm

Modelling of multilayer biological medium under molecular communication paradigm

A Predictive Model for Temperature Rise of Spindle–Bearing Integrated System

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