The effect of heat flux distribution and internal heat generation on the thermal damage in multilayer tissue in thermotherapy

Natural convection in rectangular enclosures is found in many real-world engineering applications. Included in these applications are the energy efficient design of buildings, operation and safety of nuclear reactors, solar collector design, passive energy storage, heat transfer across multi-pane windows, thermo-electric refrigeration and heating devices, and the design-for-mitigation of optical distortion in large-scale laser systems. A common industrial application of natural convection is free air cooling without the aid of fans and can happen on small scales such as computer chips to large scale process equipment. The enclosure phenomena can loosely be organized into two large classes: (1) horizontal enclosures heated from below and (2) vertical enclosures heated from the side. In addition to temperature gradient convection strength within the enclosure can vary due to the existence of heat sources with different strength. Numerical simulations are conducted for free convective flow of air with or without internal heat generation in two-dimensional rectangular enclosures of different aspect ratios. The objective of this numerical study is to investigate the effects of external temperature gradient, internal heat generation and aspect ratio (AR) of enclosure (ratio of the length of the isothermal walls to their separation distance), in free convective laminar flow of a fluid. Two-dimensional rectangular enclosures of different aspect ratio (1, 2, 4, 6, 8, and 10) with two adiabatic side walls and isothermal bottom (hot) and top (cold) walls are considered for the first configuration. Whereas for the second configuration, two adiabatic top and bottom walls, isothermal left side (cold) and right side (hot) walls are considered. Two principal parameters considered for the flow of fluid are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the isothermal walls, and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. The effect of external temperature gradient and aspect ratio on natural convection has been observed by varying the value of external Rayleigh number (RaE) equal to 2×104, 2×105, and 2×106 and keeping the internal Rayleigh number constant (RaI = 2×105). Similarly, the effect of internal heat generation and aspect ratio on natural convection has been observed by varying the value of internal Rayleigh number (RaI) equal to 2×104, 2×105, and 2×106 and keeping the external Rayleigh number constant (RaE = 2×105). Significant changes in flow patterns and isotherms have been observed for all cases. Also the variation of average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot and cold walls, and the convection strength have been calculated for all cases. It is found that the aspect ratio has a significant effect in fluid flow and heat transfer in the enclosures. The average heat flux ratio and the strength of convection increase with aspect ratio as the enclosure shape changes square (AR = 1) to shallow (AR > 1).

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Estimating internal heat flux distribution of TWT collector based on GA-BP neural network model

2018 IEEE International Vacuum Electronics Conference (IVEC) ◽

10.1109/ivec.2018.8391626 ◽

2018 ◽

Author(s):

Xingqun Zhao ◽

Xiaoting Ying ◽

Xiaohan Sun

Keyword(s):

Neural Network ◽

Heat Flux ◽

Network Model ◽

Neural Network Model ◽

Bp Neural Network ◽

Flux Distribution ◽

Internal Heat ◽

Heat Flux Distribution ◽

Bp Neural Network Model

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Numerical Solution for Variable Viscosity and Internal Heat Generation Effects on Boundary Layer Flow Over an Exponentially Stretching Porous Sheet with Constant Heat Flux and Thermal Radiation

Journal of Mechanics ◽

10.1017/jmech.2014.29 ◽

2014 ◽

Vol 30 (4) ◽

pp. 395-402 ◽

Cited By ~ 3

Author(s):

A. M. Megahed

Keyword(s):

Heat Flux ◽

Heat Generation ◽

Variable Viscosity ◽

Internal Heat ◽

Constant Heat Flux ◽

Internal Heat Generation ◽

Constant Heat ◽

Suction Parameter ◽

Viscosity Parameter ◽

Exponentially Stretching

AbstractA numerical study has been carried out to analyze the constant heat flux, internal heat generation, variable viscosity and thermal radiation effects on the flow and heat transfer of a Newtonian fluid over an exponentially stretching porous sheet. Using a similarity transformation, the governing partial differential equations are transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by using an efficient Chebyshev spectral method. The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl number on velocity and temperature are discussed by using graphical approach. Moreover, numerical results indicate that in the presence of constant heat flux, the skin-friction coefficient as well as Nusselt number is strongly affected by the viscosity parameter, suction parameter, radiation parameter and the internal heat generation parameter.

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On the Stefan Problem With Internal Heat Generation and Prescribed Heat Flux Conditions at the Boundary

ASME 2019 Heat Transfer Summer Conference ◽

10.1115/ht2019-3703 ◽

2019 ◽

Author(s):

Lyudmyla Barannyk ◽

Sidney D. V. Williams ◽

Olufolahan Irene Ogidan ◽

John C. Crepeau ◽

Alexey Sakhnov

Keyword(s):

Heat Flux ◽

Steady State ◽

Phase Change ◽

Heat Generation ◽

Separation Of Variables ◽

Outer Boundary ◽

Internal Heat ◽

Internal Heat Generation ◽

The Difference ◽

Solid Liquid Interface

Abstract We study the evolution of the solid-liquid interface during melting and solidification of a material with constant internal heat generation and prescribed heat flux at the boundary for a plane wall and a cylinder. The equations are solved by splitting them into transient and steady-state components and then using separation of variables. This results in an ordinary differential equation for the interface that involves infinite series. The initial value problem is solved numerically, and solutions are compared to the previously published quasi-static solutions. We show that when the internal heat generation and the heat flux at the boundary are close in value to each other, the motion of the phase change front takes longer to reach steady-state than when the values are farther apart. As the difference between the internal heat generation and the heat flux increases, the transient solutions become more dominant and the numerical solution of the phase change front does not reach steady-state before the outer boundary or centerline is reached. The difference between the internal heat generation and the heat flux at the boundary can be used to control the motion and speed of the interface. The problem has applications for a nuclear fuel rod during meltdown.

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