Relationship Between the Nonlocal Effect and Lagging Behavior in Bioheat Transfer

2021 ◽  
Author(s):  
Xiaoya Li ◽  
Yan Li ◽  
Pengfei Luo ◽  
Xiao Geng Tian
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Order Effect ◽  
Heat Transfer Process ◽  
Bioheat Transfer ◽  
Transfer Model ◽  
Phase Lag ◽  
Medical Systems ◽  
Conduction Model ◽  
Transfer Equations

Abstract Lots of generalized heat conduction models have been developed in recent decades, such as local thermal non-equilibrium model, phase lagging model and nonlocal heat conduction model. But no attempt was made to prove which model is better (or worse) than others, or whether there is a certain relationship between these different models. With this inspiration, we establish the nonlocal bioheat transfer equations with lagging time, and the two and three-temperature bioheat transfer equations with considering all the carries' heat conduction effect are also constructed. Comparing the two (or three)-temperature equation model with the nonlocal bioheat transfer models with lagging time, one may obtain: the lagging time tt of temperature gradient and the nonlocal characteristic length ?q in the space derivative items of heat flux have the same effect on heat transfer; when the heat transport occur among N energy carriers with considering the conduction effects of all carries, the heat transfer process are depend on the high-order effect of tqN-1, ttN-1 and ?t(2N-1) in nonlocal dual phase lag bioheat transfer model. This phenomenon is very important for biological and medical systems where numerous carriers may exist on the cellular level.

scholarly journals Analysis of non-Fourier thermal behavior for multi-layer skin model

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 61-67 ◽  
Author(s):  
Kuo-Chi Liu ◽  
Po-Jen Cheng ◽  
Yan-Nan Wang
Keyword(s):  
Heat Transfer ◽  
Wave Model ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Order Partial Differential Equation ◽  
Transfer Equations ◽  
Lag Model ◽  
Fourier Equation ◽  
Good Agreement

This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes? model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.

Heat Transfer From a Moving and Evaporating Meniscus on a Heated Surface

2003 ◽  
Author(s):  
Satish G. Kandlikar ◽  
Wai Keat Kuan
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heated Surface ◽  
Water Flow Rate ◽  
Transient Heat Conduction ◽  
Heat Transfer Process ◽  
Conduction Model ◽  
Experimental Heat ◽  
Experimental Heat Transfer

A stable meniscus is formed between a needle dispensing water over a heated circular face of a rotating copper block. The needle is offset from the axis of rotation and thus forms a moving meniscus. The water flow rate, heater surface temperature and the speed of rotation are controlled to provide a stable meniscus with complete evaporation of water without any meniscus break-up. The experimental heat transfer rate is compared with the transient heat conduction model developed here. The results indicate that the transient heat conduction plays a major role in the heat transfer process from a moving meniscus. The study provides an important insight on the role of transient conduction around a nucleating bubble in pool boiling.

scholarly journals A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 876 ◽  
Author(s):  
Stanisław Kukla ◽  
Urszula Siedlecka
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Single Phase ◽  
Heat Conduction Problem ◽  
Expansion Method ◽  
Maximum Temperature ◽  
Phase Lag ◽  
Conduction Model ◽  
Laplace Transform Technique ◽  
Finite Medium

In this paper, an investigation of the maximum temperature propagation in a finite medium is presented. The heat conduction in the medium was modelled by using a single-phase-lag equation with fractional Caputo derivatives. The formulation and solution of the problem concern the heat conduction in a slab, a hollow cylinder, and a hollow sphere, which are subjected to a heat source represented by the Robotnov function and a harmonically varying ambient temperature. The problem with time-dependent Robin and homogenous Neumann boundary conditions has been solved by using an eigenfunction expansion method and the Laplace transform technique. The solution of the heat conduction problem was used for determination of the maximum temperature trajectories. The trajectories and propagation speeds of the temperature maxima in the medium depend on the order of fractional derivatives occurring in the heat conduction model. These dependencies for the heat conduction in the hollow cylinder have been numerically investigated.

Convective Heat Transfer between Covered Kiln Wall and Material Bed

2013 ◽  
Vol 805-806 ◽  
pp. 492-495 ◽  
Author(s):  
Xiao Yan Yang ◽  
You Gang Xiao ◽  
Xian Ming Lei ◽  
Guo Xin Chen
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Heat Transfer Coefficient ◽  
Transient Heat Conduction ◽  
Transfer Model ◽  
Contact Heat ◽  
Conduction Model ◽  
Contact Heat Transfer

According to kiln structure and material movement features, the transient heat conduction model of material bed and the contact heat transfer model at the interface of covered kiln wall and material bed are built. Considering their contribution to the convective heat transfer of material bed, the convective heat transfer coefficient between covered kiln wall and material bed is proposed, and its formula is obtained, with which the convective heat transfer between covered kiln wall and material bed can be calculated conveniently, so the heat transfer prediction within the rotary kiln can be done more easily.

Numerical Investigation of Heat Transfer Characteristics of Debris Bed After Severe Accident of SFR Based on 1-D Heat Conduction Model

2018 ◽  
Author(s):  
Mengwei Zhang ◽  
Bin Zhang ◽  
Jianqiang Shan
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Transfer Process ◽  
Severe Accident ◽  
Heat Transfer Characteristics ◽  
Conduction Model ◽  
One Dimensional ◽  
The Core ◽  
Transfer Characteristics ◽  
Core Catcher

Nuclear reactor severe accidents can lead to the release of a large amount of radioactive material and cause immense disaster to the environment. Since the Fukushima nuclear accident in Japan, the severe accident research has drawn worldwide attention. Based on the one-dimensional heat conduction model, a DEBRIS-HT program for analyzing the heat transfer characteristics of a debris bed after a severe accident of a sodium-cooled fast reactor was developed. The basic idea of the DEBRIS-HT program is to simplify the complex energy transfer process in the debris bed to a simple one-dimensional heat transfer problem by solving the equivalent thermal conductivity in different situations. In this paper, the DEBRIS-HT program code is prepared by using the existing model and compared with the experimental results. The results show that the DEBRIS-HT program can correctly predict the heat transfer process in the fragment bed. In addition, the heat transfer characteristics analysis program is also used to model the core catcher of the China fast reactor. Firstly, the dryout heat flux when all of molten core dropped on the core catcher was calculated, which was compared with the result of Lipinski’s zero dimensional model, and the error between two values is only 11.2%. Then, the temperature distribution was calculated with the heat power of 15MW.

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