Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.

A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions

In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.

Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity

Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive computation.In this paper,we propose a multi-modes based constrained energy minimization generalized multiscale finite element method(MCEM-GMsFEM),which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis.Thus,MCEM-GMsFEM reveals an inherent low-dimensional representation in random space,and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems.In addition,the convergence analysis is established,and the optimal error estimates are derived.Finally,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples.The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.

Efficient Inverse Analysis for Solving a Coupled Conduction,Convection and Radiation Problem Involving Non⁃gray Participating Media

The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.

An efficient inverse approach for reconstructing time-and space-dependent heat flux of participating medium

The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method.The reconstruction task is formulated as an inverse problem,and the DFIM is used to reconstruct the unknown heat flux.No prior information on the heat flux distribution is required for the inverse analysis.All retrieval results illustrate that the time-and spacedependent heat flux of participating medium can be exactly recovered by the DFIM.The present method is proved to be more efficient and accurate than other optimization techniques.The effects of heat flux form,initial guess,medium property,and measurement error on reconstruction results are investigated.Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have periodic configurations and associated coefficients are dependent on the macro-location.Also,radiation effect at microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study.The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first.Then,the second-ordermultiscale formulas for solving temperature fields of the nonlinear problems are constructed,and associated explicit convergence rates are obtained on some regularity hypothesis.Finally,the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail.Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy.They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely,and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.

Reconstruction of Temperature Field in 3-D, Absorbing, Emitting, and Anisotropically Scattering Medium

The soft measurement technology of flame temperature field is an efficient method to learn the combustion status in furnace. Generally, it reconstructs the temperature field in furnace through the image of flame, which is a process to solve radiative inverse problem. In this paper, the flame of pulverized coal is considered as 3-D, absorbing, emitting, and anisotropically scattering non-gray medium. Through the study on inverse problem of radiative heat transfer, the temperature field in this kind of medium has been reconstructed. The mechanism of 3-D radiative heat transfer in a rectangular media, which is 2 m×3 m× 5 m and full of CO2, N2 and carbon particles, is studied with Monte Carlo method. The 3-D temperature field in this rectangular space is reconstructed and the influence of particles density profile is discussed.

Estimation of solid concentration in solid-liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study,an inverse-problem method was applied to estimate the solid concentration in a solid-liquid two-phase flow.An algebraic slip mixture model was introduced to solve the forward problem of solid-liquid convective heat transfer.The time-average conservation equations of mass,momentum,energy,as well as the volume fraction equation were computed in a computational fluid dynamics(CFD)simulation.The solid concentration in the CFD model was controlled using an external program that included the inversion iteration,and an optimal estimation was performed via experimental measurements.Experiments using a fly-ash-water mixture and sand-water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method.The estimated results were rectified using a method based on the relationship between the estimated results and estimation error;consequently,the accuracy of the corrected inversion results improved significantly.After a verification through experiments,the inverse-problem method was concluded to be feasible for predicting the solid concentration,as the estimation error of the corrected results was within 7%for all experimental samples for a solid concentration of less than 50%.The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid-liquid two-phase flow systems.