SENSITIVITY ANALYSIS FORMULATION FOR THREE-DIMENSIONAL CONDUCTION HEAT TRANSFER WITH COMPLEX GEOMETRIES USING A BOUNDARY ELEMENT METHOD

Design sensitivity analysis for parameters affecting geometry, elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method

The solution of the conjugate problem of convective-conductive heat transfer in the channels of power plants is presented. The problem of convective heat transfer in the gas phase is solved by the integral theory of heat transfer. A one-dimensional problem of conductive heat transfer in the material of the wall is solved by the finite-difference method. Relative laws of heat and mass transfer and friction are obtained by numerical integration with respect to the boundary-layer thickness. The effect of the material and geometry of the wall on the level of problem “conjugation” is studied.

Several new formulations for structural design sensitivity analysis (DSA) of elastic solids are presented that consistently account for steady and transient thermal loading, along with centrifugal and gravity loading. The approach employs implicit differentiation of the discretized boundary integral equations and facilitates the production of accurate and efficient computational procedures that obviate the need for matrix factorizations in the DSA step. For centrifugal, gravity and general thermal loading, a new DSA concept employing a particular integral technique is developed. For centrifugal, gravity and steady thermal effects, a surface integration approach is also presented, and the two methods compared. Alternative strategies for modelling the behaviour of temperature distributions of evolving shapes undergoing shape optimization and the ramifications of these strategies in the DSA process are also discussed. It is shown that, for certain classes of thermoelastic problems, shape optimization can be performed without the need to incorporate thermal analysis or DSA into the overall process. A thermoelastic surface stress sensitivity analysis formulation is presented that does not require additional numerical integration. A new thermoelastic sharp corner traction component consistent sensitivity analysis formulation is also presented. This technique is shown to work for any initial stress distribution. Numerical sensitivity results are presented for many problems with analytical solutions.

Analytical methods exist to solve the problems of hydromechanics and heat transfer, but it is not possible to obtain the solution to some inhomogeneous and nonlinear problems of hydromechanics and heat transfer by analytical methods. The solution to such problems is carried out using numerical methods. Currently, there are many textbooks and monographs on numerical methods for solving problems of hydromechanics, thermal conductivity, heat and mass transfer, and others. The article presents the results of a numerical study of the flow structure in the flow around a flat plate. The calculations are based on the numerical solution of a system of nonstationary equations using a two-fluid turbulence model. For the numerical solution of these problems, schemes of the second and fourth order of accuracy were applied. The control volume method was used for the difference approximation of the initial equations, and the relationship between velocities and pressure was found using the SIMPLE procedure. To confirm the correctness of the numerical results, comparisons were made with each other and experimental data.

Purpose: In particle therapy, treatment planning and evaluation are frequently based on biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2). In the context of the linear-quadratic model, these quantities depend on biological parameters (α, β) for ions as well as for the reference radiation and on the dose per fraction. The needed biological parameters as well as their dependency on ion species and ion energy typically are subject to large (relative) uncertainties of up to 20–40% or even more. Therefore it is necessary to estimate the resulting uncertainties in e.g. RBE or EQD2 caused by the uncertainties of the relevant input parameters. Methods: We use a variance-based sensitivity analysis (SA) approach, in which uncertainties in input parameters are modeled by random number distributions. The evaluated function is executed 10{sup 4} to 10{sup 6} times, each run with a different set of input parameters, randomly varied according to their assigned distribution. The sensitivity S is a variance-based ranking (from S = 0, no impact, to S = 1, only influential part) of the impact of input uncertainties. The SA approach is implemented for carbon ion treatment plans on 3D patient data,more » providing information about variations (and their origin) in RBE and EQD2. Results: The quantification enables 3D sensitivity maps, showing dependencies of RBE and EQD2 on different input uncertainties. The high number of runs allows displaying the interplay between different input uncertainties. The SA identifies input parameter combinations which result in extreme deviations of the result and the input parameter for which an uncertainty reduction is the most rewarding. Conclusion: The presented variance-based SA provides advantageous properties in terms of visualization and quantification of (biological) uncertainties and their impact. The method is very flexible, model independent, and enables a broad assessment of uncertainties. Supported by DFG grant WI 3745/1-1 and DFG cluster of excellence: Munich-Centre for Advanced Photonics.« less

In most issues representing physical problems, the complex geometry cannot be represented by a Cartesian grid. The multi-block grid technique allows artificially reducing the complexity of the geometry by breaking down the real domain into a number of sub-domains with simpler geometry. The main aim of this article is to show the usefulness of simple solvers in complex geometry problems, when using curvilinear coordinates combined with multi-block grids. This requires adapted solvers to a nine nodes computational cell instead of the five nodes computational cell used with Cartesian coordinates for two-dimensional cases. These developments are presented for the simple iterative methods Jacobi and Gauss-Seidel and also for the incomplete factorization method strongly implicit procedure (SIP). These adapted solvers are tested in two cases: a simple geometry (heat transfer in a circular cross-section) and a complex geometry (solidification case). Results of the simple geometry case show that all the adapted solvers have good performance with a slight advantage for the SIP solver. For increasing the complexity of the geometry, the results showed that Jacobi and Gauss-Seidel solvers are not suitable. However, the SIP method has a reasonable performance. A conclusion could be drawn that the SIP method could be used in complex geometry problems using multi-block grid technique when high precision results are not required.

Vortex generation is a potential passive technology for increasing the heat transfer rate in the air side of fin and tube heat exchangers (FTHEs). This study proposes novel configurations of a curved trapezoidal winglet vortex generator (CTWVG) with and without circular holes to improve heat transfer in FTHEs. As per the literature, the streamlined form of the trapezoidal winglet demonstrates high heat transfer enhancement with low flow loss and pressure drop. But still, different design configurations are possible to augment the heat transfer characteristics of CTWVG further. The current study investigates the novel configurations of CTWVG (i.e., CTWVG without hole, CTWVG with 1 hole, CTWVG with 2 holes, CTWVG with 3 holes and CTWVG with 6 holes). A three-dimensional computational model is utilized to evaluate the thermal-hydraulic efficiency of FTHEs fitted with CTWVGs with or without circular holes for Reynolds numbers ranging from 400 to 2000. A common flow-down configuration of the CTWVG with circular tubes array is used to reduce the wake region. The thermo-hydraulic performance and flow structure of FTHE with four inline circular tube configurations are compared without VG and CTWVG with or without holes. Pressure drop (ΔP), Nusselt number (Nu), friction factor (f), Colburn factor (j), and London area goodness factor (j/f) are used for the thermal-hydraulic performance comparison. Results show that the number of punched holes has an impact on the FTHE performance, which is measured using a dimensionless number as performance evaluation criteria (i.e., (j/jo)/(f/fo)). CTWVGs with circular punched holes significantly increase the FTHE's thermo-hydraulic performance. The results indicate that the flow resistance is reduced in all cases (i.e., VG with no holes, VG with 6 holes, VG with 3 holes, VG with 2 holes, and VG with 1 hole) with a minor decrease in the Nusselt number. The CTWVG with six holes performs better than other CTWVG configurations. At Reynolds numbers 400 and 2000, the Nusselt number for CTWVG with six holes enhanced by 75.25% and 40.10%; pressure drop increased by 107.88% and 125.51%, respectively. On the other hand, friction is reduced by a factor of 8.1% in CTWVG with 6 holes compared to CTWVG without holes. The CTWVG with six holes performs better than other CTWVG configurations reported in the literature [48,54]. HTPF has increased by 30.96% (compared to rectangular winglet [48]) and 27.69% (compared to curved rectangular winglet [54]) with respect to values reported in the literature. The London area goodness factor (LAGF) has been increased by 275% compared to Modi et al. [48].

In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn't exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

The stable method of soloing inverse problems in heat transfer and inverse problems concerning thermal stress control in elements of complex shapes is presented. Based on the discrete form of Duhamel's integral and on so-called future time steps, a simple and accurate method of solving one- and multi-dimensional inverse problems is developed. Two examples illustrating the application of the described method are presented.

Summary Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is typically needed to assess a causal conclusion’s sensitivity to unmeasured confounding. Sensitivity analysis frameworks for binary exposures have been well-established for various matching designs and are commonly used in various studies. However, unlike the binary exposure case, there still lacks valid and general sensitivity analysis methods for continuous exposures, except in some special cases such as pair matching. To fill this gap in the binary outcome case, we develop a sensitivity analysis framework for general matching designs with continuous exposures and binary outcomes. First, we use probabilistic lattice theory to show our sensitivity analysis approach is finite-population- exact under Fisher’s sharp null. Second, we prove a novel design sensitivity formula as a powerful tool for asymptotically evaluating the performance of our sensitivity analysis approach. Third, to allow effect heterogeneity with binary outcomes, we introduce a framework for conducting asymptotically exact inference and sensitivity analysis on generalized attributable effects with binary outcomes via mixed- integer programming. Fourth, for the continuous outcomes case, we show that conducting an asymptotically exact sensitivity analysis in matched observational studies when both the exposures and outcomes are continuous is generally NP-hard, except in some special cases such as pair matching. As a real data application, we apply our new methods to study the effect of early-life lead exposure on juvenile delinquency. An implementation of the methods in this work is available in the R package doseSens.

Radiative heat transfer in a complex two-dimensional enclosure with an absorbing, emitting, and isotropically scattering gray medium is investigated by using the finite-volume method. In particular, an implementation of the unstructured polygonal meshes, based on an unstructured triangular system, is introduced, thereby reducing the computation time required for the analysis of thermal radiation. By connecting each center point of the triangular meshes rather than joining the centroids of the triangular elements to the midpoints of the corresponding sides to form a polygonal element, it not only prevents concave shapes of adjacent faces, it also reduces the number of control-volume faces of the polygonal mesh. After a mathematical formulation and corresponding discretization equation for the radiative transfer equation are derived, the final discretization equation is introduced with the conventional finite-volume approaches. The present formulation is then validated by comparing results with those obtained in previous related works. All the results presented in this work show that the present method is accurate and computationally efficient for the analysis of radiative heat transfer problems in complex geometries.

Prediction of radiative heat transfer in 2D irregular geometries using the collocation spectral method based on body-fitted coordinates

Temporally and spatially unstable thermal conditions lead to transient or inhomogeneous thermo-elastic behavior of workpieces during manufacturing or geometric inspection. Temperature monitoring by means of sensors consign transient temperature fields, but do not yield information about the heat flow acting as thermal boundary condition, which is a relevant input parameter for nearly any thermal simulation. Addressing the need for efficient methods, the authors propose an approach to solve inverse heat transfer problems in complex geometries. In the presented study, locally acting heat loads are experimentally investigated based on virtual demonstrators running in FEM. The conducted method shows high potential for transient heat flow modelling in terms of accuracy and computational efficiency.

As computational fluid dynamics (CFD) simulations still take a lot of time in industry for design optimization analyses, we propose to reduce the number of required CFD simulations considerably using a new meta-algorithm. The algorithm consists of employing kriging in conjunction with simulated annealing (SA) as a design tool. The method enables effective and fast design optimization for complex fluid flow systems. In this paper, it is applied to a convective heat transfer problem in a channel with periodic heat sources with constant heat flux. We show that the geometry optimization of two dimensional thermo-fluids problems in complex geometries is made more effective and faster using kriging-simulated annealing meta-algorithm.