Heat-conducting Body Research Articles

Why Humans are Better Endurance Runners than Any Other Animal?

It is well known that only man is capable of endurance running and in this sense he has no equal among animals. Why do other animals have us beat over short distances, but are not able to run long distances as long as humans? There are different answers. Walking upright has allowed us to become some of the best distance runners in the world, but at the expense of speed. It is also believed that to run long distances on the African savannah man needed to have an effective cooling system and it is believed that man has developed one. Firstly, heat exchange improved due to the disappearance of fur. Secondly, humans learned to sweat intensively. They also attach importance to the diet and the lifestyle. There are other answers, but they have little relevance to the question discussed here. Can the above answers be considered exhaustive? We believe that there is another important factor unique to man, which ultimately allowed him to occupy the top of the food chain. This factor is the peculiarity of the heat-conducting ability of the human body. Man became a good long-distance runner because among animals he has the most highly heat-conducting body, which allowed him to effectively dissipate excess heat outside the body.

Functional-Voxel Method in Problems of Geometric Modeling of Thermal Characteristics of Objects

The paper presents an approach developed on the basis of the functional voxel method to the geometric representation of the thermal expansion of objects and temperature stresses in a material when exposed to a surface of a heat source. A discrete geometric law of a single temperature stress in an isotropic heat-conducting body is derived, applicable in the concept of functional voxel modeling. Based on this law, functional-voxel models of thermal stress are developed for a single and distributed application of a heat source. Algorithms of functional-voxel modeling of temperature stress and expansion in the case of distributed thermal loading are presented, which make it possible to construct a loading region of a complex configuration, uniformly form a contour (surface) after material expansion and obtain information about changes in the length (volume) of products. The advantages of the proposed functional-voxel approach to modeling thermal expansion and stress over approaches based on the FEM are substantiated.

Описание кратковременного процесса уравнением теплопроводности с дробными производными

The thermal conductivity models of Fourier, Cattaneo-Vernotte, Maxwell-Cattaneo-Luikov and models with fractional time derivatives of temperature and heat flux are considered. An algorithm for the numerical solution of the generalized problem of one-dimensional heat conduction is constructed. The algorithm comprises all the models listed above applying boundary conditions of the third kind and difference analogs of differential operators of the second order of accuracy in coordinate and time. The parameters (Biot number, time of thermal relaxation and thermal damping, indicators of fractional derivatives) that describe experimental transient processes are determined using the listed models applied for both in the center and on the surface of a low heat-conducting body.

Function Estimation in Inverse Heat Transfer Problems Based on Parameter Estimation Approach

A new sensitivity analysis scheme is presented based on explicit expressions for sensitivity coefficients to estimate timewise varying heat flux in heat conduction problems over irregular geometries using the transient readings of a single sensor. There is no prior information available on the functional form of the unknown heat flux; hence, the inverse problem is regarded as a function estimation problem and sensitivity and adjoint problems are involved in the solution of the inverse problem to recover the unknown heat flux. However, using the proposed sensitivity analysis scheme, one can compute all sensitivity coefficients explicitly in only one direct problem solution at each iteration without the need for solving the sensitivity and adjoint problems. In other words, the functional form of the unknown heat flux can be numerically estimated by using the parameter estimation approach. In this method, the irregular shape of heat-conducting body is meshed using the boundary-fitted grid generation (elliptic) method. Explicit expressions are given to compute the sensitivity coefficients efficiently and the steepest-descent method is used as the minimization method to minimize the objective function and reach the solution. Three test cases are presented to confirm the accuracy and efficiency of the proposed inverse analysis.

Геометрическое моделирование тепловых характеристик объектов функционально-воксельным методом

In this paper the influence of objects’ thermal processes on their correspondence to a given geometry has been considered, and an alternative apparatus for geometric modeling of bodies’ temperature stress and thermal expansion after effect of a heat source, based on a functional-voxel approach, has been proposed as well. A discrete geometric model of temperature stress at a point of thermal loading in an isotropic heat-conducting body for a functional-voxel representation has been developed, allowing simulate a single action of a heat source to obtain local geometric characteristics of thermal stress in the body. This approach, unlike traditional approaches based on the FEM, allows apply the temperature load at the object’s point taken by itself. A discrete geometric model for expansion at the point of thermal loading in an isotropic heat-conducting body for a functional-voxel representation has been developed, which allows simulate the change of an object’s local geometric characteristics during the process of material expansion from a single effect of a heat source to obtain a value upon the body volume changing. This approach, unlike traditional approaches based on the FEM, allows simulate a change in the body’s surface geometry from thermal expansion at a point taken by itself without errors arising from calculations using a mesh. Have been proposed algorithms for functional-voxel modeling of temperature stress and expansion under distributed thermal loading. These algorithms allow construct a loading region of complex configuration based on the spatial distribution and scaling of the temperature stress’s geometric model for a single point of thermal loading, uniformly form a contour (surface) after material expansion, and obtain information about the change in products’ length (volume) based on information about each point of functional space. Has been presented an example of using the proposed approach for solving a processing tool’s correction problem based on the temperature in the cutting zone and material thermal reaction. The geometric model can be used to the automated design of a processing tool path for parts cutting on CNC machines.

Thermogravitational Convection of Hybrid Nanofluid in a Porous Chamber with a Central Heat-Conducting Body

A problem with the thermogravitational energy transference of a hybrid nanofluid (Al2O3-SiO2/H2O) in a porous space with a central heat-conducting body has been presented and numerical analysis has been performed. Governing equations, transformed in terms of non-dimensional parameters, have been solved by a developed numerical algorithm based on the finite difference technique. The behavior of streamlines and isotherms was investigated, and the impact of various important characteristics is discussed. The variation in the average and local Nusselt numbers was studied; by selecting various appropriate nano-sized particle combinations in hybrid nanosuspension, the desired energy transport strength could be obtained. The results were compared and successfully validated with previous reported numerical and experimental data from the literature.

Identification of space- and temperature-dependent heat transfer coefficient

The aim of this paper is to present a very efficient and accurate numerical algorithm to identify a variable (space- and temperature-dependent) heat transfer coefficient in two-dimensional inverse steady-state heat conduction problems involving irregular heat-conducting body shapes in the presence of Dirichlet, Neumann, and Robin boundary conditions. In this numerical method, a boundary-fitted grid generation technique (elliptic) is used to discretize the physical domain (heat-conducting body) and solve for the steady-state heat conduction equation by approximating the derivatives of the field variable (temperature) by algebraic ones. This paper describes a very accurate and efficient sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of the variable heat transfer coefficient. The main advantage of the sensitivity analysis scheme is that it does not require the solution of adjoint equation. The conjugate gradient method (CGM) is used to reduce the mismatch between the computed temperature on part of the boundary and the simulated measured temperature distribution. The obtained results confirm that the proposed algorithm is very accurate, efficient, and robust.

Thermocouple Data in the Inverse Heat Conduction Problem

The presence of thermocouples inside a heat-conducting body will distort the temperature field in the body and may lead to significant bias in the temperature measurement. If temperature histories obtained from thermocouples are used in the inverse heat conduction problem (IHCP), errors are propagated into the IHCP results. The bias in the thermocouple measurements can be removed through use of appropriate detailed thermocouple models to account for the dynamics of the sensor measurement. The results of these models can be used to generate correction kernels to eliminate bias in the thermocouple reading, or can be applied as sensitivity coefficients in the IHCP directly. Three-dimensional and axisymmetric models are compared and contrasted and a simple sensitivity study is conducted to evaluate the significance of thermal property selection on the temperature correction and subsequent heat flux estimation. In this paper, a high-fidelity thermocouple model is used to account for thermocouple bias in an experiment to measure heat fluxes from solidifying aluminum to a sand mold. Correction kernels are obtained that are used to demonstrate the magnitude of the temperature measurement bias created by the thermocouples. The corrected temperatures are used in the IHCP to compute the surface heat flux. A comparison to IHCP results using uncorrected temperatures shows the impact of the bias correction on the computed heat fluxes.

Sinc Approximation of the Heat Flux on the Boundary of a Two-Dimensional Finite Slab

We consider the two-dimensional problem of recovering globally in time the heat flux on the surface of a layer inside of a heat-conducting body from two interior temperature measurements. The problem is ill-posed. The approximation function is represented by a two-dimensional Sinc series and the error estimate is given.

MODELING OF COMBINED RADIATIVE AND CONVECTIVE HEAT TRANSFER IN AN ENCLOSURE WITH A HEAT-GENERATING CONDUCTING BODY

In this paper, we present a numerical study of the radiation-natural convection interactions in a differentially heated enclosure, within which a centered, squared, heat-conducting body generates heat. A specifically developed numerical model based on the finite-volume method and the SIMPLER algorithm is used for the solution of the governing equations. The working fluid (air) is perfectly transparent to the radiation. The Rayleigh number Ra and the temperature-difference ratio ΔT* were varied parametrically. For Pr = 0.71, the results obtained show that: (i) The isotherms and streamlines are strongly affected by the radiation exchange at high Rayleigh numbers (Ra ≥ 106), (ii) the temperature of the inner body decreases under the radiation exchange effect, (iii) for a constant Ra, the average Nusselt number at the hot and cold walls (Nuh and Nuc) vary linearly with increasing ΔT*: Nuh decreases with ΔT* while Nuc increases with ΔT*. Furthermore, the radiation exchange increases both average Nusselt numbers Nuh and Nuc, especially at Ra ≥ 105, and consequently, [Formula: see text] increases.

Global Equivalence for Rigid Heat-Conducting Bodies

In a previous paper of the author, the notion of global equivalence between two deformable thermoelastic bodies B and 13' was introduced. This equivalence is understood in the sense that a global thermokinetic process for B is admissible (in the sense of Coleman and Noll) if and only if its counterpart for B', according to a suitable bijective correspondence k between B and B'i , also is admissible. In this case, B and B' are said to be globally k-equivalent. Global k-equivalence does not imply piecewise k-equivalence, that is, the global equivalence of arbitrary k-corresponding subbodies of B and B'. Here we present two maximality theorems of global equivalence for a rigid heat-conducting body B: one in the thermodynamic theory with no heat sources and the other in the thermodynamic theory with heat supply. By these theorems, given the rigid heat-conducting body B referred to its configuration -% in both the theories we characterize the constitutive equations for all rigid heat conductors B' that have a configuration A' with '(13') = '5(B) and are globally k-equivalent to B for k = t-y oy.

A numerical study on three-dimensional conjugate heat transfer of natural convection and conduction in a differentially heated cubic enclosure with a heat-generating cubic conducting body

A comprehensive numerical study has been conducted to investigate three-dimensional, steady, conjugate heat transfer of natural convection and conduction in a vertical cubic enclosure within which a centered, cubic, heat-conducting body generates heat. The physical model considered here assumes that a temperature difference exists across the enclosure (right cold wall and left hot wall) and the body generates a constant amount of heat. Under these conditions, the flow inside the enclosure is driven by two temperature differences: a temperature difference across the enclosure and a temperature difference caused by the heat source. A ratio of these two temperatures is a key parameter in this study. The steady, three-dimensional governing equations are written in a dimensionless form with dimensionless parameters that decide the heat transfer and flow characteristics in this system. The analysis is conducted by observing variations of the velocity vectors, pathlines, and isotherms for different Rayleigh numbers and temperature-difference ratios. The details of the three-dimensional flow and isotherms are described in order to investigate the effects of three-dimensionalities on the fluid flow and thermal characteristics in the enclosure. The variations of Nusselt numbers on the hot and cold walls are also presented to show the overall heat transfer characteristics inside the enclosure.

Mixed convection in an enclosure with a heat-conducting body

Combined free convection and forced convection in a square enclosure with a finite-size heat source is studied numerically. A square heat-conducting body is located somewhere within the enclosure. The present study simulates a practical system, such as an air-cooled electronic equipment with heat components or an oven with heaters. Emphasis is placed on the influences of the configurations and physical properties of the enclosure. The developed mathematical model is governed by the coupled equations of stream function, vorticity transport, and energy, and is solved by employing the cubic spline collocation method. The computation is carried out for wide ranges of Reynolds and Grashof numbers. The results indicate that both the heat transfer coefficient and the dimensionless temperature in the body center strongly depend on the configurations of the system studied, such as size, location, and thermal conductivity of the conducting body and the location of the outflow opening. Detailed results of the interaction between forced airstream and the bouyancy-driven flow by the heat source are demonstrated by the distributions of the isotherms and streamlines and the variations of the heat transfer coefficient.

NUMERICAL STUDY ON TRANSIENT HEAT TRANSFER AND FLUID FLOW OF NATURAL CONVECTION IN AN ENCLOSURE WITH A HEAT-GENERATING CONDUCTING BODY

A comprehensive numerical study has been conducted to investigate transient heat transfer and flow phenomena of natural convection of three different fluids of sodium, air, and water in a vertical square enclosure within which a centered, squared, heat-conducting body generates heat. The physical model considered here is that a temperature difference exists across the enclosure (right cold wall and left hot wall) all the time and the body generates a constant amount of heat at an initial dimensionless time of tau0. At time tau0 the amount of heat generated by the body is suddenly increased to 10 times as large as that at time tau0. Under this situation, the flow inside the enclosure is driven by two temperature differences: a temperature difference across the enclosure and a temperature difference caused by the heat source. A ratio of these two temperatures is a key parameter in this study. We also consider the effects of Prandtl number and thermal conductivity ratio on the heat transfer and flow in the enclosure. The unsteady and two-dimensional governing equations are written in a dimensionless form with dimensionless parameters that decide the heat transfer and flow characteristics in this system. The analysis proceeds by observing variations of the streamlines and isotherms with respect to the dimensionless time for different Rayleigh numbers, temperature-difference ratios, Prandtl numbers, and thermal conductivity ratios. The variations of average Nusselt numbers on the hot and cold walls are also presented with respect to the dimensionless time, to show the transient behavior of overall heat transfer characteristics inside the enclosure.

Solving an Inverse Heat Conduction Problem by a “Method of Lines”

We consider a Cauchy problem for the heat equation in the quarter plane, where data are given at x = 1 and a solution is sought in the interval 0 < x < 1. This inverse heat conduction problem is a model of a situation where one wants to determine the surface temperature given measurements inside a heat-conducting body. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In an earlier paper we showed that replacement of the time derivative by a difference stabilizes the problem. In this paper we investigate the use of time differencing combined with a “method of lines” for solving numerically the initial value problem in the space variable. We discuss the numerical stability of this procedure, and we show that, in most cases, a usual explicit (e.g., Runge-Kutta) method can be used efficiently and stably. Numerical examples are given. The approach of this paper is proposed as an alternative way of implementing space-marching methods for the sideways heat equation.

Comparison of some inverse heat conduction methods using experimental data

This paper compares several methods of finding the surface heat flux using transient temperature measurements inside a heat-conducting body. Experimental data is used with a known heat flux history. The methods include function specification with several future approximations, Tikhonov regularization, iterative regularization and specified functions over large time regions with Green's functions. The first three methods are used with the residual principle and the results are quite similar. If the heat flux has a simple time variation over large time regions, taking advantage of that feature can improve the results, as shown by the Green's function analysis.

EFFECT OF A CENTERED CONDUCTING BODY ON NATURAL CONVECTION HEAT TRANSFER IN AN ENCLOSURE

The effect of a centered, square, heat-conducting body on natural convection in a vertical square enclosure was examined numerically. The analysis reveals that the fluid flow and heat transfer processes are governed by the Rayleigh and Prandtl numbers, the dimensionless body size, and the ratio of the thermal conductivity of the body to that of the fluid. For Pr = 0.71 and relatively wide ranges of the other parameters, results are reported in terms of streamlines, isotherms, and the overall heat transfer across the enclosure as described by the Nusselt number. Heat transfer across the enclosure, in comparison to that in the absence of a body, may be enhanced (reduced) by a body with a thermal conductivity ratio less (greater) than unity. Furthermore, the heat transfer may attain a minimum as the body size is increased. These and other findings are justified through a careful examination of the local heat and fluid flow phenomena.

THERMALLY INDUCED VIBRATIONS IN AN ELASTIC BODY WITH A SPHERICAL CAVITY

An elastic heat-conducting body with a cavity can be set in vibration if the temperature of the cavity varies cyclically with time. A simple closed solution can be derived if the geometry is spherical and if the temperature oscillates harmonically. The amplitude of the stresses increases with increasing inertia. If the velocities of temperature waves and elastic waves coincide, no resonancelike amplification of the stresses occurs.

Inverse heat-conduction problem by finite-element formulation

The paper is concerned with the inverse problem of a heat-conduction model using the finite-element method. The problem is to estimate the surface temperature and surface heat flux using the time history of measured temperature at some interior points of a heat-conducting body. The finite-element formulation estimates the temperature distribution inside the body, and then the surface heat flux is determined so as to minimize the sum of squares of the difference between the estimated and measured temperatures at the interior points. As a numerical experiment, the technique is applied to the inverse problem of the thin-skinned heat-transfer model with a position-dependent surface heat flux. Numerical results show the effectiveness of the proposed technique from the viewpoint of numerical accuracy.

Conditions for a minimum entropy-production rate in a heat-conducting body

Conditions for a minimum entropy-production rate in a heat-conducting body