Analytical Temperature Distribution Research Articles

Heat Distribution within the Wellbore While Drilling

Analysis of the drilling fluid temperature in a circulating well is the main objective of this study. Initially, different analytical temperature distribution models were studied. Variables that have significant effect on temperature profile are observed. Since the verification of the analytical model is not probable for many cases, a computer program that uses a finite element method is employed to simulate different well conditions. Three different wells are modeled by using rectangular elements with four nodes. Maximum drilling fluid temperature data corresponding to significant variables are collected from these models. These data are then used to develop an empirical correlation in order to determine maximum drilling fluid temperature. The proposed empirical correlation can estimate the temperature distribution within the wellbore with an average error of less than 16%, and maximum drilling fluid temperature with an average error of less than 7%.

Three‐Dimensional Radiative Hydrodynamics for Disk Stability Simulations: A Proposed Testing Standard and New Results

Recent three-dimensional radiative hydrodynamics simulations of protoplanetary disks report disparate disk behaviors, and these differences involve the importance of convection to disk cooling, the dependence of disk cooling on metallicity, and the stability of disks against fragmentation and clump formation. To guarantee trustworthy results, a radiative physics algorithm must demonstrate the capability to handle both the high and low optical depth regimes. We develop a test suite that can be used to demonstrate an algorithm's ability to relax to known analytic flux and temperature distributions, to follow a contracting slab, and to inhibit or permit convection appropriately. We then show that the radiative algorithm employed by Mejía and Boley et al. and the algorithm employed by Cai et al. pass these tests with reasonable accuracy. In addition, we discuss a new algorithm that couples flux-limited diffusion with vertical rays, we apply the test suite, and we discuss the results of evolving the Boley et al. disk with this new routine. Although the outcome is significantly different in detail with the new algorithm, we obtain the same qualitative answers. Our disk does not cool fast due to convection, and it is stable to fragmentation. We find an effective α ≈ 10-2. In addition, transport is dominated by low-order modes.

Three-dimensional reconstruction of the intra-cluster medium

We propose and test a new method based on Richardson-Lucy deconvolution to reconstruct three-dimensional gas density and temperature distributions in galaxy clusters from combined X-ray and thermal Sunyaev-Zel'dovich observations. Clusters are assumed to be axially symmetric and arbitrarily inclined with respect to the line-of-sight. No equilibrium assumption other than local thermal equilibrium is needed. We test the algorithm with synthetic observations of analytically modeled and numerically simulated galaxy clusters and discuss the quality of the density and temperature reconstructions in idealised situations and in presence of observational noise, deviations from axial symmetry and cluster substructure. We find that analytic and numerical gas density and temperature distributions can be accurately reconstructed in three dimensions, even if observational noise is present. We also discuss methods for determining the inclination angle from data and show that it can be constrained using X-ray temperature maps. For a realistic cluster and including observational noise the three-dimensional reconstructions reach a level of accuracy of about 15%.

Thermal analysis on metal-foam filled heat exchangers. Part I: Metal-foam filled pipes

This paper presents an analytical study of the forced convection heat transfer characteristics in high porosity open-cell metal-foam filled pipes. The Brinkman-extended Darcy momentum model and two-equation heat transfer model for porous media were employed. Based on the analytical solutions, the velocity and temperature distributions in metal-foam filled pipes were obtained. The effects of the microstructure of metal foams on overall heat transfer were examined. The results show that the pore size and porosity of metal-foams play important roles on overall heat transfer performance. The use of metal-foam can dramatically enhance the heat transfer but at the expense of higher pressure drop.

Easy and rapid computation of the transfer of heat from annular fins of nearly optimal profile with the finite‐difference technique and the shooting method

It is undeniable that the annular fin of hyperbolic profile with constant thermal conductivity and uniform convective coefficient is important in many applications of heat transfer engineering. The importance of this fin configuration stems from its close resemblance to the annular fin of optimal cross section capable of delivering maximum heat transfer for a given volume of material. This paper addresses two simple numerical procedures for solving the generalized Bessel equation that governs the temperature variation in annular fins of hyperbolic profile, one is the finite‐difference technique with an uncharacteristic coarse mesh and the other is the shooting method. Certainly, the central objective here is to avoid the evaluation of the elegant, but intricate exact analytic temperature distributions and companion fin efficiencies containing modified Bessel functions of fractional order.

Direct estimation of time-dependent boundary heat flux

We present a non-iterative direct method to estimate time-varying boundary heat flux in a one-dimensional heat conduction domain with heated and insulated walls. The proposed method relates the temporal variation of the surface heat flux to the temperature variation at the heated surface based on the analytical temperature distribution. Several illustrative examples are examined to verify the performance of the proposed method. The uncertainty analysis of the estimated heat fluxes is discussed. The proposed method may also be useful to make sufficiently accurate initial guesses for more sophisticated method which usually adopt the iterative scheme

On the optimal design of gas-cooled peltier current leads

We perform the optimal design of gas-cooled Peltier current leads (PCLs), such that their resulting heat leaking into superconducting magnets can be minimized. Superior to previous investigations, the effect of gas cooling on both the Cu lead and the thermoelectric element in a PCL is taken into consideration. Analytical temperature distribution is derived as well as the concerned heat leaking into superconducting magnets. Numerically iterative calculations are, therefore, avoided. Moreover, temperature-entropy diagrams are constructed to distinguish conventional all-Cu leads from PCLs with and without gas cooling. Both the heat leak and the input power of current leads can be easily identified from the areas subtended by the isotherms on the simple two-dimensional temperature-entropy plane.

Estimation of orthotropic thermal conductivity of honeycomb material

AbstractAn experimental–computational hybrid system for measurement of thermal conductivity of orthotropic materials is developed. The system consists of two experimental parts and a finite element analysis part. First, the temperature distribution generated by uniform heating is measured with a thermal video system, and the thermal conductivity of Z direction is calculated. Second, the temperature distribution generated by small area heating is measured with the system. In the final step, thermal transfer analyses simulating the experiment support efficient data, and thermal conductivity of in‐plane directions is estimated by comparison between experimental and analytical temperature distributions. The orthotropic equivalent thermal conductivity of honeycomb materials obtained by this system agreed with the theoretical values. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(8): 617–625, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10063

Repetitive laser pulse heating with a convective boundary conditionat the surface

Repetitive laser pulses deposit sufficient energy to provideuniform-like heating at the surface of a substrate. This improves the surface properties of thesubstrate so treated. In the present study, an analytical solution forthe temperature distribution due to repetitive laser pulse heating witha convective boundary condition at the surface is obtained. A Laplacetransformation method is used when obtaining the analytical solution for theheat transfer equation. The effects of the pulse parameter(β/γ) and the Biot number (Bi) on the resulting temperature profilesfor the possible attainment of a steady temperature at the surface duringrepetitive laser pulse heating is explored. The consecutive pulses with decreasingintensities are employed in the analysis while Bi is varied as2×10-4⩽Bi⩽0.2. It is found that it is unlikely that the temperature profilefollows the pulse profile. The effect of Bi on the temperatureprofiles resulted from the repetitive pulses becoming significant when Bi⩾10-2.

Forced Convection Heat Transfer to Phase Change Material Slurries in Circular Ducts

Conclusions Expressions for the analytical temperature distribution and efŽ ciency of a heat pipe Ž n were derived and compared with experimental data. Two heat pipe Ž n cases were studied,  ush mounted and inserted into the object. The derived expressions are useful as a design tool. They allow the designer to compare heat pipe Ž ns to standard Ž ns before doing a detailed heat pipe design. Further researchcould focus on variations in heat pipe design and geometry.Thesecouldincludenonconstantpropertiesandboundary conditions.For this work, the wall cross-sectionalarea, the internal convectioncoefŽ cient, and the external convectioncoefŽ cient were assumed constant. The impact of these assumptions on accuracy should be investigated. It would also be interesting to extend the analysis to Ž ns in radiation environments.

Estimation of Orthotropic Thermal Conductivity of Honeycomb Material.

An experimental-computational hybrid system for measurement of thermal conductivity of orthotropic materials is developed. The system consists of two experimental parts and a finite element analysis part. Firstly, a temperature distribution generated by an uniform heating is measured with a thermal video system, and a thermal conductivity of Z direction is calculated. Secondary, a temperature distribution generated by a small area heating is measured with the system. In the final step, thermal transfer analyses simulated the experiment support efficient data, and thermal conductivity of in-plane directions are estimated by comparing between experimental and analytical temperature distributions. The orthotropic equivalent thermal conductivity of honeycomb materials given by this system agreed with the theoretical values.

A finite-element analysis of temperature distributions in spade drilling

The temperature generated in drilling has a critical influence on tool wear and tool life. This paper describes the use of the finite-element method for calculating the transient drill temperature for spade drills with arbitrary drill point angles. Increasing the drill point angle of the spade drill shortens the cutting edge and increases the drill temperature. The effects of the cutting speed and feed on the drill temperature responses have been investigated. Temperature calculations are compared with temperatures measured using the thermocouple method, the agreement being reasonable. The analytical drill temperature distributions can be used to evaluate the working conditions from the standpoint of the thermal analysis.

Analytical Solution of Heat Conduction in a Multi-Layer Orthotropic Cylinder Subject to Periodic and Asymmetric Heat Flux

The problem of heat conduction in a multi-layer two-dimensional orthotropic cylinder subject to asymmetric and periodic heat flux on the outer wall was solved analytically. The dimensional analysis of the problem revealed that the heat conduction through the cylinder is a function of the Biot number (Bi) and four non-dimensional parameters per layer. These layer-dependant parameters include: frequency ratio (α*m), thickness ratio (x*m), radial conduction ratio (K*rm), and tangential conduction ratio (K*tm). The derivation is valid for an arbitrary number of layers. The number of possible combinations increases dramatically with the number of layers. Thus as an example, the results for a cylinder composed from three layers, are presented and discussed. The results showed that the magnitude of heat conduction in a multi-layer orthotropic cylinder can be significantly different from those of an isotropic cylinder subject to the same externally imposed heat flux. The solution could be extended to an arbitrary varying imposed heat flux through the use of Fourier series and the principle of superposition. The solution also includes the analytical periodic temperature distribution across the cylinder. This could be used to study the effect of thermal stress fatigue in each layer and at the interface of adjacent layers.

Modelling of pulsed current weld microstructures

Microstructural modification caused by pulsed arc welding was investigated. An analytical temperature distribution model was used to identify process parameters for two series of experiments. Mild ...

Analysis of close-paced brush-fiber interfaces for spacecraft thermal management

A new interpenetrating-brush thermal interface is analyzed and evaluated for application to space-based thermal management. The interface consists of fibers attached to oppositely facing substrates. Each fiber is attached to one or the other substrate but not both. Heat transfer occurs through conduction and radiant exchange between interpenetrating fibers of opposite substrates. Linearization of the radiation terms results in an analytical temperature distribution along the fibers. The thermal performance of the interface is expressed in terms of a thermal effectiveness and an effective conductance-length ratio, both of which depend on the radiation/conduction number. For thin enough fibers, the heat transfer approaches that of the case in which all fibers are attached to both substrates. A fiber length (parameter-dependent) for optimum heat transfer is identified and agrees with previously published results. Such interfaces offer both high thermal effectiveness and compliance and are well suited for internal and external spacecraft applications. Nomenclature A = total jc-sectional area of fibers on one side, m2 Ah = base (substrate) area, m2 a = single fiber (fin) cross-sectional area, m2 d = fiber diameter, m £ = effectiveness factor F = view factor T = transfer function h = unit surface conductance, W/m2 • K K '= thermal conductance, kA/Ld, W/K

An Analytical Solution of a One-Dimensional Thermal Contact Conductance Problem With One Heat Flux and One Insulated Boundary Condition

Heat transfer across surfaces in imperfect contact occurs in many practical situations. Since the thermal contact conductance problem has appeared in the literature, substantial efforts have been made to estimate the thermal conductance across the interface. Some of the techniques recently developed of estimating thermal contact conductance are based on experimental temperature data at one or several interior positions of the contacting solids and the calculation of the temperature at these locations for known contact conductance. Consequently, an accurate and efficient method for computing temperature distributions because quite important. FDM and FEM are most widely used. However, for most contact conductance computation methods, only the temperatures at the contacting regions and several other positions near the interface need to be determined, so the general FDM and FEM are not particularly efficient in solving this problem. This paper presents an analytical temperature distribution solution to the one-dimensional symmetric system with heat flux on one outside surface and insulation on the other. This analysis provides a theoretical basis for transient measurement of thermal contact conductance. While it is common practice in steady-state measurements to use a water-cooled heat sink, it is possible to limit the transient solution to time interval prior tomore » any detectable temperature increase at the cold end. This effectively eliminates the need for water cooling and permits the use of an insulated boundary. The analytical solution to the mentioned problem obtained shows that for a symmetric system the temperature distribution solution includes two sets of distinct eigenfunctions.« less

On the determination of thermal phenomena during drilling—Part I. Analytical models of twist drill temperature distributions

Analytical temperature distributions along the cutting edge and on the flank face of a twist drill are described. The analysis is based on the assumption that the material being machined by the drill lips can be represented by a series of concentric elements. Jaeger's classical technique was used to obtain a steady state solution while a transient solution evolved from a closed-form approach to a semi-infinite solid having a constant surface heat flux. The theoretical approach also identified important physical quantities, such as the absorption coefficient of the work material, which affect the cutting temperatures. Experimental data are presented in Part II of this paper and are compared with other results that appear in the literature.

On the determination of thermal phenomena during drilling—Part II. Comparison of experimental and analytical twist drill temperature distributions

The analytical models, developed in Part I of this paper, for estimating the temperature distributions along the cutting edge and on the clearance face of a twist drill are evaluated using an experimental technique that measures average drill flank temperatures. While the transient model tends to overestimate the values of the average flank temperatures, especially during drilling to a one diameter hole depth, the temperatures predicted from the steady state model agree reasonably well with the experimental results. The difference between the analytical and experimental results varied with the physical and thermal properties of the powder metallurgy work materials used in this experiment. The analytical drill temperature distribution models are also compared with others found in the literature.

Variable conductance heat pipe performance analysis - Zero-to-full load

Test data for an aluminum/ammonia/nitrogen variable conductance heat pipe (VCHP) with a central core wick are presented and used to develop an analytical model for predicting evaporator temperature as a function of heat load and environmental conditions. These data show that VCHP performance at very low heat loads is dominated by heat losses from the so-called primary adiabatic section. The present formulation is an extension of an earlier VCHP model that was found suitable for engineering calculations over a heat-load range of about 20-100% of full load; the extended model presented here includes the operating range of 0-100% of full heat load. The extended model postulates a uniform condensation flux q0 in the nonadiabatic transport section, and a second but different uniform condensation flux ql in the active condenser. A set of nonlinear, transcendental, algebraic equations describes the performance of a simple VCHP. An incomplete definition of the two condensation fluxes requires a double-iteration procedure with respect to q0 and tc to solve the set of equations. A comparison of analytical temperature distributions and experimental data points shows that the present model is adequate for most engineering applications. Nomenclature Ac = internal cross-section area for vapor/gas transport Ar = reservoir surface area for heat transfer Aw = conduction cross section of wick plus wall c — local molar density of vapor and noncondensable gas mixture D = local diffusion coefficient of vapor/gas mixture h = local heat-loss coefficient (convection plus linearized radiation) H = local latent heat of vaporization kw = thermal conductivity of pipe wall and wick structure / = axial length tc = condensation front location Lj = nondimensional length, ^j/^3 mg = mass of noncondensabl e gas Mv = vapor molecular weight pg = gas partial pressure pv = vapor partial pressure q0 = condensation heat flux in primary transport section q = condensation heat flux in active condenser section

Transient analytical temperature distributions in cylindrical packed beds volumetrically heated by radiogenic decay energy

Analytical solutions are presented for the problem of the transient distribution of fluid and solid phase temperatures in a packed, porous, cylindrical particle bed with constant thermophysical properties. The packed particle bed is volumetrically heated by radiogenic decay energy from fission products. Flowing through the particle bed by forced convection is a single-phase fluid, either subcooled liquid or superheated vapor. The dynamic response of the packed bed is for low Reynolds numbers. In this case the transient will develop through the packed bed slowly enough for interphase heat transfer to keep the fluid and solid phase temperatures from having large differences. The two-dimensional, time-dependent Modified Dispersion-Concentric Model (D-C model) is used in the analysis of this problem. The D-C model energy equations are solved using Green's function. The mathematical solution characteristics for the transient fluid and solid phase temperature distributions are presented for three different volumetric heat generation terms: two-dimensional, time-dependent; simplified two-dimensional, time-dependent; and two-dimensional, time-independent. Using the two time-dependent volumetric heat generation terms, a comparison is presented for the transient fluid and solid phase temperatures and the radioactive decay heat power coming from the fission products in the particles.