Determination of temperature field created by planar heat source in a solid body consisting of three parts in mutual thermal contact

We present a solution of, a one-dimensional heat conduction equation for a solid body consisting of three parts. The exterior parts possess identical thermal properties. The thermal properties of the inner part differ from the outer ones. The temperature field is created by a planar heat source located between one outer and one inner part. This solution can be used in measurements of thermal properties of an inner body by the pulse transient method assuming that the thermal properties of outer bodies are known.     

On estimating thermal diffusivity using analytical inverse solution for unsteady one-dimensional heat conduction

A modified procedure for calculating the thermal diffusivity of solids based on temperature measurements at two points and the semi-infinite boundary condition is presented. The method makes use of a solution to the unsteady one-dimensional inverse heat conduction problem for the semi-infinite solid. The procedure gives accurate results based on temperature changes produced by an arbitrary fluctuating heat flux source at the boundary.     

A thermal resistance analysis on forced convection with viscous dissipation in a porous medium using entransy dissipation concept

The analytical solution of a two-equation model presented in an earlier study is examined. Heat transfer characterization is classified into two regimes which are dominated by fluid conduction or solid conduction and interstitial heat exchange, respectively by using the entransy dissipation concept. The computed pattern of variation of thermal resistance with shape factor S at a fixed Brinkman number for a low ratio of the fluid to solid effective thermal conductivities implies the occurrence of temperature gradient bifurcation as S decreases. Therefore, the thermal diffusion term in the fluid phase in the two-equation model is not negligible for both regimes.     

Application of homotopy perturbation method and inverse prediction of thermal parameters for an annular fin subjected to thermal load

In this work, application of the homotopy perturbation method (HPM) and an inverse solution for estimating unknown thermal parameters such as the variable thermal conductivity parameter (β), the thermogeometric parameter (K), and the nondimensional coefficient of thermal expansion (χ) in an annular fin subjected to thermal stresses is presented. Initially, to obtain the nondimensional temperature distribution from the heat equation, the forward method is employed using an approximate analytical solution based on HPM. Thereafter, a closed form solution for the temperature-dependent thermal stresses is obtained using the classical theory of thermoelasticity coupled with HPM solution containing the temperature distribution. Next, for satisfying a particular stress criterion which makes relevance in selecting appropriate configurations for selecting the finned system, unknown thermal parameters are obtained using an inverse approach based on the Nelder–Mead simplex search minimization technique. The objective function is taken as the sum of square of the residuals between the measured stress field and an initially guessed value which is updated iteratively. It is found that more than one type of temperature distribution may yield a given stress distribution, thereby giving rise to different fin efficiencies. The agreement between the actual and the predicted results was found to be satisfactory.     

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.     

Influence of thermal sensitivity of the materials on temperature and thermal stresses of the brake disc with thermal barrier coating

The time-dependent frictional heating of a disc with applied thermal barrier coating (TBC) on its working surface was investigated. To determine the temperature fields in the coating and the disc a one-dimensional friction heat problem during braking was formulated, with taking into account the dependence of thermal properties of materials from temperature. A model was adopted for materials with a simple non-linearity, i.e. materials whose thermal conductivity and specific heat are temperature dependent, and their ratio – thermal diffusivity is constant. The linearization of the corresponding boundary-value heat conduction problem was made by the Kirchhoff transformation and the linearizing multipliers method. A numerical-analytical solution to the obtained problem was found by Laplace transform method. Knowing the temperature distributions, quasi-static thermal stresses in the strip (TBC) with taking into account change in temperature mechanical properties, were determined. The distribution of temperature and thermal stresses in the strip made from ZrO₂ deposited on the UNS G51400 steel disc, was investigated.     

Influence of thermal stresses on thermal diffusion of hydrogen

Thermal diffusion of hydrogen atoms in zirconium taking into account thermal stresses is investigated. As mathematical model the steady-state temperature in the hollow cylinder is considered. The first invariant of the tensor of thermal stresses in the hollow cylinder has a logarithmic dependence on the radial coordinate. Such dependence permits an exact analytical solution of diffusion kinetics problem in view of thermal stresses.     

Simple measurement of thermal diffusivity and thermal conductivity using inverse solution for one-dimensional heat conduction

A new method is proposed for measuring thermal diffusivity and thermal conductivity simultaneously using the inverse solution for one-dimensional unsteady heat conduction. Unlike previous method proposed by authors, the new procedure does not require the temperature measurement for a long time duration after the temperature starts changing at a sensor position; and then a selection of time duration can be chosen such that the measured temperature change becomes large enough to ensure a required accuracy for the estimated values of thermal diffusivity and thermal conductivity. The measurement is usually completed within 3 min until the temperature rise at the thermocouple position reaches a certain temperature level, for example 1% of an error level. This method has the additional advantage of being independent of the surface condition, except for the requirement of two or three sensing positions in the material. The accuracy of the estimated values is also similar to the error level of the sensor at these positions.     

Inverse identification of temperature-dependent thermal conductivity via genetic algorithm with cost function-based rearrangement of genes

A new application of the cost function-based rearrangement of genes (proposed by Liu (2008) [1]) is presented in this paper through the genetic algorithm-based solution of the inverse heat conduction problem of identifying the temperature dependent thermal conductivity of a solid material using transient temperature histories. The inverse problem was defined according to the evaluation of the BICOND thermophysical property measurement method. Through the solution of the inverse problem (using simulated measurements), different approaches of the application of the rearrangement of genes were studied and compared. Application of the rearrangement significantly improved the convergence performance and accuracy of the inverse solution compared to a real-valued genetic algorithm, which was adapted to the problem by the authors. In the algorithm that performed best, the rearrangement was applied in an approach different from Liu’s. The effect of random noise added to the temperature history and the effect of regularization was also studied. With significant improvement in computational efficiency, the proposed algorithm is likely to be very effective in evaluation of real measured temperature histories to determine thermophysical properties.     

New challenge in advanced thermal energy transportation using functionally thermal fluids

The present review article presents the current status of some researches on thermal energy transportation using functionally thermal fluid, which is a mixture of heat transfer medium like water and other material with or without phase change like a paraffin wax as a latent heat storage material. This functionally thermal fluid offers attractive opportunities for thermal energy transportation and heat transfer enhancement of heat exchanger. This article describes classification and characteristics of functionally thermal fluids and their application. Referring to functionally thermal fluid for the usage of sensible heat, some visco-elastic fluids for flow drag reduction in a thermal energy transport system such as aqueous polymer solution and surfactant solution are mentioned. On the other hand, this article describes heat transfer and hydrodynamic characteristics of some phase change slurries like ice slurry, phase change microemulsion slurry, phase change microencapsule slurry, clathrate slurry and shape-stabilized paraffin and polyethylene pellets as functionally thermal fluids using latent heat between solid and liquid phases. Finally, it leads to the conclusion that some functionally thermal fluids are very useful for the advanced thermal energy transportation and heat exchanger systems.     

Series solution of convective radiative conduction equation of the nonlinear fin with temperature dependent thermal conductivity

In this study, differential transform method (DTM) is used to evaluate the analytical solution of the nonlinear fin problem with temperature dependent thermal conductivity. Results are presented for the dimensionless temperature distribution and fin efficiency for a range of values of the problem parameters. Using DTM, the differential equation and related boundary conditions are transformed into a recurrence set of equations and finally, the coefficients of power series are obtained based on the solution of this set of equations. Results of this method are compared with the variational iteration method (VIM) and numerical solutions. Here, it is shown that the results of DTM are more accurate than the VIM with lesser calculation cost, which is the main innovation of the current study.     

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation,Part I: Methodology

This work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.     

Determination of the thermal properties of ceramic sponges

The knowledge of thermal properties of technical components or internals in chemical reactors is often a key characteristic for planning and designing chemical engineering processes. As an alternative to packed beds or packings, sponges turned out to be used in new application fields in chemical and process engineering. Therefore an experimental study was performed to investigate the two-phase thermal conductivity of solid ceramic sponges made of alumina, mullite and oxidic-bonded silicon carbide (OBSiC) at moderate temperatures. A two-dimensional model is used for analysing the measured temperature profiles and for calculating the thermal conductivity. It can be observed, that the thermal conductivity increases with decreasing porosity and is nearly constant when the pore size (ppi number) is varied. The thermal conductivity data are modelled by an approach similar to the well known Krischer model. Compared to a packed bed of spherical particles, the values of the thermal conductivity of sponges turn out to be about five times higher.     

Numerical simulation of thermal loading produced by shaped high power laser onto engine parts

Recently a new method for simulating the thermal loading on pistons of diesel engines was reported. The spatially shaped high power laser is employed as the heat source, and some preliminary experimental and numerical work was carried out. In this paper, a further effort was made to extend this simulation method to some other important engine parts such as cylinder heads. The incident Gaussian beam was transformed into concentric multi-circular patterns of specific intensity distributions, with the aid of diffractive optical elements (DOEs). By incorporating the appropriate repetitive laser pulses, the designed transient temperature fields and thermal loadings in the engine parts could be simulated. Thermal–structural numerical models for pistons and cylinder heads were built to predict the transient temperature and thermal stress. The models were also employed to find the optimal intensity distributions of the transformed laser beam that could produce the target transient temperature fields. Comparison of experimental and numerical results demonstrated that this systematic approach is effective in simulating the thermal loading on the engine parts.     

Transient thermal behavior of porous media under oscillating flow condition

An analytical characterization of the heat transfer in an oscillating flow through a porous medium is presented in this work. Based on a two-equation model, two important dimensionless parameters are identified as the ratio of the thermal capacities between the solid and fluid phases and the ratio of the interstitial heat conductance between the phases to the fluid thermal capacity. The analytic solutions are obtained for both the fluid and solid temperature variations, and the heat transfer characteristics between the phases are classified into four regimes. In addition, a criterion for the validity of the local thermal equilibrium is suggested in a simple form as the ratio of the two time scales intrinsically involved in any transient heat transfer in porous media, namely the time scale relevant to the thermal inertia of porous media and the time scale pertinent to the transient variation of the boundary condition.     

Experimental determination of the effective thermal capacity function and other thermal properties for various phase change materials using the thermal delay method

The recently presented thermal delay method is an improved version of the well-known T-history method, which is widely used for thermal properties measurement of phase change materials (PCM). The most important difference between the thermal delay and the T-history methods is that the former is based on the use of thermal delay (i.e. temperature difference) between PCM and a reference fluid at any specified time while the latter makes use of their time delay at any specified temperature. Although the thermal delay method has been documented in our previous publication, measurements are performed of the known and indisputable values of ethyl alcohol thermal capacity and the latent heat of the double distilled water (WFI), which confirm the accuracy of the method. Additional comparisons with values provided by PCM producing companies show disagreements lower than 1.7%. The main volume of measurements of the present study includes the following thermal properties of various practically interesting PCM: (a) the temperatures at the ends of the two-phase region; (b) the liquid and solid PCM thermal capacities; (c) the phase change heat; (d) the heat storage capacity during any specified temperature range; and (e) the effective thermal capacity function, which is a very important and useful property for practical applications. The above function is provided for each one of the PCM examined in the form of diagrams, as well as in the form of analytical expressions derived by curve fitting to the processed experimental values. All measurements were repeated 20 times and the results were averaged in order to minimize errors from accidental incidents.     

Phase change characteristics of ethylene glycol solution‐based nanofluids for subzero thermal energy storage

Nanofluids, particularly water‐based nanofluids, have been extensively studied as liquid–solid phase change materials (PCMs) for thermal energy storage (TES). In this study, nanofluids with aqueous ethylene glycol (EG) solution as the base fluid are proposed as a novel PCM for cold thermal energy storage. Nanofluids were prepared by dispersing 0.1–0.4 wt% TiO₂ nanoparticles into 12, 22, and 34 vol.% EG solutions. The dispersion stability of the nanofluids was evaluated by Turbiscan Lab. The liquid–solid phase change characteristics of the nanofluids were also investigated. Phase change temperature (PCT), nucleation temperature, and half freezing time (HFT) were investigated in freezing experiments. Subcooling degree and HFT reduction were then calculated. Latent heat of solidification was measured using differential scanning calorimetry. Thermal conductivity was determined using the hot disk thermal constant analyzer. Experimental results show that the nanoparticles decreased the PCT of 34 vol.% EG solution but minimally influenced the PCT of 12 and 22 vol.% EG solutions. For all nanofluids, the nanoparticles decreased the subcooling degree, HFT, and latent heat but increased the thermal conductivity of the EG solutions. The mechanism of the improvement of the phase change characteristics and decrease in latent heat by the nanoparticles was discussed. The nanoparticles simultaneously served as nucleating agent that induced crystal nucleation and as impurities that disturbed the growth of water crystals in EG solution‐based nanofluids. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental investigation and development of new correlations for thermal conductivity of CuO/EG–water nanofluid

In the present study, the thermal conductivity of CuO/EG–water nanofluid in different solid concentrations and temperatures has been experimentally investigated. Using a two-step method, the nanofluid has been produced in different solid concentrations ranging from 0.1% to 2% and temperatures up to 50 °C. The thermal conductivity of the nanofluid has been experimentally measured using the KD2 Pro instrument. Based on the experimental data, new correlations for predicting the thermal conductivity of CuO/EG–water at different temperatures have been proposed. The results show that with the increase of the solid concentration, the thermal conductivity of the nanofluid increases. Furthermore, the thermal conductivity of the nanofluid increases while the temperature increases. This increase is by far more noticeable in higher solid concentrations compared with lower solid volume fraction. This means that it is the presence of nanoparticles in the base fluid that causes the increase of the effect of temperature on the thermal conductivity.     

Thermal performance of an MHD radiative Oldroyd‐B nanofluid by utilizing generalized models for heat and mass fluxes in the presence of bioconvective gyrotactic microorganisms and variable thermal conductivity

The current paper analyzes the thermal and concentration attributes with the temperature‐dependent mass diffusion coefficient and thermal conductivity for the flow of an Oldroyd‐B nanoliquid over a stretchable configuration using the Buongiorno model under the application of boundary layers. The mechanisms of heat and mass transport are modeled by using the revised definitions of heat and mass fluxes. Mathematical expressions for the conservation laws are transformed into ordinary differential expressions by making the appropriate changes. The resulting complexly structured expressions are handled via an optimal homotopy procedure. The impact of influential variables on the desired solutions is plotted, tabulated, and discussed in detail. Comparative analysis of the thermal wall flux coefficient, concentration flux coefficient, density magnitude of the motile microorganisms, and reduced dimensionless stresses with already published research as a limiting case of this exploration is presented for the validity of the proposed scheme, and an excellent agreement is observed, which confirms the reliability of the homotopic solution.     

Minimization of thermal resistance in an air cooled porous matrix made up of solid spheres with heat generation

In this paper an analytical model was developed to minimize the thermal resistance of an air cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of local thermal equilibrium. The analytical solution of the optimum sphere diameter was found to be independent of the heat generation rate of the solid spheres, but was dependent on the applied pressure drop and fluid properties. The analytical model compared very well to a numerical model found in a computational fluid dynamics code when air and liquid water properties were used for the fluid phase and wood and silica/sand properties were used for the solid phase.