Variation Of Thermal Diffusivity Research Articles

Soret and dufour impacts on radiative power-law fluid flow via continuously stretchable surface with varying viscosity and thermal conductivity

The intricate dynamics of mixed convective thermic and species transport in a power-law flowing fluid through a continuously stretched surface are investigated. The uniqueness of this study lies in the consideration of fluid variable thermic conductivity and viscosity, which introduces a higher degree of realism into the analysis. The transformation of similarity is used to transform the fundamental governing equations, and after that, the set of equations is processed numerically utilizing a non-similarity local approach. Furthermore, the effects of Soret and Dufour represent the cross-diffusion phenomena, accounting for the energy exchange with the surroundings. These factors collectively influence the stretching surface’s gradient velocity, affecting the thermal and species concentration rates. The findings offer a comprehensive understanding of these complex interactions, paving the way for optimizing thermic and species transport processes in various industrial applications. This study, therefore, holds significant potential for enhancing efficiency and performance in relevant industrial sectors. The main terms are the combinations of Dufour and Soret numbers that significantly impact the flow rate profile and mass transfer field. The coupled study of the nonlinear velocity, energy distribution and chemical mixture variance made the study more impactful in practicality. Skin friction variation shows limited impact with variations in the Soret number. The enhanced thermal gradient results in improved non-similarity parameters, yet it demonstrates a decrease with an increase in variable thermal diffusivity. There is a decrease in the temperature gradient as the buoyancy term reduces, while an increase is observed with changes in the Prandtl number. Similarly, the Nusselt number experiences a comparable impact due to changes in the Soret number.

Microstructure-thermal transport property correlation after cold/cryo rolling deformation of alloy D9

ABSTRACT Plastic deformation alters the microstructure of a material due to the formation of twins, high density of dislocations and strain-induced phases and grain refinement. Such microstructural modifications can affect thermal transport properties of a material. In this work, variation in thermal diffusivity (TD) was investigated in cold worked (CW) and cryo rolled (CR) alloy D9 (ASTM designation A771/UNS S38660), using laser flash analyser after 20–80% thickness reduction. Deformed samples were characterised using XRD and microscopy techniques for structure and microstructure modifications besides correlating with the change in hardness. Temperature dependence of thermal diffusivity was measured from room temperature up to 1273 K. Microstructural features confirmed the formation of deformation-induced martensite in CR specimen. This was accompanied by up to 172% increase in hardness in 80% CR compared to annealed specimen. The dislocation density estimated from XRD structural profile showed an increase with the percentage of deformation. For all specimens, thermal diffusivity showed an increasing trend with temperature but decreased with deformation. The reduction in thermal diffusivity was non-negligible beyond 40% thickness reduction for all deformed specimen and was substantial specifically for CR alloy D9.

Analysis of axisymmetric thermoelastic diffusive half-space with variable material properties using hyperbolic two-temperature model

The aim of the current study is to investigate the variable thermal conductivity and diffusivity impact on the transient response of an axisymmetric thermodiffusive elastic half-space under axisymmetric thermal, mechanical, and concentration loads in the light of hyperbolic two-temperature generalized fractional thermoelastic diffusion model. With the help of Kirchhoff’s transform, the governing equations are converted into linear form. The resulting equations are solved by imposing the combined Laplace–Hankel transform. In converted space, the solutions for different field quantities are presented in compact form. The copper material is considered for numerical computation. By employing a mathematical inversion procedure, the solutions are converted into the original space. Numerically computed solutions for various physical quantities are illustrated in the form of graphs to show the impact of variable thermal conductivity and diffusivity, hyperbolic two temperature, and fractional parameters. Validation of the obtained results is also presented.

Analysis of a hollow cylinder with variable thermal conductivity and diffusivity by fractional thermoelastic diffusion theory

Based on fractional thermoelastic diffusion theory, an infinite hollow cylinder with variable thermal conductivity and diffusivity is studied. The inner surface of the hollow cylinder is free and subjected to thermal and chemical shocks, while the outer surface is fixed and adiabatic. The closed forms of dimensionless displacement, temperature, chemical potential, stress, and concentration in the Laplace transform domain are given by eigenvalue method. These physical quantities are then numerically obtained through the inverse Laplace transformation. The effects of fractional order parameters, variable thermal conductivity and diffusivity on these quantities are discussed. The present model may be helpful for better understanding the thermoelastic diffusion problems in actual engineering.

Thermo‐physical characterisation of natural rocks and impact analysis of variations in their thermo‐physical properties on thermal storage performance

AbstractIn this study, the thermal characterisation of natural rock samples from Zimbabwe for low‐temperature industrial thermal energy storage (TES) applications was carried out. Thermal stability, specific heat capacity, thermal diffusivity, thermal conductivity and density were determined. Variations in these parameters were evaluated and their impact on thermal storage performance was analysed. Basalt and dolerite samples from different locations were found to have average specific heat capacities of 826 and 853 J/kg K, respectively, at room temperature. Insignificant variations were observed with differences of 3.4% for basalt and 1.7% for dolerite samples. Also, negligible differences of 0.3% and 0.7% in densities for rocks of the same type but of different origins were obtained for basalt and dolerite samples, respectively. However, significant variations in thermal diffusivity of all the igneous and metamorphic samples were observed with quartzite rock exhibiting the highest value of 2.1 × 10−6 m2/s, while the values for the other samples range from 0.9 × 10−6 to 1.6 × 10−6 m2/s. This implies that the thermal efficiency of sensible TES systems that use different or the same rock types from different locations can be significantly high to be overlooked. Thermo‐gravimetric analysis results revealed that the rock samples studied have good thermal stability for low‐temperature heat storage applications.

Universal thermal profiles with polynomial thermal diffusivity in a channel flow

Fluids used in heat transfer applications range in a wide spectrum of Prandtl numbers. An aspect that is commonly neglected is the influence of variable thermal diffusivity in turbulent heat transfer. A mathematical model was developed in the past few years [1, 2] to address the influence of the variable thermal diffusivity on the turbulent heat transfer. In this work we explore the influence of the friction Reynolds number Reτ, the molecular Prandtl number Pr and the coefficients λi+ of the temperature dependent thermal diffusivity, up to the fourth-order, to the Universal Profiles in a channel flow. This choice minimizes the influence of the boundary and initial conditions. The numerical simulations in the limit of constant thermal diffusivity are validated against literature DNS data. The results show that the influence of the friction Reynolds number is limited, while high molecular Prandtl numbers increase the fluctuating thermal diffusivity heat flux. The factor that influences the solution the most is the thermal diffusivity coefficients, showing that, in certain conditions, the fluctuating thermal diffusivity heat flux is non-negligible even for low Prandtl numbers. The results show that the terms introduced by the model proposed in [1, 2] are non-negligible when the thermal diffusivity in the boundary layer doubles compared to its bulk value. It is suggested that the model presented in [1, 2] could be particularly suitable in cryogenic applications.

Phase change in a one-dimensional functionally graded material

Functionally graded materials (FGMs) are a class of materials with engineered microstructure to achieve spatial variation in properties so as to serve a desired function. While FGMs have been well-researched for their structural properties, there is a lack of investigation of FGMs in solid-liquid phase change heat transfer processes. A well-designed functionally graded phase change material (FG-PCM) may overcome some of the well-known limitations of the phase change process. In order to investigate this possibility, this work presents a theoretical model to predict phase change propagation in a one-dimensional FG-PCM containing an arbitrary spatial variation in thermal conductivity, thermal diffusivity and latent heat. The problem is solved using the method of eigenfunction expansion to determine the temperature distribution, wherein, spatial variation in thermophysical properties listed above is accounted for by deriving a first-order matrix ordinary differential equation in the coefficients of the series solution. Results are found to correctly reduce to the well-known Stefan solution under special conditions. The impact of variation in thermophysical properties is investigated in detail. It is found that while spatial variation in thermal conductivity and latent heat has a significant effect on the rate of phase change, the impact of the thermal diffusivity function is negligible for realistic values of the Stefan number. The effect of the Stefan number governing this problem on the rate of melting is investigated. The nature of phase change under linear (1+aξ), polynomial (1+aξn) and exponential (eaξ) functional forms of thermophysical properties is investigated. It is shown that an appropriate choice of these spatial functions may help overcome the well-known self-limiting nature of phase change and produce a nearly-linear phase change propagation curve. For example, results show 33% increase in phase change propagation for a linear (1+5ξ) variation in thermal conductivity compared to baseline. The theoretical tools developed here may help design and optimize functionally graded PCMs towards improved phase change heat transfer in applications of practical interest.

Variable thermal conductivity and mass diffusivity effects in a free convective flow of doubly stratified non-darcian porous medium over a vertical plate

The research in this article is carried out to study incompressible and unsteady free convective flow on a semi-infinite isothermal vertical plate in a doubly stratified non-Darcian porous media with variable mass diffusivity and variable thermal conductivity. The governing non-linear partial differential equations of flow were calculated by applying an implicit finite difference scheme of Crank-Nicolson type. Various parametric impacts on concentration profiles, temperature, velocity, as well Sherwood number, Nusselt number and skin friction, were examined and presented in graphs. It is examined that there exists a significant temperature decrease for high Darcy number in stratified fluids. Also, it is detected that the presence of stratification produces a considerable drop in skin friction while increases the mass and heat transfer rate. Comparison of current outcomes well agreed with the available solutions.

Innovative stochastic finite difference approach for modelling unsteady non-Newtonian mixed convective fluid flow with variable thermal conductivity and mass diffusivity

A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. One part finds the solution for the deterministic equation, and the second part is the numerical approximation for the integral part of the Wiener process term in the stochastic partial differential equation. The scheme’s stability and consistency in the mean square sense are also ensured. Additionally, a respective mathematical model of the boundary layer flow of Casson fluid on a flat and oscillatory plate is formulated. Wiener process terms perturb the model to be studied. This scheme will be solved in contexts including deterministic and stochastic. The influence of different parameters on velocity, temperature, and concentration profiles is demonstrated in various graphical representations. The main objective of this study is to present a reliable numerical approach that surpasses the limitations of traditional numerical methods to analyze non-Newtonian mixed convective fluid flows with varying transport parameters. Our objective is to demonstrate the capabilities of the new stochastic finite difference scheme in enhancing our comprehension of stochastic fluid flow phenomena. This will be achieved by comprehensively examining its mathematical foundations and computer execution. Our objective is to develop a revolutionary method that will serve as a valuable resource for scientists and engineers studying the modeling and understanding of stochastic unstable non-Newtonian mixed convective fluid flow. This method will address the challenges posed by the fluid’s changing thermal conductivity and mass diffusivity.

Reflection of plane waves in a nonlocal double poroelastic semiconducting medium with variable thermal conductivity and mass diffusivity

AbstractThe present investigation is concerned with the reflection phenomena of plane waves in a homogeneous, isotropic, nonlocal, photothermoelastic semiconducting medium under the effects of double porosity, variable thermal conductivity and mass diffusivity. The formulation is applied to generalized thermoelasticity based on the Lord–Shulman theory. The problem is solved analytically and it is shown that there exist six coupled longitudinal waves in addition to an independent transverse wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have been calculated analytically and computed numerically for a specific material with the help of MATLAB programming. The numerical results of reflection coefficients are presented graphically to show the effects of double porosity, photothermal transport process, nonlocality, variable thermal conductivity and mass diffusivity. It is verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence and there is no energy dissipation at the boundary surface. Some special cases of interest have also been inferred from the current investigation.

Local-scale heterogeneity of soil thermal dynamics and controlling factors in a discontinuous permafrost region

Abstract In permafrost regions, the strong spatial and temporal variability in soil temperature cannot be explained by the weather forcing only. Understanding the local heterogeneity of soil thermal dynamics and their controls is essential to understand how permafrost systems respond to climate change and to develop process-based models or remote sensing products for predicting soil temperature. In this study, we analyzed soil temperature dynamics and their controls in a discontinuous permafrost region on the Seward Peninsula, Alaska. We acquired one-year temperature time series at multiple depths (at 5 or 10 cm intervals up to 85 cm depth) at 45 discrete locations across a 2.3 km2 watershed. We observed a larger spatial variability in winter temperatures than that in summer temperatures at all depths, with the former controlling most of the spatial variability in mean annual temperatures. We also observed a strong correlation between mean annual ground temperature at a depth of 85 cm and mean annual or winter season ground surface temperature across the 45 locations. We demonstrate that soils classified as cold, intermediate, or warm using hierarchical clustering of full-year temperature data closely match their co-located vegetation (graminoid tundra, dwarf shrub tundra, and tall shrub tundra, respectively). We show that the spatial heterogeneity in soil temperature is primarily driven by spatial heterogeneity in snow cover, which induces variable winter insulation and soil thermal diffusivity. These effects further extend to the subsequent summer by causing variable latent heat exchanges. Finally, we discuss the challenges of predicting soil temperatures from snow depth and vegetation height alone by considering the complexity observed in the field data and reproduced in a model sensitivity analysis.

A WILLIAMSON NANOFLUID WITH MOTILE MICROORGANISMS ACROSS A VERTICAL EXPONENTIALLY STRETCHING POROUS SHEET WITH VARYING THERMAL CHARACTERISTICS

The present work demonstrates a boundary layer movement of an incompressible non-Newtonian Williamson nanoliquid. The boundary layer is around an exponentially stretching permeable vertical surface. Moving motile microorganisms are implicated in the movement throughout a permeable medium considering modified Darcy law. The buoyancy-driven flow is presumed, where the density is expressed as being multiplied by gravity and chosen as a linear function of heat, nanoparticle, and microorganism concentrations. Analogous to the exponentially stretching sheet, an exponential variable magnetic strength is taken normal to the surface. Variable thermal conductivity and mass diffusivity are considered together with chemical reactions. The motivation for this study arises from the involvement of microorganisms in the flow and the contribution of its density equation with the velocity, temperature, and nanoparticles system of equations with suitable boundary restrictions. The fundamental governing scheme of nonlinear partial differential equations (PDEs) is transferred to ordinary ones (ODEs) by employing convenient similarity transforms. These equations are analyzed by the homotopy perturbation method (HPM). Therefore, a major objective graphical formation of the distributions is concluded to recognize the impacts of the produced nondimensional physical factors. Some important physiognomies are concluded from the results. The nanoparticle distribution enhances most of the effective parameters and in turn improves heat transmission, which is a good finding that can be useful in several applications. Microorganisms tend to collect with the growth of the Lewis number and infinity value, whereas its condensation damps with the rise of the bioconductivity and the Peclet number. Those results can be useful in identifying factors that help to get rid of microbes, viruses, and harmful bacteria from surfaces.

Non-destructive estimation of mechanical properties in Usibor® 1500 via thermal diffusivity measurements: A thermographic procedure

The study investigated the anti-correlation between thermal diffusivity and Ultimate Tensile Strength (UTS) in Usibor® 1500 steel. The non-destructive pulsed laser spot thermography technique was used to analyze fifteen boron steel specimens with varying bainite/martensite phase percentages, while the UTS was measured through uniaxial tensile tests. A 23 % thermal diffusivity difference was found between fully martensitic and fully bainitic structures, with UTS varying by around 90 %. The strong anti-correlation was confirmed (Spearman coefficient −0.98) and an empirical power-law equation was derived to estimate UTS based on thermal diffusivity variations. The approach showed an R-squared value over 0.84, providing a non-destructive thermographic procedure for UTS estimation in Usibor® 1500 steel, offering valuable material property insights.

Rotating MHD Williamson nanofluid flow in 3D over exponentially stretching sheet with variable thermal conductivity and diffusivity

Nanofluids are a topic of great interest for researchers due to their remarkable performance in most heat transport applications. Williamson fluids have also gained importance due to their numerous uses in many fields. Exponentially stretching sheets with variable thermal conductivity and diffusivity is another topic of importance in fluid mechanics. Moreover, rotating MHD fluids have various applications in the industry. So, in particular, we would study rotating MHD Williamson nanofluid having variable diffusivity and thermal conductivity flowing above an exponentially stretching sheet. In this work, we proposed modified wavelets method to find the solutions of the developed mathematical model of the considered problem. The effectiveness of the developed scheme is certified by the help of tables and graphs. It is worthy to point out that the skin friction coefficient in x and y direction increases gradually against the selection of magnetic field effects and Williamson parameter. Tabular study presented to show that the suggested algorithm is convergent, and it can be extended to more physical models on non-Newtonian type.

Heat extraction calculations for deep coaxial borehole heat exchangers: matrix analytical approach

SUMMARY Deep boreholes represent a source of clean energy. Therefore, effective calculations of potential extraction of heat from boreholes for realistic models of the Earth’s crust with variable thermal conductivity and diffusivity are needed. We deal with heat extraction in a quasi-steady state from coaxial boreholes where downward and upward flows of pumped fluid (water) are separated by an inner pipe and connected only at the bottom. We first obtain theoretical estimates of heat extraction for a thermally isolated inner pipe and a model of the ground with constant thermal diffusivity and conductivity. Then, we develop a new analytical matrix method for a general layered ground model that enables us to include depth-dependent ground properties as well as heat exchange between the downward and upward flows of fluid in the borehole. Our straightforward and fast approach is thus suitable for various parametric studies or as a tool for benchmarks of numerical software. A key role in heat extraction from coaxial boreholes is played by the inner-pipe thermal resistance. We apply our method to the parametric study showing the dependence of pumped water temperature and total heat extraction from the borehole on realistic borehole geometries under different amounts of water pumping. The calculations are performed for a 3 km deep borehole as the representative of present deep boreholes used for extraction of geothermal energy and for a 10 km deep borehole. Drilling of such a superdeep borehole has just started in China and our results demonstrate potential limits of geothermal energy extraction from such great depths.

Significance of Hall current and Ion slip in a three-dimensional Maxwell nanofluid flow over rotating disk with variable characteristics and gyrotactic microorganisms

In varied practical situations, the assumption of constant values are considered for approximations or simplifications to make computations more adaptable. Nevertheless, when there is a requirement for precision, accuracy, and exact results, the consideration of variable characteristics becomes essential. Considering the same, the article’s uniqueness lies in studying variable thermal conductivity, variable viscosity, and variable mass diffusivity as governing factors. This study analyzes the movement of a three-dimensional Maxwell nanofluid across a rotating deformable disk deliberating the Hall current and Ion slip impact. In addition, the analysis seeks to boost the stability of the nanofluid flow by incorporating the impact of bio-convection. The velocity slip and convective constraints are enforced at the boundary. The Von Karman transformations are engaged, and accordingly, a numerical solution is computed. Graphical illustrations are used to highlight the significant effects of the problem. The findings revealed that the fluid velocity decreases in both the azimuthal and radial directions for different estimations of the variable viscosity and Deborah number. Additionally, the fluid velocities in the azimuthal and radial directions exhibit opposite trends for Hall current and Ion slip. The endorsement of the presented results is also provided in this study.

Stability analysis of radiative-magnetive Ag −MoS 2/water hybrid nanofluid flow due to a permeable exponential surface with variable thermal conductivity, mass diffusivity and binary chemical reaction: an entropy generation

ABSTRACT This investigation concentrated on the /water hybrid nanofluid to solve the problem of heat-mass transmission across a permeable stretching/contracting sheet with the impacts of radiant heat and inclined magnetic force field. Here, we additionally take into account hybrid nanofluids with variable thermal conductivity, variable mass diffusivity, Joule dissipation, binary chemical reactions with velocity, and thermal and solutal slip conditions. Before being numerically solved by the MATLAB function bvp4c, the controlling PDE is converted into nonlinear coupled ordinary differential equations by appropriate similarity transformation. The findings also point to the presence of dual solutions in the stretching/contracting sheet region for a given value of the mass suction parameter, with stable upper branch solution and unstable lower branch solution. As a result of the velocity and temperature gradients, the entropy generation equation is constructed. The effects of the selected parameters are discussed and visually displayed for the velocity, temperature, concentration, skin friction coefficient, local Nusselt number, and Sherwood number. Due to some selected flow parameters, the pattern of entropy formation and assessment of the Bejan number are anticipated. Furthermore, it is discovered that when the volume percentage of nanoparticles increases, the Sherwood number decreases, and the skin friction coefficient increases with the rate of heat transmission. The Bejan number and entropy generation rate both increase with the volume proportion of nanoparticles and the radiant heat parameter, according to the visual simulations created using the present model.

Modified thermal and solutal fluxes through convective flow of Reiner-Rivlin material

Heat transport in mixed convection Reiner-Rivlin liquid flow due to stretching cylinder is addressed. Cattaneo-Christov double diffusive relation is utilized to discuss heat and solutal transport features. Variable thermal conductivity and mass diffusivity impacts are incorporated. Adequate transformations are used to reduce non-linear differential expressions for dimensionless expressions. The given non-dimensional expressions are solved through implementation of Optimal homotopy analysis technique (OHAM). Physical features of fluid flow, concentration and temperature against influential parameters are examined. Clearly higher mixed convection parameter boost the liquid flow. Decay in temperature is detected against thermal relaxation time. Similar impact of temperature is witnessed by curvature and thermal conductivity variables. Velocity enhances against Reiner-Rivlin material variable. Decline in concentration is detected for higher Schmidt number. Concentration boosts against mass diffusivity parameter. Higher solutal relaxation time parameter leads to decline concentration. Reduction in temperature is noticed for Prandtl number whereas opposite behavior witnessed for heat transport rate. An increment in mass transport rate occurs for mass diffusivity and solutal relaxation time variables.

Thermoelastic interactions in a rotational medium having variable thermal conductivity and diffusivity with gravitational effect

ABSTRACT This research work is related with the investigation of thermodynamical interactions for a rotational thermodiffusive medium including gravitational effect. To differentiate it from existing works, thermal conductivity and mass diffusivity are considered as variables. The governing equations are formulated under Green–Lindsay (G-L) theory by using Kirchhoff's transformation. Thermal and chemical shocks of constant intensity are imposed on the boundary surface. By using normal mode technique, solutions for the variables considered such as displacement, stress, temperature and chemical potential are achieved. Numerical results are computed for copper material. The impacts of variable thermal conductivity, variable diffusivity, rotation and gravity on different physical fields in the medium are depicted through various figures.

Entropy Analysis on Magneto-Convective and Chemically Reactive Nanofluids Flow Over a Stretching Cylinder in the Presence of Variable Thermal Conductivity and Variable Diffusivity

The current paper is on the boundary layer flow of a magnetohydrodynamic nanofluids (Cu, Al2O3 nanoparticles with base fluid water) flow over a linearly stretching cylinder. We have analyzed the entropy generation with heat and mass transfer in mixed convection, thermal radiation, viscous dissipation, variable thermal conductivity, variable mass diffusivity, and binary chemical reaction with activation energy. Convective boundary conditions are also considered here. No such attempt is yet made by the researchers on hybridization and entropy optimization model by considering variable thermal conductivity and variable mass diffusivity with binary chemical reaction with convective boundary conditions induced by a stretching cylinder. The efficient implicit Runge-Kutta-Fehlberg method with shooting technique is used for numerical solutions to the transformed-converted non-linear system of equations. The study is motivated by analyzing the effects on the nanofluid velocity, skin friction coefficient, temperature distribution, Nusselt number, nanoparticles concentration, and Sherwood number inside the boundary layer. The impact of solid volume fraction, chemical reaction, and activation energy with entropy generation is the key findings of the current investigation. Variable thermal conductivity and variable diffusivity parameters hike temperature and concentration profile, respectively. Entropy and Bejan number are increasing functions for curvature parameters.