Variable Thermal Conductivity Research Articles

Variable thermal conductivity in context of Green‐Naghdi theory of thermo‐microstretch solids

AbstractThe present work aims to study the influence of variable thermal conductivity in generalized thermoelastic solid with microstretch within the framework of the Green‐Naghdi theory. The analytical methodology is adopted for obtaining exact expressions of displacement components, stresses, couple stresses, micro stress distribution and temperature distribution. The effect of variable thermal conductivity is illustrated graphically in two and three dimensions for the above physical quantities by taking different values of thermal conductivity.

Nonlinear-Mixed Convection Flow with Variable Thermal Conductivity Impacted by Asymmetric/Symmetric Heating/Cooling Conditions

Nonlinear-Mixed Convection Flow with Variable Thermal Conductivity Impacted by Asymmetric/Symmetric Heating/Cooling Conditions

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.

Nanofluid dissipative stagnation point flow of Casson type over a stretched sheet influenced by a variable surface heat flux and magnetic field

The studied problem focuses on the flow of Casson nanofluid induced by a stretched surface in the presence of a magnetic field and exposed to variable surface heat flux, with an emphasis on enhancing thermal efficiency. This research aims to highlight the flow of Casson nanofluid at the stagnation point on a stretching sheet, taking into account the influence of heat generation and variable thermal conductivity. The fluid being examined exhibits a steady-state two-dimensional flow. The formulation of the model involves deriving partial differential equations, which are later converted into ordinary differential equations using similarity transformations. This particular research stands out by introducing an innovative mathematical model for Casson nanofluid, taking into account variable surface heat flux and covering several implications that have not been explored in current literature. We utilize the shooting method to compute numerical solutions for the formulated equations. Graphical representations are used to illustrate the numerical results for velocity, concentration, and temperature distribution. Furthermore, tabulated findings encompass the Sherwood number, skin friction coefficient, and local Nusselt number. A comparison with a previous study from the literature was conducted, demonstrating a robust agreement between our results and theirs. Several compelling findings indicate that the local Nusselt number rises as the velocity ratio parameter, suction parameter, thermal conductivity parameter, and heat flux exponent increase. Conversely, the Casson parameter, magnetic number, heat generation parameter, and thermophoresis parameter are observed to lower the local Nusselt number.

Impact of Variable Thermal Conductivity and Viscosity on Powell-Eyring Fluid in the Presence Of Thermal Radiation through a Porous Medium

This work uses a mathematical model to investigate the impact of physical factors on the non-isothermal flow of Powell-Eyring fluid with variations in thermal conductivity and viscosity through a porous medium. The governing equations defining the flow, mass, and energy transfer issue are converted into nonlinear ordinary differential equations via selected transformation variables, and the resultant problem is numerically solved using the Galerkin weighted residual technique. This approach is implemented with Maple 18 program. The examination of the findings revealed that the radiation parameter, variations of thermal conductivity, and viscosity characteristics had a substantial impact on the flow system. This presentation includes a visual picture and explanation of how different physical characteristics affect the flow system.

Irreversibility scrutiny of SWCNT and MWCNT nanofluid convective flow using Darcy-Forchheimer rule in an upright microchannel with variable thermal conductivity and Brownian motion and thermophoresis

Carbon nanotubes are used to attain greater thermal transfer rates in a various of enormous applications in the field of microsystem, emission, conductive polymers, fibers, and fabrics. Hence the aim of this article is to explore the entropy generation analysis of single wall carbon nanotubes and multiwall carbon nanotubes flow in an upright micro channel with variable thermal conductivity. The exponential heat source and non-linear thermal radiation were considered. The micro channel retains the no slip and convective boundary conditions. The Buongiorno model was used in this study, which emphasizes the light on Brownian motion and thermophoresis phenomena that occur during the fluid flow. Darcy- Forchheimer model is also taken into account. The governing equation numerically solved by employing Runge-Kutta Fehlberg's fourth-fifth order. The repercussion of this study upholds that the inflates of variable thermal conductivity magnify the thermal field. Entropy production inflates at right wall of the channel with augmented Brownian parameter and exhibits exactly opposite behavior at left wall of the channel. One of the important tasks of the investigation was to compare SWCNT and MWCNT. The findings confirmed that multiwall carbon nanotubes exhibit more magnificent heat and mass transfer than single wall carbon nanotubes.

Utilization of variable thermal conductivity and diffusion coefficient on non-Newtonian Prandtl model with modified heat and mass fluxes

PurposeThis study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.Design/methodology/approachThe governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.FindingsGraphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.Originality/valueThe reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

Computation analysis of unsteady second grade biomagnetic micropolar blood base nanofluid flow with motile gyrotactic microorganisms

ABSTRACT The primary aim of this research is to investigate the impact of an external magnetic field on bacteria that are surrounded by a large quantity of magnetite nanoparticles. The study utilizes magnetite F e 3 O 4 nanofluid using blood as a base fluid with variable thermal conductivity, in which a synthetic bacterium moves within a biological cell. The focus of the study lies in analyzing the non-steady movement of a micropolar fluid in a two-dimensional context, specifically in the presence of a curved porous wall. Suitable transformations are used to transform the nonlinear PDEs to their corresponding nonlinear ODEs. The HAM (Homotopy Analysis Method) is used to find the mathematical results. The impact of various key parameters is studied by using numerical tables and graphs. This study shows that the velocity curves of the pure blood is higher than those magnetite/blood. Clinical disease shows that perilous tumors have weakened blood flow. This study demonstrates that higher parameter values lead to an improvement in the blood velocity profile, indicating that medication therapy reduces tumor size and aids in countering distorted cells. Furthermore, the research reveals that an increase in the concentration of magnetite nanoparticles corresponds to an increase in the distribution of blood temperature. The findings of this study highlight the significant role played by thermal conductivity in enhancing the rate of heat transfer.

Peristaltic transport of nanofluid with temperature dependent thermal conductivity: A numerical study

Peristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices.

Darcy–Forchheimer flow of Carreau fluid over a curved stretching surface with slip condition and variable thermal conductivity

The aim of this study is to perform analysis of nonlinear mixed convection flow of Carreau fluid due to curved stretched surface with slip condition. Furthermore, the effect of Darcy–Forchheimer and MHD is taken into consideration. The energy equation is modified by considering the variable thermal conductivity with Joule heating effect. The governing equations of the problem are highly nonlinear partial differential equations subjected to boundary conditions. Similarity transformations are used to transform nonlinear PDEs into ODEs. The numerical technique is used to solve this problem via bvp4c. The main outcomes of this research are that the impact of Forchheimer and porosity parameter tends to decrease the fluid velocity for shear thickening case. The velocity slip condition increases the fluid velocity only near the surface but the fluid velocity away from the surface does not get affected. The changing thermal conductivity raises the temperature of the fluid near the boundary. Furthermore, the impacts of various parameters on the velocity and temperature profiles are demonstrated. The values of local Nusselt number and skin friction for a different parameter are provided.

Heat generation and melting heat transfer effects on MHD flow of Carreau fluid in a porous medium

AbstractWe consider heat and mass transfer analysis of magnetohydrodynamic (MHD) Carreau fluid flow along a stretching sheet in a permeable medium with impacts of melting condition, heat generation, double diffusion, and variable thermal conductivity. The novelty of the present work is to study the effects of melting heat transfer and heat generation on MHD flow of Carreau fluid along a stretched sheet in a porous medium with influence of Dufour and Soret effects, and variable thermal conductivity. Similarity transformations procedure is used which transform the partial differential equations (PDEs) of fluid flow model into nonlinear dimensionless ordinary differential equations (ODEs). We obtained numerical solutions of ODEs and the effects of assorted governing parameters are investigated. The results showed that boosting melting parameter increases velocity and concentration fields and reduces temperature profile. Enhancing heat source parameter increases temperature profile, concentration profile observing decline for modified Dufour parameter, Schmidt number, and Soret number, and velocity of the fluid decline for magnetic and porosity parameters. Impact of governing parameters on physical quantities comprising Nusselt number, skin friction, and Sherwood number is evaluated numerically. The accuracy of our results are established in comparison with previous research for skin friction coefficient and Nusselt number.

Effect of Chemical Reaction and Variable Thermal Conductivity in MHD Williamson Nanofluid Flow with Gyrotactic Microorganisms

The primary objective of this study deals with numerical analysis of gyrotactic microorganisms in Williamson nanofluids under the influence of chemical reaction and variable thermal conductivity along with porous medium. Using the similarity transformations, the non-linear PDEs are transformed into ODEs. RK-Fehlberg with a shooting strategy utilised to address ODEs with the influence of MATLAB software. Effect of Permeability, Prandtl number, magnetic field, Williamson parameter, Schmidt number, Peclet number, the profiles of velocity, temperature, concentration, and motile microbe density are explored in detail, and the potential results are displayed in graphs. The density number, Nusselt number, skin friction coefficient, and Sherwood number displayed in tables.

A two‐stage reliable computational scheme for stochastic unsteady mixed convection flow of Casson nanofluid

AbstractResearchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms the validity of current stochastic modeling tools by providing examples of stochastic simulations in conjunction with numerical solutions for incompressible flows. A numerical technique for solving deterministic and stochastic models is developed in this work. Our approach employs the Euler‐Maruyama method for stochastic modeling, representing a stochastic version of the third‐order explicit‐implicit scheme. For the deterministic model, the scheme is third‐order accurate. The consistency and stability of the constructed scheme are provided in the mean square sense. The scheme is the predictor–corrector type that is built on two time levels. Moreover, a mathematical model of the Casson nanofluid flow with variable thermal conductivity is given with the effect of the chemical reaction. The appropriate transformations are used to condense the set of partial differential equations (PDEs) down to one that is dimensionless. The scheme is applied for the deterministic and stochastic models of dimensionless flow problems. The velocity profile's deterministic and stochastic behavior are shown using contour plots. Results show that growing values of the thermal mixed convection parameter enhance the velocity profile. This article presents the progress made in stochastic computational fluid dynamics (SCFD) and highlights the energy‐related aspects of our discoveries. Our computational approach and stochastic modeling techniques provide new insights into the energy properties of Casson nanofluid flow, specifically regarding the variability of thermal conductivity and chemical processes. Our objective is to clarify the complex interaction of these factors on energy dynamics. This article presents a contemporary summary of the latest SCFD advancements. Additionally, it highlights potential directions for future research and unresolved issues that require attention from the members of the field of computational mathematics.

Effectiveness of Maxwell velocity and smoluchowski thermal slip constraints in presence of non-uniform heat source

Magnetohydrodynamic flow of nanomaterial by a stretched boundary is addressed. Entropy generation is examined. Variable fluid characteristics are considered. Buongiorno thermal enhancement model in presence of Darcy-Forchheimer expression is addressed. Nonlinear thermal radiation, non-uniform heat source and dissipation are considered in thermal expression. Slip conditions in chemically reactive flow are addressed. Here Maxwell slip velocity and Smoluchowski slip temperature are under consideration. Impact of Arrhenius activation energy is deliberated. Optimal homotopy analysis approach (OHAM) is utilized for construction of convergent solutions. Graphical description for liquid motion, entropy rate, concentration and temperature are examined. Higher magnetic variable has reverse effect on entropy rate and velocity. Higher temperature and entropy rate are seen for radiation parameter. Higher temperature dependent conductivity parameter has opposite effect on liquid motion and entropy rate. Liquid flow has same impact for both porosity and velocity slip parameters. Larger thermal slip variable lead to decrease thermal distribution while reverse impact holds for heat source. Concentration has opposite trend through both random and thermophoresis parameters. An enhancement in thermal distribution and entropy rate are seen through variable thermal conductivity. An intensification in entropy rate has been noticed through concentration dependent conductivity variable. The considered configuration has relevance for detecting cooling towers, polymer extrusion, spinning of filaments, cable coating and metallurgical processes.

Significance of quadratic radiation and variable thermal conductivity on heat transfer of hybrid nanofluid using Xue model: A Legendre wavelet approach

Carbon nanotubes have a broad spectrum of applications in thermal management, enhanced cooling, lubricants, sensors and detections, environmental remediation, biomedical, and drug delivery. Motivated by its industrial applications, this work analyses the effects of nonuniform heat source/sink and quadratic thermal radiation on the thermal characteristics of hybrid nanofluid flow over a curved stretching sheet using the Legendre wavelet collocation technique (LWCT). The base fluid is found to be composed of ethylene glycol and water in the ratio of 30:70, and the nanoparticles are taken as single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) in the ratio of 2% each. The thermal conductivity models, namely Xue, modified Maxwell and Hamilton-Crosser, are compared for heat transfer enhancement. From the results up to 5% volume fraction, the Xue model shows the maximum rate of heat transfer enhancement, while the above 5% Hamilton-Crosser model shows the maximum rate of heat transfer enhancement. The temperature profiles of existing hybrid nanofluid are increased with a heat source, radiation and variable thermal conductivity. Moreover, the graphs describing the local Nusselt number display the heat transfer rate depreciation with an increase in variable thermal conductivity and radiation parameters.

Stefan flow of nanoliquid passing a plate surface with changeable fluid properties

This article describes the significance of ‘Stefan suction/blowing’ on the forced flow of nanoliquid past the surface of a ‘plate’ with temperature-obeying ‘thermal conductivity’ and ‘fluid viscosity’ with ‘zero nanoparticle flux’ at the ‘plate’ that has not till been attended by anyone and thus it points to the originality of present investigation and here lies the novelty of our work. Nanofluid flow is modeled with the help of ‘Buongiorno's two-phase model’ which contains the instantaneous virtue of thermophoresis diffusion and Brownian movement. This investigation shows that the speed of heat transport is remarkably augmented by the variable ‘thermal conductivity’ and variable ‘viscosity parameters’ which is the main contribution of this research. Due to changeable viscosity, reducing nature of velocity as well as the reducing nature of concentration of the nanoparticles near the ‘plate’ are observed. Due to Stefan's blowing parameter, fluid velocity augments but ‘temperature’ is observed to reduce for mounting values of Stefan's blowing parameter. 3.2 % reduction in skin-friction coefficient is noted when variable viscosity parameter reduces from -6 to -8. Moreover, 7.1 % reduction in heat transfer as well as mass transfer is noted when the variable thermal conductivity parameter rises from 0.2 to 0.4. The consequence of this inspection exposes a variation of exciting diversity which claims extra exploration of the present study.

Probe beam deflection technique with liquid immersion for fast mapping of thermal conductance

Frequency-domain probe beam deflection (FD-PBD) is an experimental technique for measuring thermal properties that combines heating by a modulated pump laser and measurement of the temperature field via thermoelastic displacement of the sample surface. In the conventional implementation of FD-PBD, the data are mostly sensitive to the in-plane thermal diffusivity. We describe an extension of FD-PBD that introduces sensitivity to through-plane thermal conductance by immersing the sample in a dielectric liquid and measuring the beam deflection created by the temperature field of the liquid. We demonstrate the accuracy of the method by measuring (1) the thermal conductivity of a 310 nm thick thermally grown oxide on Si, (2) the thermal boundary conductance of bonded interface between a 3C-SiC film and a single crystal diamond substrate, and (3) the thermal conductivities of several bulk materials. We map the thermal boundary conductance of a 3C-SiC/diamond interface with a precision of 1% using a lock-in time constant of 3 ms and dwell time of 15 ms. The spatial resolution and maximum probing depth are proportional to the radius of the focused laser beams and can be varied over the range of 1–20 μm and 4–80 μm, respectively, by varying the 1/e2 intensity radius of the focused laser beams from 2 to 40 μm. FD-PBD with liquid immersion thus enables fast mapping of spatial variations in thermal boundary conductance of deeply buried interfaces.

Experimental Analysis of Moisture-Dependent Thermal Conductivity, and Hygric Properties of Novel Hemp-shive Insulations with Numerical Assessment of Their In-Built Hygrothermal and Energy Performance.

The use of lime as a binder in hemp-lime considerably increases the drying time of hemp-lime after casting. Furthermore, lime is a non-renewable mineral resource. As such, this paper explores the effectiveness of using an alternative non-mineral binder instead of lime to formulate a novel hemp-shive insulation. The moisture-dependent thermal conductivity, adsorption isotherm, vapour diffusion resistance factor, and in-built hygrothermal performance of four variants of a novel bio-based insulation were investigated. The hygrothermal performance of the novel hemp-shive insulation was compared with that of a previously developed novel hemp-lime insulation. No significant variation in thermal conductivity of hemp-shive insulations between the equilibrium moisture contents (EMC) at 0% and 50% relative humidity (RH) was observed, but there was a substantial increase in thermal conductivity hemp-shive insulations when the material reached the EMC at 98% RH. The average dry thermal conductivity values of hemp-shive and hemp-lime insulations were also similar. The adsorption isotherms of hemp-shive insulations were determined at 0%, 20%, 50%, 70%, 90%, and 98% relative humidity steps. At 98% RH, the moisture adsorption capacity of hemp-shive insulations was 4-to-5-times higher than that of hemp-lime insulation. Hemp-shive insulations' vapour diffusion resistance factor (µ value) was about double the µ value of hemp-lime insulation. Hemp-shive insulations exhibited 4-to-5-times higher water absorption resistance than that of hemp-lime insulation. Numerically determined porosity values of hemp-shive agree with the values of wood-based insulation materials of similar density. Finally, using all experimentally acquired data as inputs, dynamic whole-building hygrothermal simulations were carried out and the results show that novel hemp-shive insulation materials perform at a similar level to the hemp-lime insulation in terms of heating and cooling energy demand but require 45% less energy for humidification. However, the relative humidity inside the hemp-shive wall remains higher than 70%, which can potentially induce mould growth.

Bioconvective flow of Maxwell nanoparticles with variable thermal conductivity and convective boundary conditions

Owing to recent development in the thermal sciences, scientists are focusing towards the wide applications of nanofluids in industrial systems, engineering processes, medical sciences, enhancing the transport sources, energy production etc. In various available studies on nanomaterials, the thermal significance of nanoparticles has been presented in view of constant thermal conductivity and fluid viscosity. However, exponents verify that in many industrial and engineering process, the fluid viscosity and thermal conductivity cannot be treated as a constant. The motivation of current research is to investigates the improved thermal aspects of magnetized Maxwell nanofluid attaining the variable viscosity and thermal conductivity. The nanofluid referred to the suspension of microorganisms to ensure the stability. The insight of heat transfer is predicted under the assumptions of radiated phenomenon. Additionally, the variable thermal conductivity assumptions are encountered to examine the transport phenomenon. Whole investigation is supported with key contribution of convective-Nield boundary conditions. In order to evaluating the numerical computations of problem, a famous shooting technique is utilized. After ensuring the validity of solution, physical assessment of problem is focused. It is claimed that velocity profile boosted due to variable viscosity parameter. A reduction in temperature profile is noted due to thermal relaxation constant.

Analysis of mixed convective stagnation point flow of hybrid nanofluid over sheet with variable thermal conductivity and slip Conditions: A Model-Based study

This research looks at the stagnation point flow of MHD Al2O3-Cu/H2O hybrid nanofluid against a permeable, vertically extending surface that uses thermal radiation and how different models of thermal conductivity affect it. This study is unique because it looks at how changes in thermal conductivity, mixed convection, and the slip velocity of hybrid nanofluids affect the stretching surface. It also looks at how changes in temperature, skin-friction coefficient, Nusselt number, and velocity affect convective thermal boundary conditions. With the use of boundary layer approximations, the complicated system of PDEs is simplified. The dimensionality of these PDEs and the boundary conditions they include are eliminated by applying certain modifications. Combining a local non-similarity approach up to the second truncation level with MATLAB's built-in finite difference code (bvp4c), one can obtain the results of the updated model. The research demonstrates and analyzes the impact of different factors on fluid flow and heat transfer characteristics in the studied flow situations. This is done by comparing the computed data with available literature and presenting the findings in graphical form. Tables are generated to present the numerical fluctuations of the drag coefficient and Nusselt number. This study shows how important thermal conductivity is in the mixed convection of hybrid nanofluids and looks into what happens when the thermal conductivity parameter is changed. Significantly, an augmentation in this parameter results in an elevation in the temperature distribution of the hybrid nanofluid while simultaneously reducing the rate of heat transfer across various models. Furthermore, increasing the nanoparticle volume fraction parameter leads to higher temperature and Nusselt number profiles while reducing skin friction. The mixed convection parameter has a notable impact on increasing the friction coefficient on the stretched vertical surface. However, because these elements function as regulating variables, it decreases when the magnetic, mass suction, and velocity slip parameters are present. The results also demonstrate notable discrepancies in the mean Nusselt values generated by various thermal conductivity models. According to the analysis, the Hamilton-Crosser model has the lowest average Nusselt numbers, followed by the Yamada-Ota model and the Xue model, in that order.