Variable Thermal Conductivity Research Articles

Heat Transfer Analysis of Memory-Dependent Derivative in Biological Tissue Subjected to a Moving Heat Source

Abstract A new bioheat transfer equation is developed by introducing the memory-dependent derivative into dual-phase lag model. The heat transfer process of memory-dependent derivative in biological tissue under a moving heat source is studied. Besides, thermal conductivity is usually no longer constant at high temperature. The nonlinear temperature governing equation with considering variable thermal conductivity is formulated and the solutions are obtained by the methods of Kirchhoff and Laplace transformations. The influences of heat source velocity, variable thermal conductivity, relaxation time, and kernel function on the variation of temperature are analyzed.

Flow analysis of Williamson model over a moving surface with nonlinear convection/diffusion and variable thermal conductivity

This article analyses the flow across a moving surface using the magnetohydrodynamic (MHD) Williamson fluid model in detail, accounting for the effects of diffusion, nonlinear convection, and variable thermal conductivity. The heat transmission within the system is impacted by the changing thermal conductivity, which can also significantly alter the flow behavior. The effects of the moving surface on flow forms in porous media are explained here using the Darcy model. The similarity transformations are used to convert the underlying nonlinear partial differential equations into a collection of ordinary differential equations. The work uses a numerical RK4 technique to examine the complex incompressible fluid flow behavior on a moving surface. The study’s conclusions provide insight into the intricate flow patterns and shear layer forms brought on by the interaction of fluid and surface motion while taking varied thermal conductivity into account. The findings give important information for the design and optimization of engineering applications involving changeable thermal characteristics and advance our understanding of fluid dynamics in geophysical and atmospheric systems. Physical descriptions are used to depict how flow parameters behave in relation to velocity, temperature, and concentration distributions.

Thermal performance appraisal of hybrid and nanofluid flow between a cone and a disk with variable thermal conductivity, viscous dissipation, and Joule heating

In many engineering systems, hybrid and nanofluids are influenced by their respective thermophysical characteristics. Lately, several models have been envisaged to foresee the hybrid and nanofluid attributes. The properties of hybrid nanofluids (HNFs) as potential heat transfer fluids are controlled by numerous aspects such as solid part size, volume fraction, and temperature. Considering the interesting facts of the hybrid and nanofluid flows, we in this exploration examined the thermal performance comparison of both types of fluid flows. The nanofluid and HNF are composed of molybdenum disulfide (MoS[Formula: see text]/kerosene oil and silicon dioxide–molybdenum disulfide (SiO2–MoS[Formula: see text]/kerosene oil, respectively. The flows are taken in a canonical gap between the cone and the disk. Both the cone and the disk may be rotating or stationary. The novelty of the computational model is enhanced by discussing the effects of viscous dissipation, Joule heating, and the variable thermal conductivity with convective condition. The Tawari and Das model is designed to analyze the heat transfer performance of the assumed fluid flows. The assumed fluid model is transmuted into the set of differential equations that are dealt numerically with the bvp4c MATLAB approach. The results are displayed in tables and graphical forms. For elevating estimations of the Eckert number, the heat transmission rate is found to be more significant in the disk than cone. It is also learned that hybrid nanoliquid heat transfer performance outperforms nanoliquid. The fluid velocity increases by raising the nanoparticle volume fraction [Formula: see text], and is decreasing for a higher magnetic field parameter. With the elevating estimates of thermal conductivity, it is shown that the cone transmits heat more quickly whereas the disc transmits heat more slowly. The thermal conductivity parameter increases the probability of collision of the liquid particles, that ultimately upsurges fluid heat transmission rate.

Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle

Abstract The thermo-diffusion applications of nanofluid subject to variable thermal sources have been presented. The significance of Darcy–Forchheimer effects is attributed. The flow comprises the mixed convection and viscous dissipation effects. Furthermore, the variable influence of viscosity, thermal conductivity, and mass diffusivity is treated to analyze the flow. The analysis of problem is referred to convective mass and thermal constraints. The analytical simulations are proceeded with homotopy analysis method. The convergence region is highlighted. Novel physical contribution of parameters is visualized and treated graphically. It is noted that larger Brinkman number leads to improvement in heat transfer. The concentration pattern boosted due to Soret number. The wall shear force enhances with Hartmann number and variable thermal conductivity coefficient.

Overlapping Grid-Based Spectral Collocation Technique for Bioconvective Flow of MHD Williamson Nanofluid over a Radiative Circular Cylindrical Body with Activation Energy

The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes.

Experimental study on evaluation of density, P-wave velocity, thermal conductivity, and thermal diffusion coefficient of granite after thermal treatments by using PCA

Temperature significantly influences the physical parameters of granite, resulting in variations in the rock's thermal conductivity. In order to examine the impact of changes in multiple physical parameters of granite at different temperatures on the thermal conductivity of rocks, Principal Component Analysis (PCA) was employed to determine the correlation between granite at different temperatures and various physical parameters, including density (ρ), P-wave velocity (P), thermal conductivity (KT), and thermal diffusion coefficient (KD). Utilizing the linear contribution rate, a single indicator 'y' was derived to comprehensively represent the thermal conductivity of rocks. Research findings indicate that within the temperature range of 150–450 °C, the 'y'-value is relatively high, signifying favorable thermal conductivity of the rock. Notably, longitudinal wave velocity demonstrates higher sensitivity to temperature changes compared to other physical parameters.

A Comparative Study of Newtonian and Non-Newtonian Nanofluids with Variable Thermal Conductivity Over a 3-D Stretching Surface

This study presents a comprehensive numerical and statistical analysis of the flow, heat/mass transfer management of Newtonian and non-Newtonian nanofluid over a bidirectional Darcy-Forchheimer stretching sheet. The external effects of MHD, Joule heating, thermal radiation, heat generation/absorption, Brownian motion, thermal diffusion and chemical reaction are taken into account. It is presumed that the thermal conductivity of fluid varies linearly with temperature. The non-linear coupled P.D.Es are converted into nonlinear coupled O.D.Es using similarity transformation. These equations are solved using MATLAB by implementing four-stage Lobatto IIIa formula and the outcomes of numerous flow parameters are presented graphically. In addition to numerical investigations, a comprehensive statistical analysis is performed using R-software to evaluate the sensitivity of key input parameters towards variable thermal conductivity. The values of local wall friction, local wall heat flux, and wall mass flux for various parameters are tabulated. The study reveals that the heat transmission is significant for dilatant fluids (156.8%) when compared to the pseudoplastic fluids (113.8%). Enriching the values of the Brownian motion parameter suppresses the molecular diffusion while a contrary nature is observed for the thermal diffusion parameter. Further, the mass transfer coefficient shows a very strong negative correlation with variable thermal conductivity parameter for Shear thinning fluids, whereas for Newtonian and Shear thickening fluids it shows a very strong positive correlation.

Insight into the peristaltic motion through a tapered channel with Newton’s cooling subject to viscous dissipation, Lorentz force, and velocity slip

Peristalsis has gained significant attention due to its numerous applications in the medical field, engineering, and manufacturing industries. Therefore, the current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by viscous fluid through a tapered channel. The viscosity of the liquid differs over the thickness of the channel, and temperature-dependent thermal conductivity is considered. The constitutive relation for energy is formulated with the addition of viscous dissipation and heat generation/absorption. The assumption of velocity slip along with the convective boundary condition energizes the thermal system as well as the flow phenomena. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution were obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity. The effects of various relevant parameters on flow properties were investigated through graphical analysis. The results show that the maximum velocity does not occur in the middle of the tapered channel, but moves toward the upper wall with the increase in the variable viscosity difference between the walls. The application of viscosity is essential in many engineering and industrial processes.

Study on Impact of Variable Thermal Conductivity or Laser Pulse on Reflected Elastic Waves in a Semiconductor Medium

Study on Impact of Variable Thermal Conductivity or Laser Pulse on Reflected Elastic Waves in a Semiconductor Medium

Study of hybrid nanofluid flow in a stationary cone-disk system with temperature-dependent fluid properties

Cone-disk systems find frequent use such as conical diffusers, medical devices, various rheometric, and viscosimetry applications. In this study, we investigate the three-dimensional flow of a water-based Ag-MgO hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties. How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds’s linearized model for variable viscosity and Chiam’s model for variable thermal conductivity. The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids, incorporating the experimental data. This model is developed as a coupled system of convective-diffusion equations, encompassing the conservation of momentum and the conservation of thermal energy, in conjunction with an incompressibility condition. A self-similar model is developed by the Lie-group scaling transformations, and the subsequent self-similar equations are then solved numerically. The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed. Additionally, the Nusselt number for the disk surface is calculated. It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system, while the thermal conductivity parameter has the opposite effect.

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.

Enhancement of heat transfer due to nonlinear radiative Burgers nanofluid with triple diffusion and heat source effects

This investigation predicts the assessment of mass and heat transfer due to Burgers nanofluid. The investigation is further supported by triple diffusion flow. Variable thermal conductivity is accounted to endorse the thermal flow. In the heat equation, the extension is suggested by utilizing the external heat source and nonlinear radiated phenomenon. Computations for modeled problems are achieved by the shooting method. The fundamental role of parameters governing flow is noticed which is physically attributed. It is observed that the heat transfer rate is enhanced due to the modified Dufour number. The solutal concentration declined for the regular Lewis number. Furthermore, the nanoparticles concentration reduces due to the nano-Lewis number. The depicted results convey novel applications in chemical processes, cooling control systems, refrigeration, solar energy, extrusion processes, etc.

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.

Analysis of thermal conductivity variation in magneto-hybrid nanofluids flow through porous medium with variable viscosity and slip boundary

Hybrid nanoparticles, which are nanoparticles composed of multiple materials or phases, find applications in various fields due to their unique properties resulting from the combination of different materials. In such fluids, viscosity changes significantly in response to alterations in temperature or pressure. For example, these fluids become less viscous as they are heated and more viscous as they are cooled. Similarly, in certain situations, the application of a temperature variation can cause a change in viscosity. This property is commonly observed in materials like polymers and some oils. The article aims to investigate the heat transfer and flow behavior of fluid from an elastic sheet of hybrid nanoparticles, considering the temperature-dependent variable viscosity and thermal conductivity. The obtained equations for the mathematical model are partial differential equations converted to ODEs by applying a suitable similarity transformation. The findings show that the magnetic field opposes fluid motion. Our main findings are that adding nanoparticles to the base fluid significantly increased its heat conductivity. This improvement has great potential for uses requiring effective heat transmission, especially in engineering systems where heat dissipation plays a crucial role. The study also reveals the complex relationships that influence thermal conductivity, including slip boundary effects, viscosity fluctuations, magnetohydrodynamic effects, and porous media dynamics. Understanding these interactions is critical for optimizing heat transport processes in porous media applications. Comprehending these interplays is essential for refining heat transport mechanisms in applications involving porous media. The graphical representations are used to explain the physical behavior of various model parameters. Previous outcomes are also contrasted with the current ones. The findings show that the magnetic field opposes fluid motion.We range the subsequent list of values for parameters in every graph unless indicated accordingly.ϵ=0.1,Pr=2,M=0.5,R=0.2,K=5,fw=0.1,s=0.1 ,λ=1,φ1=0.02,φ2=0.04.

Exploring the effects of TiO2${\rm TiO}_2$–Ag/water hybrid nanofluid on MHD flow over a permeable exponentially stretching–shrinking sheet with radiative heat transfer and slip conditions

AbstractThe objective of this article is to study the importance of velocity and thermal slip in the exponentially stretching or shrinking sheet with the megnetohydrodynamic (MHD) hybrid nanofluid flow along with magnetic field, radiative, heat generation effects. This study has practical importance in enhancing heat transfer efficiency, improving energy conversion and optimizing thermal management systems. The findings can also contribute to the development of sustainable energy systems and aid in assessing the stability and safety of nanofluid applications. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformation. The ODEs are solved using bvp4c solver in MATLAB. The dual solutions are achieved for specific range of the stretching or shrinking parameter and mass suction parameter. The first solution is physically significant after considering stability analysis. The hybrid nanofluid has numerous real‐life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical, and drug reduction. The skin‐friction increases but Nusselt number decreases over the stretching sheet whereas the opposite effect shows over shrinking sheet for the both solution with the increasing velocity slip parameter. On the other hand, The Nusselt number decreases over the shrinking or stretching sheet for both solutions with the increasing in the thermal slip parameter. The skin friction increases over shrinking sheet but decreases over stretching sheet for the first solution with increasing silver volume fraction parameter and porosity parameter (). Enhancing magnetic field parameter leads to the skin friction increases over the shrinking sheet but decreases over stretching sheet but Nusselt number shows opposite trend. The Nusselt number decreases over shrinking sheet but increases over stretching sheet for the first solution with increasing porosity parameter (). The Nusselt number decreases over shrinking or stretching sheet as the increases heat generation () and variable thermal conductivity parameter () but Nusselt number shows opposite trend as the increases radiative parameter ().

Influence of stress history on thermal conductivity of saturated fine-grained soils

This research investigated variations in thermal conductivity <i>k</i> for normally consolidated (NC) and overconsolidated (OC) saturated fine-grained soils at different levels of vertical effective stress. A series of undrained heating tests were performed using a specially designed consolidometer with central radial heating arrangement and temperature measurements within a soil specimen. For different soils investigated in this research, <i>k</i> correlated well with soil consolidation characteristics (compression index <i>λ</i> and swelling index <i>κ</i>) and vertical effective stress <i>σ</i><sub>v</sub>ʹ at both NC and OC states. However, the rates of increment of steady- and transient-state values of <i>k</i> (<i>k</i><sub>st</sub> and <i>k</i><sub>tr</sub>, respectively) with <i>σ</i><sub>v</sub>ʹ differed from one soil to another. For OC clays, both <i>k</i><sub>tr</sub> and <i>k</i><sub>st</sub> increased with preconsolidation stress <i>σ</i><sub>c</sub>ʹ. A set of equations were proposed to estimate both <i>k</i><sub>st</sub> and <i>k</i><sub>tr</sub> for saturated fine-grained soils as functions of <i>σ</i><sub>v</sub>ʹ, <i>λ</i>, <i>κ</i>, and stress history. At a particular value of <i>σ</i><sub>v</sub>ʹ, the dependence of <i>k</i> on overconsolidation ratio (OCR) and <i>σ</i><sub>c</sub>ʹ marked the importance of considering stress history in the determination of <i>k</i>. The influence of soil mineral composition on <i>k</i> was also explored. Quantification of soil mineralogical composition and available data on mineral thermal conductivity enabled prediction of <i>k</i><sub>tr</sub> with reasonable accuracy.

Irreversibility Analysis for Magnetized and Nonlinear Convection Flow of Carreau Fluid Past a Nonlinear Surface with Higher-Order Adherence Factor

Studying entropy generation allows scientists and engineers to optimize processes, design more efficient systems, and develop sustainable technologies. These studies aim towards minimizing energy losses, reducing environmental impacts, and advancing the frontiers of thermodynamics and energy science. As such, the current investigation expunges the dynamics of heat, flow, entropy and irreversibility analysis for a magnetized and dissipative Carreau fluid flow over a nonlinearly stretching sheet. The model is subject to thermal and electrical conductivity variations, higher-order adherence factors and nonlinear convective motion over an inclined nonlinear surface. Herein, the heat source in the flow system is considered space and temperature-dependent. The mathematical model presented in PDE systems is transformed to ODEs via similarity transformation. Numerically, the solutions to the distribution profiles are approximated via Chebyshev Collocation Method (CCM) with the pseudospectra (differentiation matrix) technique. In the limited case, the results here benchmark existing literature. Our findings identified that thermal irreversibility dominated the entire flow system, further entropy generation and irreversibility enhancement requires more thermal energy. We as well elucidate that alteration of both heat source modulation affects the heat transfer coefficient while Joule heating effect generates inner energy which induces the Carreau fluid energy. Carreau fluid, Entropy generation Momentum slip, Nonlinear Convection, Pseudo spectral method

Study of mass and heat transfer for peristaltic transport of cross nanofluid through a curved channel

AbstractNanoparticles have significant applications in drug delivery systems, heat exchanges, treatment of several diseases and chemical reactions. The Cross non‐Newtonian nanofluid model for heat and mass transfer inspection with diethylene glycol‐based fluid is highlighted in this study. The magnesium aluminate nanoparticles are used to evaluate nanofluid characteristics. The current investigation explores the numerical results for magnetohydrodynamics (MHD) peristaltic movement of Cross‐nanofluid via a curved channel under the influences of thermal radiation, heat sink/source and Joule heating. The effects of viscous dissipation, thermophoretic, variable thermal conductivity and Brownian diffusion coefficients in the presence of mass and thermal convection are also taken into consideration. Flow problem is modeled using fundamental conservation laws, and the resulting nonlinear partial differential equations (PDEs) are reduced to a system of nonlinear ordinary differential equations (ODEs) by employing long wavelength and a small Reynolds number approximations. Simplified systems of ODEs are addressed by adopting numerical technique via the NDSolve built‐in command in Mathematica. Furthermore, graphical presentations explain the behavior of relevant flow parameters. Results indicate that better values of the magnetic number and the thermophoresis parameter increase the rate of mass transfer. Results indicate that the nanofluid's temperature increases by improving values of the Brinkman number and falls with the thermal radiation parameter. It is also stated that the nanofluid's velocity reduces near the lower wall for greater values of Hartman number. Moreover, heat transfer rate improves for larger values of the heat generation parameter and curvature parameter.

Magnetohydrodynamic study of Micropolar fluid flow in the porous walled channel with variable viscosity and thermal conductivity: HAM Solution

This article examines the production of entropy and the heat transfer rate in the passage of micropolar fluid through a channel. The micropolar fluid takes place through the porous walled channel under the presence of an external magnetic field acting in the perpendicular direction of the flow. In this work, the thermal conductivity and viscosity of the fluid is considered variable and are the function of the temperature. Here, we consider two-dimensional creeping flow with two different forms of temperature boundary conditions, namely, Newtonian heating (NH) boundary constraints and specified surface temperature (SST) boundary conditions. The flow of the micropolar fluid in the proposed problem is governed by the coupled non-linear PDEs. These PDEs are first transformed into the ODEs by the use of some suitable similarity transformations and then obtained ODEs are further solved by using the semi-analytic Homotopy Analysis Method (HAM). This article shows the effect of various flow parameters on the fluid’s velocity, heat transfer rate, temperature of the fluid, and entropy production for both types of thermal boundary conditions. Through this article, it is concluded that the entropy production is minimal for Newtonian heating (NH) boundary conditions as compared to specified surface temperature (SST) boundary conditions. This result suggests that the NH boundary condition is more suitable for electrical appliances as compared to the SST boundary condition. This type of model is applicable in nuclear reactors, engineering appliances, heat reservoirs, etc.

Heat transfer analysis of magnetohydrodynamics peristaltic fluid with inhomogeneous solid particles and variable thermal conductivity through curved passageway

PurposeThe particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.Design/methodology/approachThe mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.FindingsThe fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.Originality/valueThis study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.