Temperature Dependence Of Thermal Conductivity Research Articles

Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model

In the literature, one can find numerous modifications of Fourier’s law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme’s stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics.

Unusual temperature dependence of thermal conductivity due to phonon resonance scattering by point defects in cubic BN

Unusual temperature dependence of thermal conductivity due to phonon resonance scattering by point defects in cubic BN

A comprehensive analysis of magnetized Non-Newtonian nanofluids ' peristaltic mechanism for optimized fluid flow and heat transfer

Magnetized non-Newtonian models nowadays have attracted many researchers because it is an exciting field in the collaboration of material science, fluid dynamics, and applied physics. Their unique properties and adaptability render them invaluable across various technological and industrial applications, promising further innovations as research advances. This research unveils the intricate rheological and thermal behavior of magnetized non-Newtonian nanofluids undergoing peristaltic motion. The study aims to enhance engineering design techniques for optimal biophysiological performance by incorporating second-order slip, convective conditions, and temperature-dependent thermal conductivity. The Buongiorno nanofluid model is adopted to investigate heat and mass transfer phenomena, while the Prandtl non-Newtonian fluid model is employed to comprehend the complex rheological characteristics of the fluid. A long-wavelength approximation with a low Reynolds number was employed to simplify the governing equations. Analytical solutions have been obtained by solving the nonlinear transformed equations using the Homotopy perturbation technique. The findings are validated with previous literature and indicate that magnetic fields play a key role in controlling peristaltic flow behavior and nanofluid pumping rates. Moreover, the interplay between non-Newtonian rheology and nanofluid parameters significantly affects temperature distribution patterns. An increase in the species Biot number and thermophoresis parameter leads to improved concentration behavior. Conversely, a reversible trend is noted with the augmentation of the Prandtl number, Eckart number, variable thermal conductivity, and Brownian motion parameters. This research provides new insights into magnetohydrodynamic transport mechanisms in peristaltic systems. The modeling approach, coupled with analysis, lays the background for improved fluid circulation, oxygen delivery, waste removal, and nutrient transport in biomedical applications. Specifically, the findings are important for advancing the design of peristaltic pumps tailored for targeted drug delivery and optimizing fluid flow within gastrointestinal tracts.

The impact of rotation on the onset of cellular convective movement in a casson fluid saturated permeable layer with temperature dependent thermal conductivity and viscosity deviations

In this effort, we examined the impact of rotation on the arrival of cellular convective motion in a Casson fluid saturated permeable layer with temperature dependent thermal conductivity and viscosity deviations. The problem is important to cellular foams prepared from plastics, ceramics, and metallic where radiation conductivity is revealed as a power function of temperature. The altered Darcy model is used to characterize the rheological performance of Casson fluid flow in permeable medium. The approximate analytical solution and numerical solution correct to one decimal place are presented utilizing the Galerkin method. The analysis reveals that the influence of thermal conductivity disparity parameter and the rotation is to delay the convective motion whereas; the viscosity disparity parameter and the Casson parameter have dual impact on the convective motion in the presence of rotation. The range of the convective cell drops with increasing the thermal conductivity disparity parameter, the viscosity disparity parameter, the Casson parameter and rotation parameter. In the absence of rotation, the range of the convective cell does not depend on the Casson parameter and the viscosity disparity parameter. Further, the existing results are compared with the existing literature under the particular case of this study.

Assessment of thermochromic phantoms for characterizing microwave ablation devices.

Thermochromic gel phantoms provide a controlled medium for visual assessment of thermal ablation device performance. However, there are limited studies reporting on the comparative assessment of ablation profiles assessed in thermochromic gel phantoms against those in ex vivo tissue. The objective of this study was to compare microwave ablation zones in a thermochromic tissue mimicking gel phantom and ex vivo bovine liver, and to report on measurements of the temperature dependent dielectric and thermal properties of the phantom. Thermochromic polyacrylamide phantoms were fabricated following a previously reported protocol. Phantom samples were heated to temperatures in the range of 20 - 90 °C in a temperature-controlled water bath, and colorimetric analysis of images of the phantom taken after heating were used to develop a calibration between color changes and temperature to which the phantom was heated. Using a custom, 2.45 GHz water-cooled microwave ablation antenna, ablations were performed in fresh ex vivo liver and phantoms using 65 W applied for 5 min or 10 min ( n = 3 samples in each medium for each power/time combination). Broadband (500 MHz - 6 GHz) temperature-dependent dielectric and thermal properties of the phantom were measured over the temperature range 22 - 100 °C. Colorimetric analysis showed that the sharp change in gel phantom color commences at a temperature of 57 °C. Short and long axes of the ablation zone in the phantom (as assessed by the 57 °C isotherm) for 65 W, 5 min ablations were aligned with extents of the ablation zone observed in ex vivo bovine liver. However, for the 65 W, 10 min setting, ablations in the phantom were on average 23.7% smaller in short axis and 7.4 % smaller in long axis than those observed in ex vivo liver. Measurements of the temperature dependent relative permittivity, thermal conductivity, and volumetric heat capacity of the phantom largely followed similar trends to published values for ex vivo liver tissue. Thermochromic tissue mimicking phantoms provide a controlled, and reproducible medium for comparative assessment of microwave ablation devices and energy delivery settings, though ablation zone size and shapes may not accurately represent ablation sizes and shapes observed in ex vivo liver tissue under similar conditions.

Thermophysical Characterization of Materials for Energy-Efficient Double Diaphragm Preforming

The Double Diaphragm Preforming (DDPF) process uses vacuum pressure and heat to pre-shape dry carbon fabric reinforcements between flexible diaphragms in liquid composite molding (LCM). Accurate modeling of heat transfer within DDPF requires knowledge of the thermophysical properties of the constituent materials under processing conditions. This study investigates the thermal conductivity of silicone diaphragms and carbon fabrics with embedded thermoplastic binder webs, utilizing transient plane source (TPS) and modified transient plane source (MTPS) methods, respectively. Additionally, the specific heat of silicone, carbon fibers (both chopped and powdered), and binder were measured using differential scanning calorimetry (DSC). Mixed samples comprising chopped fibers with 1.8 wt% binder and powdered fibers with 3.6 wt% binder was also analyzed with DSC. This study also examined the influence of reheating cycles on the specific heat of carbon fiber—3.6 wt% binder samples—and the effect of compaction and vacuum on the thermal conductivity of carbon fabrics with an embedded binder. While silicone exhibited linear-specific heat behavior, the thermoplastic binder showed non-linearity due to phase change. The combined carbon fiber-binder samples demonstrated slight non-linear specific heat variations depending on reheating cycles. The thermal conductivity of the fabric preforms decreased with the addition of thermoplastic binder and under vacuum-compaction conditions. The established temperature-dependent specific heat relationships and thermal conductivity provide valuable data for optimizing DDPF preforming parameters and enhancing energy efficiency in composite manufacturing.

Analysis of the tri-hybrid Maxwell nanofluid flow with temperature-dependent thermophysical characteristics on static and dynamic surfaces employing Levenberg-Marquardt artificial neural networks

Using the Levenberg-Marquardt Artificial Neural Network (LM-ANN) model, this study applies computational neuroscience to the analysis of flow, heat, and mass transport characteristics. The novel characteristics of MHD Maxwell tri-hybrid nanofluid passing through static and moving wedge with temperature-dependent thermophysical properties (thermal conductivity, viscosity, diffusivity, and electrical field) in permeable, radiative, and mixed convection processes are investigated in this paper. Nonlinear PDEs are transformed into nonlinear ODEs using similarity variables. A dataset for the LM-ANN is generated across various scenarios by varying parameters such as the temperature-dependent viscosity parameter ( 0.07 − 0.1 ) , variable diffusivity parameter ( 0.4 − 2.5 ) , thermal buoyancy parameter ( 0.1 − 0.5 ) , nonlinear thermal buoyancy parameter ( 0.2 − 0.5 ) , thermal radiation ( 1 − 1.5 ) , buoyancy ratio parameter ( 0.2 − 0.5 ) , chemical reaction parameter ( 1 − 3 ) , and Schmidt number ( 1 − 3 ) using the Bvp5c numerical algorithm. The testing, training, and validation procedure of LM-ANN is utilized to examine the estimated solutions of specific situations, and the proposed algorithm is then validated. After that, the proposed LM-ANN is validated using regression analysis, MSE, and histogram analysis. The prescribed approach impeccably mirrors the recommended and cited findings, evincing a precision level within the realm of 10−9. Results indicate that increasing the permeability parameter from 1 to 1.2 and the temperature-dependent thermal conductivity parameter from 0.4 to 2.5 enhances the Nusselt number. Additionally, increasing the chemical reaction parameter from 1 to 3 leads to an increase in the Sherwood number. The significance of this study lies in its potential applications in industries such as aerospace, chemical processing, and energy systems, where efficient heat and mass transfer processes are crucial. For instance, the findings can be applied to enhance cooling techniques in high-performance aerospace components, optimize reactor designs in chemical plants, and improve thermal management in power generation systems.

The influence of temperature (up to 120 °C) on the thermal conductivity of variably porous andesite

The thermal conductivity of volcanic rock is an essential input parameter in a wide range of models designed to better understand volcanic and geothermal processes. However, although volcanoes and geothermal reservoirs are often characterised by temperatures above ambient, laboratory thermal conductivity measurements are often performed at ambient temperature. In addition, there are currently few data on the temperature dependence of thermal conductivity for andesite, a common volcanic rock. Here, we provide elevated-temperature (up to 120 °C) laboratory measurements of thermal conductivity for variably porous (∼0.05 to ∼0.6) and variably glassy andesites from Mt. Ruapheu (New Zealand) using the transient hot-strip method. Our data show that (1) the thermal conductivity of these andesites has little to no temperature dependence and, therefore, (2) there is also no influence of porosity on the temperature dependence of thermal conductivity. We compare our new data with compiled published data to show that the thermal conductivity of volcanic rocks may decrease, remain constant, or increase as a function of temperature. We show that the thermal conductivity of amorphous glass and crystalline material increase and decrease, respectively, as temperature increases. We therefore interpret the temperature dependence of the thermal conductivity of volcanic rock to be dependent on glass content. The thermal conductivity of the studied andesites, the microstructure of which can be characterised by phenocrysts within a variably glassy groundmass, has little to no temperature dependence because the decrease in the thermal conductivity of the crystalline materials, due to decreases in lattice thermal conductivity, is offset by the increase in the thermal conductivity of the amorphous glass. A simple modelling approach, using the temperature dependence of the thermal conductivity of glass and crystalline material, provides a crystal content of 0.26 for a thermal conductivity independent of temperature, a common crystal content for andesite dome rock. Our findings imply that calculations of heat transfer through partially glassy volcanic rocks need not consider a temperature-dependent thermal conductivity, but that decreases and increases in thermal conductivity with temperature should be expected for fully crystallised or devitrified volcanic rocks and completely glassy volcanic rocks, respectively. We highlight that more experimental studies are now required to assess the evolution of thermal conductivity as a function of temperature in a wide range of volcanic rocks with different crystallinities.

Continuous composite longitudinal fins under oscillating boundary conditions: a lattice Boltzmann solution

PurposeTransient response of continuous composite material (CCM) fin made of high thermally conductive composite material is presented. The continuously varying effective properties of composite material such as thermal conductivity, heat capacity and density have been modelled using the Mori-Tanaka homogenization theory and rule of mixture. Additionally, temperature dependency of thermal conductivity, heat generation (composite materials) and convection coefficient (fluid properties) have also been incorporated. Different base boundary conditions are addressed such as oscillating heat flow, oscillating temperature, step-changing heat flow and step-changing temperature. At the other boundary, the fin is assumed to have a convective tip.Design/methodology/approachLattice Boltzmann method is implemented using an in-house source code for obtaining the numerical solution of typical non-linear heat balance equation of the aforementioned problem under various transient base boundary conditions.FindingsThe effects of various thermal parameters such as material diffusivity ratio and conductivity ratio, area ratio and Biot number on transient response of fin and temperature distribution of fins are studied and interpreted. The heat transfer rate and time for attainment of steady state temperature of metal matrix composite (MMC) fin are found to be proportionally dependent on their diffusivity ratio. Additionally for higher values of area ratio and biot number, MMC fins are reported to dissipate the heat more efficiently in comparision to homogeneous fins in terms of time required to attain the steady state and surface temperature.Practical implicationsResponse of transient fin associated with advanced class of material can facilitates the practicing engineers for designing high-performance and/or miniaturized thermal management devices as used in electronic packaging industries.Originality/valueStudies of composite fin consisting of laminating second layer of material over the first layer have been reported previously, however transient response of CCM fin fabricated by continuously varying the volume fraction of two materials along the fin length has not been reported till date. Such material finds its application in thermal management and electronic packaging industries. Results are plotted in form of a graph for different application-wise material combinations that have not been reported earlier, and it can be treated as design data.

Impacts of neutral collisions and finite electron inertia on longitudinal thermal instability of two-component radiative plasma for star formation in interstellar medium (ISM)

The impact of neutral friction, finite electron inertia and radiative heat-loss function on the thermal instability of viscous two-component plasma has been explored, integrating the impacts of thermal conductivity. A general dispersion relation is gained by means of the normal mode analysis scheme with the assist of appropriate linearized perturbation equations of the problem, and an amended circumstance of thermal instability is acquired. For the case of longitudinal propagation, it is obvious that the circumstance of thermal instability is independent of the finite electron inertia, magnetic field strength and viscosity of two components but relies on the radiative heat-loss function, thermal conductivity and neutral particle. From the curves, it is clear that the temperature-dependent heat-loss function, thermal conductivity and viscosity of two components represent stabilizing impact, while finite electron inertia and neutral collision depict destabilizing impact. Results discussed in this problem are helpful for star formation in ISM.

Heat Transfer Management of Thermal and Electronics Systems using Convective-Radiative Porous Fins with Thermal Contact Resistance and Diabatic Tip

The miniaturization of electronics, electrical, thermal, mechanical and optical devices and systems calls for increasing demand for efficient cooling systems with higher thermal efficiency. The use of passive mode of cooling using fins has provided unprecedented results. However, the previous transient analyses of the extended surfaces have been done without proper considerations of the imperfect contact between the fin base and the prime surface. Also, the tip of the passive device has been assumed to be adiabatic. However, the present article explores the significances of thermal contact resistance and diabatic tip on the transient thermal response of straight fin with temperature-dependent thermal conductivity and magnetic field under radiative-convective conditions. The nonlinear model is analyzed numerically using generalized Integral Transform Techniques and the numerical results are verified by the exact solution for the linear thermal model. The parametric explorations reveal that the adimensional local temperature in the conductive-radiative fin increases when the conductive-convective, conductive-radiative and magnetic field parameters increase. However, under the assumption of perfect thermal contact between the prime surface and the base of the fin, the adimensional temperature in the fin will decrease as the conductive-convective, conductive-radiative and magnetic field parameters increase. The fin temperature is significantly affected by the Biot numbers under the comparably low values of the conductive-convective, conductive-radiative, magnetic field and thermal conductivity parameters. The effects of the fin thermal conductivity parameter along the fin length depend on the respective values of thermal contact Biot number at the base of the fin and the end cooling Biot number at the tip of the fin. When the thermal conductivity parameter is amplified, the fin adimensional temperature increases when thermal contact Biot number at the base of the fin is zero and the end cooling Biot number at the tip of the fin is very large. This study will help in accurate analysis and design of heat sinks and passive devices for heat transfer enhancement for thermal and electronic systems.

Temperature-dependent thermal conductivity in Green–Naghdi (type III) thermoelastic half-space with hydrostatic initial stress

Temperature-dependent thermal conductivity in Green–Naghdi (type III) thermoelastic half-space with hydrostatic initial stress

Aluminum/Graphene Thermal Interface Materials with Positive Temperature Dependence.

Graphene is widely used in excellent thermal interface materials (TIMs), thanks to its remarkably high in-plane thermal conductivity (k∥). However, the poor through-plane thermal conductivity (k⊥) limits its further application. Here, we developed a simple in situ growth method to prepare graphene-based thermal interface composites with positively temperature-dependent thermal conductivity, which loaded aluminum (Al) nanoparticles onto graphene nanoplatelets (GNPs). To evaluate the variations in thermal performance, we determined the thermal diffusivity and specific heat capacity of the composites using a laser-flash analyzer and a differential scanning calorimeter, respectively. The Al nanoparticles act as bridges between the nanoplatelets, enhancing the k⊥ of the 1.3-Al/GNPs composite to 11.70 W·m-1·K-1 at 25 °C. Even more remarkably, those nanoparticles led to a unique increase in k⊥ with temperature, reaching 20.93 W·m-1·K-1 at 100 °C. Additionally, we conducted an in-depth investigation of the thermal conductivity mechanism of the Al/GNPs composites. The exceptional heat transport property enabled the composites to exhibit a superior heat dissipation performance in simulated practical applications. This work provides valuable insights into utilizing graphene in composites with Al nanoparticles, which have special thermal conductivity properties, and offers a promising pathway to enhance the k⊥ of graphene-based TIMs.

The Temperature-Dependent Thermal Conductivity of C- and O-Doped Si3N4: First-Principles Calculations

The Temperature-Dependent Thermal Conductivity of C- and O-Doped Si3N4: First-Principles Calculations

A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity

A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier–Stokes equations coupled to the convection–conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conductivity are temperature-dependent under the Boussinesq assumption. The proposed method consists of four steps all based on a viscosity-splitting algorithm where the convection and diffusion terms of both velocity and temperature solutions are separated while a viscosity term is kept in the correction step at all times. This procedure preserves the original boundary conditions on the corrected velocity and it removes any pressure inconsistencies. As a main feature, our method allows the temperature to be transported by a non-divergence-free velocity, in which case we show how to handle the subtle temperature convection term in the error analysis and establish full first-order error estimates for the velocity and the temperature solutions and 1/2-order estimates for the pressure solution in their appropriate norms. The theoretical results are examined by an accuracy test example with known analytical solution and using a benchmark problem of Rayleigh–Bénard convection with temperature-dependent viscosity and thermal conductivity. We also apply the method for solving a problem of unsteady flow over a heated airfoil. The obtained results demonstrate the convergence, accuracy and applicability of the proposed time viscosity-splitting method.

Impact of solar radiation in the presence of temperature-dependent thermal conductivity of non-Newtonian Casson flow on natural convection heat transfer in plume generated due to the combined effects of heat source and aligned magnetic field

Understanding the non-Newtonian Casson fluid is crucial for addressing various challenges in industrial, biological, and environmental applications. In this novel research, Casson fluid with temperature-dependent variable thermal conductivity is analyzed by a natural convective plume generated by horizontal line heat source. The plume system is under the influence of solar radiation and an aligned magnetic field. The momentum equation is transmuted for Casson fluid, while energy equation transmuted for solar radiation and variable thermal conductivity. The coupled partial differential equations changed into ordinary differential equation by employing stream function formulation. For computational evaluation, bvp4c built-in tool of MATLAB is employed in combination with Shooting technique in order to analyze both missing and specified boundary conditions. The upshots of Casson parameter β 1 , thermal conductivity variable γ 1 , radiation parameter Rd , magnetic force parameter S , Prandtl number Pr and magnetic Prandtl number γ on specified and missing conditions are highlighted in the graphical illustrations. The computed outcomes for missing conditions depicts that for Casson parameter β 1 velocity f ′ and temperature θ drops while current density increased with increment in β 1 . Whereas, for specified boundary conditions, the skin friction f ″ and magnetic flux ϕ ′ decreases while heat transfer rate θ ′ enhances for increasing β 1 . For missing conditions, the increasing thermal conductivity variable γ 1 causes velocity f ′ , current density ϕ ″ , and temperature θ to drop. While for specified conditions, the skin friction f ″ , magnetic flux ϕ ′ increases but heat transfer rate θ ′ exhibits reverse trend with enhancing γ 1 . Additionally, a validation analysis has been performed by comparing the values of f ′ ( 0 ) for various values of Pr with prior work, while excluding the other parameters to check its limitations at the boundary layer.

Tailoring thermoelectric performance of n-type Bi2Te3 through defect engineering and conduction band convergence

Bi2Te3, an archetypical tetradymite, is recognised as a thermoelectric (TE) material of potential application around room temperature. However, large energy gap (ΔEc ) between the light and heavy conduction bands results in inferior TE performance in pristine bulk n-type Bi2Te3. Herein, we propose enhancement in TE performance of pristine n-type Bi2Te3 through purposefully manipulating defect profile and conduction band convergence mechanism. Two n-type Bi2Te3 samples, S1 and S2, are prepared by melting method under different synthesis condition. The structural as well as microstructural evidence of the samples are obtained through powder x-ray diffraction and transmission electron microscopic study. Optothermal Raman spectroscopy is utilized for comprehensive study of temperature dependent phonon vibrational modes and total thermal conductivity ( κ ) of the samples which further validates the experimentally measured thermal conductivity. The Seebeck coefficient value is significantly increased from 235 μVK−1 (sample S1) to 310 μVK−1 (sample S2). This is further justified by conduction band convergence, where ΔEc is reduced from 0.10 eV to 0.05 eV, respectively. To verify the band convergence, the double band Pisarenko model is employed. Large power factor (PF) of 2190 μWm−1K−2 and lower κ value leading to ZT of 0.56 at 300 K is gained in S2. The obtained PF and ZT value are among the highest values reported for pristine n-type bulk Bi2Te3. In addition, appreciable value of TE quality factor and compatibility factor (2.7 V−1) at room temperature are also achieved, indicating the usefulness of the material in TE module.

Precise integration boundary element method for solving nonlinear transient heat conduction problems with temperature dependent thermal conductivity and heat capacity

The precise integration boundary element method (PIBEM) is used to solve nonlinear transient heat conduction problems with temperature dependent thermal conductivity and heat capacity in this article. At first, a boundary-domain integral equation can be obtained by using the fundamental solution for steady linear heat conduction problems. Secondly, the domain integrals are converted into boundary integrals by using the radial integration method to get a pure boundary integral equation, which can retain the advantage of dimension reduction of the boundary element method. Then, after discretization, a first-order nonlinear differential equation system in time is obtained, and the precise integration method with predictor-corrector technique is used to solve the system of nonlinear equations. In the end, several numerical examples are presented to verify the accuracy and stability of the presented method. The results obtained by the presented method are less affected by the time step size and satisfactory results can be obtained even for a large time step size.

Numerical investigation of the impact of temperature-dependent thermal conductivity and viscosity on thermo-particle heat transfer through stationary sphere and using plume

Numerical investigation of the impact of temperature-dependent thermal conductivity and viscosity on thermo-particle heat transfer through stationary sphere and using plume

Dynamic simulation of unsteady Casson–Carreau fluid flow considering temperature-dependent variable-properties and thermo-solutal mixed convection over flat and slendering sheets

The present investigation delves into the intricate interplay between surface effects and fluid dynamics, focusing on the flow characteristics of Casson and Carreau fluids endowed with temperature-dependent thermophysical properties. Specifically, the study explores the ramifications of radiative, mixed convection, and magnetized processes on heat and mass transfer phenomena. A comprehensive mathematical model is developed to analyze the behavior of Casson–Carreau fluids in conjunction with microscopic particles and gyrotactic microorganisms over both flat and slender surfaces. Leveraging similarity transformations, the governing equations are transformed into dimensionless form, facilitating numerical solutions using the bvp5c solver in MATLAB. The ensuing numerical and graphical analyses elucidate key physical quantities, including local skin friction coefficients, gyrotactic microorganism density, Nusselt number, and Sherwood number, across a spectrum of physical parameters. Notably, the investigation underscores the profound influence of flat surfaces on flow patterns and highlights the heightened consumption of fluid particles with increasing variable diffusivity and thermal conductivity. Moreover, enhanced values of parameters such as variable motile microorganism diffusion coefficient, Brownian motion parameter, and temperature-dependent thermal conductivity parameter are found to augment the Nusselt number, indicative of intensified heat transfer rates. This research underscores the imperative of comprehending the intricate dynamics of fluid flow and heat transfer, offering actionable insights for enhancing engineering designs and addressing multifaceted challenges across domains encompassing chemical engineering, environmental science, and biomedical applications.