Axial Conduction Research Articles

Design and multi-objective optimization of a new annular constructal bifurcation Stirling regenerator using response surface methodology

The irreversible losses such as the flow loss and axial heat conduction loss in traditional porous regenerators have limited the specific power and thermal efficiency of Stirling engines to a great degree. Thereby, the objective of this paper is to design and optimize a novel annular constructal bifurcation regenerator for diminishing the flow and axial heat conduction losses in the regenerator based on constructal concept and response surface methodology. First, the bifurcation type structure units with an inclined angle to the flow direction and the layered approach were applied to construct the regenerator matrix. Thereafter, the numerical simulations were employed to investigate the gas flow and heat transfer characteristics of the constructal bifurcation regenerator. Based on the numerical data, the quadratic polynomial regression models between the geometric parameters and the regenerator performance were established using response surface methodology, and the specific effects of the geometric dimensions were analyzed via 2-D and 3-D response surface plots. Subsequently, a multi-objective optimization was conducted to minimize the flow resistance and maximize the heat transfer rate by genetic algorithm. A most eclectic solution with the global friction factor f = 3.478 and the number of heat transfer units NTU = 1.135 was selected from the optimal Pareto front. Finally, the overall performance of the constructal bifurcation regenerator was compared with that of the porous regenerator and the parallel geometry regenerator. The results indicate that a low flow resistance, low axial heat conduction, and high thermal performance are obtained by the constructal bifurcation regenerator. Therefore, it is reasonable to conclude that the annular constructal bifurcation regenerator achieves a high comprehensive performance, with the potential to improve the performance of Stirling engines. The findings of this paper may provide some new ideas and guidelines for the design and optimization of the regenerator structures.

Heat transfer enhancement of nanofluid flow at the entry region of microtubes

A numerical investigation on laminar nanofluid flow and convective heat transfer at the entry region of microtubes subjected to constant wall temperature and constant heat flux boundary conditions has been carried out employing a multiphase Eulerian–Lagrangian method. The impacts of the Peclet number (175 ≤ Pe ≤ 3500), nanoparticle volume fraction (0.1 ≤ φ ≤ 1.0%), and nanoparticle diameter (40 ≤ dp ≤ 130 nm) on thermal characteristics of Al2O3-water nanofluid flow through a microtube are analyzed in detail. The results indicate that the influence of the Reynolds number on apparent friction factor and the impact of the axial heat conduction on the Nusselt number for the nanofluids have to take into account in the entry region. Compared with the influences of particle concentration and particle size, the entrance effect dominates pressure drop and thermal performance of the nanofluids near the entrance of the channel. As the dimensionless axial distance increases, the entrance effect is weakened, and the influences of particle concentration and particle size are gradually reflected in flow and heat transfer results. Besides, the particle effects on thermal performance of the nanofluids are earlier and higher than that on flow resistance. Performance evaluation demonstrates that the nanofluids in the entrance region have not only heat transfer enhancement but also a good economy. When Pe = 175, the PEC of Al2O3-water nanofluids with particle concentrations of 0.1, 0.2, 0.5, and 1% increased by 104.0, 103.1, 113.8, and 128.5% under constant heat flux condition, respectively, at the dimensionless axial distance x* = 0.01 compared with deionized water; the PEC improved by 74.6, 77.2, 85.6, and 102.5% under constant wall temperature condition compared with deionized water, respectively.

Many paths to one goal: Identifying integrated rice root phenotypes for diverse drought environments.

Drought is a major source of yield loss in the production of rice (Oryza sativa L.), and cultivars that maintain yield under drought across environments and drought stress scenarios are urgently needed. Root phenotypes directly affect water interception and uptake, so plants with root systems optimized for water uptake under drought would likely exhibit reduced yield loss. Deeper nodal roots that have a low metabolic cost per length (i.e., cheaper roots) via smaller root diameter and/or more aerenchyma and that transport water efficiently through smaller diameter metaxylem vessels may be beneficial during drought. Subsets of the Rice Diversity Panel 1 and Azucena × IR64 recombinant inbred lines were grown in two greenhouse and two rainout shelter experiments under drought stress to assess their shoot, root anatomical, and root architectural phenotypes. Root traits and root trait plasticity in response to drought varied with genotype and environment. The best-performing groups in the rainout shelter experiments had less plasticity of living tissue area in nodal roots than the worst performing groups. Root traits under drought were partitioned into similar groups or clusters via the partitioning-around-medoids algorithm, and this revealed two favorable integrated root phenotypes common within and across environments. One favorable integrated phenotype exhibited many, deep nodal roots with larger root cross-sectional area and more aerenchyma, while the other favorable phenotype exhibited many, deep nodal roots with small root cross-sectional area and small metaxylem vessels. Deeper roots with high theoretical axial hydraulic conductance combined with reduced root metabolic cost contributed to greater shoot biomass under drought. These results reflect how some root anatomical and architectural phenes work in concert as integrated phenotypes to influence the performance of plant under drought stress. Multiple integrated root phenotypes are therefore recommended to be selected in breeding programs for improving rice yield across diverse environments and drought scenarios.

Shallow roots of different crops have greater water uptake rates per unit length than deep roots in well-watered soil

PurposeCommonly, root length distributions are used as a first approximation of root water uptake profiles. In this study we want to test the underlying hypothesis of a constant water uptake rate per unit root length over depth.MethodsRoot water uptake profiles were measured using a novel sensor technology. Root length was measured with MRI and by scanning harvested roots. Experiments were performed with pot-grown barley (Hordeum vulgare), maize (Zea mays), faba bean (Vicia faba), and zucchini (Cucurbita pepo).ResultsFor barley, maize, and faba bean, we found that roots in the top 15 cm had significantly greater water uptake rates per unit length than roots in the bottom 30 cm. For zucchini, the trend was similar but not significant. Therefore, variation of root water uptake rates with depth could be explained only partly (61–71%) by a variation of root length with depth.ConclusionThe common approximation of root water uptake profiles by root length distributions relies on constant water uptake rates per unit root length. This hypothesis does not hold in our study, as we found significantly greater water uptake rates per unit length in shallower than in deeper roots. This trend was consistent among species, despite the partly strong variation in physiological parameters. We suggest that this is caused by a decreasing axial transport conductance with depth. This might result in a general underestimation of water uptake rates in shallow soil layers when they are approximated by the root length distribution.

Microchannel counter-current heat exchanger analysis highlighting equitability of conventional heat transfer theory in both macro and micro domains

Some of the early experimental investigations on microchannel surfaces could not be explained using the macroscale heat transfer theory, creating doubts regarding its applicability. However, the data analysis in those studies has often been done neglecting performance deteriorating effects like axial heat conduction. The axial conduction effect is often overlooked in macroscale applications depending on the operating conditions. Nevertheless, recent studies have proved that the axial conduction effect becomes significantly dominant when the fluid free-flow area and solid cross-sectional area are comparable with the scaling down channel dimensions. Anticipating that the axial conduction effect overshadows the actual information of the microscale heat transfer characteristics, an approach taking care of the latter should be adopted. Kroeger’s analysis, an established macroscale method, has been used to analyze microchannels heat exchangers. The results are compared against those obtained from a three-dimensional conjugate computational model of a miniaturized exchanger. A good agreement between them indicates that the macro-scale exchanger analysis (including axial conduction) with the conventional correlations usually recommended for macro channels can also predict the thermal performance of the heat exchanger in the micro-realm. If axial conduction is neglected, performance deterioration in microscale heat exchanger effectiveness can be as high as 43%.

A 1D Reduced-Order Model (ROM) for a Novel Latent Thermal Energy Storage System

Phase change material (PCM)-based thermal energy storage (TES) systems are widely used for repeated intermittent heating and cooling applications. However, such systems typically face some challenges due to the low thermal conductivity and expensive encapsulation process of PCMs. The present study overcomes these challenges by proposing a lightweight, low-cost, and low thermal resistance TES system that realizes a fluid-to-PCM additively manufactured metal-polymer composite heat exchanger (HX), based on our previously developed cross-media approach. A robust and simplified, analytical-based, 1D reduced-order model (ROM) was developed to compute the TES system performance, saving computational time compared to modeling the entire TES system using PCM-related transient CFD modeling. The TES model was reduced to a segment-level model comprising a single PCM-wire cylindrical domain based on the tube-bank geometry formed by the metal fin-wires. A detailed study on the geometric behavior of the cylindrical domain and the effect of overlapped areas, where the overlapped areas represent a deviation from 1D assumption on the TES performance, was conducted. An optimum geometric range of wire-spacings and size was identified. The 1D ROM assumes 1D radial conduction inside the PCM and analytically computes latent energy stored in the single PCM-wire cylindrical domain using thermal resistance and energy conservation principles. The latent energy is then time-integrated for the entire TES, making the 1D ROM computationally efficient. The 1D ROM neglects sensible thermal capacity and is thus applicable for the low Stefan number applications in the present study. The performance parameters of the 1D ROM were then validated with a 2D axisymmetric model, typically used in the literature, using commercially available CFD tools. For validation, a parametric study of a wide range of non-dimensionalized parameters, depending on applications ranging from pulsed-power cooling to peak-load shifting for building cooling application, is included in this paper. The 1D ROM appears to correlate well with the 2D axisymmetric model to within 10%, except at some extreme ranges of a few of the non-dimensional parameters, which lead to the condition of axial conduction inside the PCM, deviating from the 1D ROM.

Influence of axial heat conduction in solid walls and fins on the overall thermal performance of an additively manufactured high-temperature heat exchanger

Due to the increasing use of high-temperature processes in mobile applications, the demand for compact and efficient high-temperature heat exchangers continues to rise. However, with increasingly reduced installation space, the parasitic effect of axial heat conduction in the wall material of the heat exchanger is also gaining considerable influence. In this manuscript, the influence of axial heat conduction in the wall and fin material on the thermal performance of an additively manufactured high temperature heat exchanger is to be examined. For this purpose, an analytical calculation model as well as the analytical solution method is presented and successfully validated by means of experimentally recorded measurement data of an additively manufactured heat exchanger, which was tested at temperatures up to 750 °C. Subsequently, the calculation programme is used to determine the influence of the axial heat conduction on the effectiveness as well as on the NTU value of an additively manufactured Plate-Fin heat exchanger. The results show a drop in the NTU value of up to 50% at balanced flow compared to the case without heat conduction, which reduces the effectiveness and thus the performance of the heat exchanger by up to 5.5%.

Conjugate Heat Transfer of Laminar Air Flow in Rectangular Mini Channel

Conjugate heat transfer has significant implications on heat transfer characteristics, particularly in thick wall applications and small diameter pipes. In this study, a three-dimensional numerical investigation was carried out using commercial CFD software “ANSYS FLUENT” to study the influence of conjugate heat transfer of laminar flow in mini channels at constant heat flux wall conditions. Two parameters were studied and analyzed: the wall thickness and thermal conductivity and their effect on heat transfer characteristics such as temperature profile and Nusselt number. Thermal conductivity of (0.25, 10, 202, and 387) W/m2C and wall thickness of (1, 5, and 50) mm were used for a channel of (1*2) mm cross-sectional dimensions. Taking the Reynolds number 800 for all cases. The results demonstrate that the conjugate conduction impact is observed at high conductivities and for large wall thicknesses in the studied materials. This impact flattened the wall temperature distribution along the channel wall instead of being an augmented linear profile. Also, it flattens the local Nusselt number due to the axial heat conduction along the walls. It reduces the effect of the entrance region of high Nusselt number while making the fluid temperature profile curved and redistributing the wall heat flux and accumulating it toward the leading edge. A decrease was observed in the average Nusselt number of 8% when increasing wall thickness from 1 mm to 50 mm for the same thermal conductivity of 10 W/m2C, while an increase in Nusselt number of 19% with thermal conductivity changes from 0.25 W/m2C to 10 W/m2C.

Analytical Study on Intricacies of Axial Conduction in Microchannel Heat Sinks

Abstract Microchannel heat sinks are potential devices that remove heat flux from high power density miniaturized electronic components. While the large surface-area-to-volume ratio and high heat transfer coefficient are the key features rendering benefits, the small flow rate and short channel lengths alongside high solid cross section to fluid free flow area make them susceptible to intense axial conduction loss. The conventional models for macrodevices based on the one-dimensional energy equation are often inappropriate in the microdomain. A novel multidimensional analytical model (capable of capturing axial heat transfer in microchannel heat sinks) has been used to study the thermal performance over a varied range of geometric and flow parameters. The effect of axial conduction has been seen in the solid–fluid temperature profiles, interfacial flux distribution and the average amount of heat transferred axially. The results indicate a skewed flux distribution at the fluid–solid interface leading to nonlinear temperature variation when axial conduction is dominant. Moreover, it has been shown that nonlinearity in the fluid temperature introduces significant errors in experimental data reduction, leading to apparently very low Nusselt number estimation. Moreover, this erroneous data interpretation is also linked to the prediction of a strong Reynolds number dependency of the average Nusselt number in the laminar flow regime.

Spatiotemporal responses of rice root architecture and anatomy to drought

AimsGrowth reductions and yield losses from drought could be mitigated by developing rice genotypes with more efficient root systems. We examined spatiotemporal responses to drought in order to determine whether roots developing in upper vs. deeper soil layers respond differently to drought stress.MethodsRoot anatomical and architectural phenotypes of two rice genotypes, Azucena (drought tolerant) and IR64 (drought susceptible), were measured weekly in well-watered and vegetative-stage drought stress treatments in solid medium with stratified moisture availability. Basal and apical segments were collected from older, deeper nodal roots and apical segments from younger, shallow roots for assessment of anatomy and lateral rooting phenotypes. The relationship between root anatomy and root respiration rates was tested in solution culture and solid medium.ResultsCompared to IR64, Azucena had deeper root systems and larger diameter roots in both treatments but reduced its living tissue area in response to drought, while IR64 roots exhibited less plasticity in root diameter. Root respiration rates were positively correlated with root diameter and living tissue area, providing evidence that root anatomy affects the metabolic cost of tissues. In response to drought, Azucena showed reduced theoretical axial hydraulic conductance in shallow roots and at the base of deep roots but slightly greater conductance at the tip of deep roots, while IR64 displayed low plasticity in metaxylem phenotypes.ConclusionWe propose that the plasticity of root phenotypes in Azucena contributes to its drought tolerance by reducing the metabolic cost of soil exploration and improving the efficiency of water transport.

Phenotyping and modeling of root hydraulic architecture reveal critical determinants of axial water transport.

Water uptake by roots is a key adaptation of plants to aerial life. Water uptake depends on root system architecture (RSA) and tissue hydraulic properties that, together, shape the root hydraulic architecture. This work investigates how the interplay between conductivities along radial (e.g. aquaporins) and axial (e.g. xylem vessels) pathways determines the water transport properties of highly branched RSAs as found in adult Arabidopsis (Arabidopsis thaliana) plants. A hydraulic model named HydroRoot was developed, based on multi-scale tree graph representations of RSAs. Root water flow was measured by the pressure chamber technique after successive cuts of a same root system from the tip toward the base. HydroRoot model inversion in corresponding RSAs allowed us to concomitantly determine radial and axial conductivities, providing evidence that the latter is often overestimated by classical evaluation based on the Hagen–Poiseuille law. Organizing principles of Arabidopsis primary and lateral root growth and branching were determined and used to apply the HydroRoot model to an extended set of simulated RSAs. Sensitivity analyses revealed that water transport can be co-limited by radial and axial conductances throughout the whole RSA. The number of roots that can be sectioned (intercepted) at a given distance from the base was defined as an accessible and informative indicator of RSA. The overall set of experimental and theoretical procedures was applied to plants mutated in ESKIMO1 and previously shown to have xylem collapse. This approach will be instrumental to dissect the root water transport phenotype of plants with intricate alterations in root growth or transport functions.

Probing the Accuracy of Experimental Data on Nusselt Numbers Within Miniature Heat Sinks

Abstract Achieving accurate experimental data in conjugate heat transfer studies to calculate Nusselt number can be challenging due to its complex three-dimensional thermal hydraulics nature. This study is devoted to evaluating the accuracy and reliability of experimental approaches used to calculate the Nusselt number in miniature heat sinks. It is observed that three major parameters including (1) axial heat conduction within the solid substrate of heat sinks, (2) thermal contact resistance, and (3) assumed uniform wall temperature, as well as wall heat flux distributions, influence the reported experimental data in the literature. The results obtained from the developed analytical and computational models in this study revealed that the assumptions of local uniform wall temperature and heat flux distributions for small-scale heat sinks result in underestimated Nusselt numbers calculated from experiments. At lower Reynolds number (<200) flows in miniature heat sinks with a high solid to fluid thermal conductivity ratio (>> 1), it is shown that the fluid bulk temperature should be measured away from the heat sink inlet and outlet to minimize the effect of axial heat conduction within the solid substrate of the microscale heat sinks on calculated Nusselt numbers. As the third important parameter, the influence of thermal contact resistance on the Nusselt number calculation in a miniature heat sink is studied where thermal slip length is considered. Finally, the concurrent effects of thermal contact resistance and thermal developing region are considered to explicate the obtained trends in the experimental Nusselt numbers dataset.

Genetic analysis of root vascular traits in a population from two temperate japonica rice ecotypes

ABSTRACT The genetic basis for root vascular traits in rice, despite its direct impacts on root axial and radial hydraulic conductivity, has not been widely studied compared with deep rooting traits. We used five phenotyping datasets (i.e. from maturity stage grown in upland field in 2013, and from vegetative and maturity stages grown in upland and lowland fields in 2019) to quantify the genotypic variations and genomic regions of root vascular traits in a temperate japonica mapping population (from lowland Otomemochi (OTM) and upland Yumenohatamochi (YHM)). YHM had larger stele transversal area (STA) and total late metaxylem area (LMXA), as well as higher deep root ratio and total root length at deeper layers (>30 cm) than OTM. Root vascular traits were significantly different among progenies in each dataset, and the size of genotype-by-environment interactions was comparable. Root vascular traits were not positively correlated with deep rooting traits. From the multi-environment analysis of all five datasets, four key genomic regions related to STA in both joint and separate analyses were detected on chromosome 2 (RM3703-RM6379, RM6933-RM3857), chromosome 4 (RM1388-RM5503) and chromosome 12 (RM247-RM155), with the first and third collocated with deep rooting traits. QTL-by-environment interaction was comparable to the main additive effect. This study is the first report on genomic regions of root vascular traits in a japonica mapping population.

Study on the Time-Varying Characteristics of In-Situ State Temperature Field of Drilled Work Piece Based on Unsteady Heat Conduction

In-Situ state heat conduction in drilling workpiece results in time-varying temperature field, which affects the final machining accuracy. From the joint action of many factors, such as geometry, material, and thermal convection characteristics, it is difficult to accurately model and describe the time-varying characteristics of the temperature field. Therefore, the time-varying model of the In-Situ state temperature field is analyzed in this paper, which lays a foundation for establishing a high-precision multi-physical field model. First, following the geometric characteristics of the drilling hole and the three-dimensional heat transfer mechanism, the heat transfer model of the drilled part is established, and the relationship between the temperature field and the physical parameters of the workpiece is characterized. Then, combining radial and axial unsteady heat conduction mechanisms, the dimensionless temperature calculation method is adopted to realize the construction of a temperature time-varying model. After that, the model parameters are revised according to the In-Situ state evolution process of the checkpoints. Finally, the experiments are carried out to calculate the credibility of the model. The results show that the prediction model is consistent with the experimental data, and the credibility of non-room temperature dynamic interval is 99.23%, which can effectively reflect the real temperature field conduction process.

A novel method of measuring microtube wall temperatures by thermocouples to investigate sCO2 flows

Experimental study on convective heat transfer through microtubes encounters many challenges such as measuring the wall temperature of the tube with a reasonable uncertainty, relatively high heat loss from the outer surface of the tube, and difficulty in measuring the fluid bulk temperature at the tube outlet. These issues become exacerbated with flow at low Reynolds numbers. The present study presents a new method to measure the tube wall temperature with a small solder cast where a thermocouple is embedded. The net heat flux to flows, determined with the heat loss on the outer surface and the axial heat conduction, is integrated to obtain the local mean enthalpy of fluid and then the fluid mean temperature along the tube. Thus, convection heat transfer coefficients are calculated without measuring the mean temperature at the outlet. The new method is successfully validated with laminar water flows through a horizontally configured microtube, 0.501 mm in inner diameter. All Nusselt numbers are found to lie between 4.36 and 4.36 + 10%. Finally, the method developed in this study is applied to supercritical CO2 flowing upward at 8.0 MPa through a microtube, 0.509 mm in inner diameter. For both high and low mass flow rates, a local maximum of the convection heat transfer coefficient is observed at a location where the film temperature is close to the pseudo-critical temperature. On the other hand, the second local maximum of the convection heat transfer coefficient appears only at low mass flow rates.

Thermodynamic analysis of the non-ideal cryogenic packed bed regenerator for the liquid air energy storage system

Liquid air energy storage (LAES) is one of the most recent technologies introduced for grid-scale energy storage. The cryogenic regenerator, which can greatly affect the system efficiency, is the key component of the system. A non-ideal packed bed regenerator for the LAES system was investigated. The cold energy loss and the axial heat conduction of the packed bed regenerator exist in the intermittent period between the charging and discharging process, which significantly degrades the system performance. With rock particles used as the cold energy storage medium, the axial temperature distributions of the packed bed regenerator with different initial temperatures and intermittent periods were compared. Also, the cold energy loss with different boundary conditions was analysed. The results show that the intermittent period exacerbates the negative impact of the axial heat conduction on the performance of the packed bed, and the thickness of the thermocline decreases as the inlet temperature of the cold end decreases. Moreover, as the cold energy loss increases, the cold energy storage efficiency of the packed bed decreases significantly.

Root and xylem anatomy varies with root length, root order, soil depth and environment in intermediate wheatgrass (Kernza®) and alfalfa.

Deep roots (i.e. >1 m depth) are important for crops to access water when the topsoil is dry. Root anatomy and hydraulic conductance play important roles in the uptake of soil water, particularly water located deep in the soil. We investigated whether root and xylem anatomy vary as a function of root type, order and length, or with soil depth in roots of two deep-rooted perennial crops: intermediate wheatgrass [Thinopyrum intermedium (Kernza®)] and alfalfa (Medicago sativa). We linked the expression of these anatomical traits to the plants' capacity to take up water from deep soil layers. Using laser ablation tomography, we compared the roots of the two crops for cortical area, number and size of metaxylem vessels, and their estimated root axial hydraulic conductance (ERAHCe). The deepest roots investigated were located at soil depths of 2.25 and at 3.5 m in the field and in rhizoboxes, respectively. Anatomical differences were characterized along 1-m-long individual roots, among root types and orders, as well as between environmental conditions. For both crops, a decrease in the number and diameter, or both, of metaxylem vessels along individual root segments and with soil depth in the field resulted in a decrease in ERAHCe. Alfalfa, with a greater number of metaxylem vessels per root throughout the soil profile and, on average, a 4-fold greater ERAHCe, took up more water from the deep soil layers than intermediate wheatgrass. Root anatomical traits were significantly different across root types, classes and growth conditions. Root anatomical traits are important tools for the selection of crops with enhanced exploitation of deep soil water. The development and breeding of perennial crops for improved subsoil exploitation will be aided by greater understanding of root phenotypes linked to deep root growth and activity.

Pseudogauge dependence of the spin polarization and of the axial vortical effect

The mean spin polarization vector of spin 1/2 particles in a relativistic fluid at local thermal equilibrium (LTE) in different pseudogauges (PGs), i.e., with different choices for the decomposition of orbital and spin angular momentum, is obtained. The spin polarization obtained in the canonical PG differs from the one obtained in the Belinfante PG. It is found that this difference can not be written by replacing the thermal vorticity with the spin potential in the usual polarization formula. Other PG choices affect the contribution of thermal shear to the spin polarization. Therefore, the choice of a PG affects the predictions for the polarization measured in heavy-ion collisions. In general, it is shown that the Wigner function of a noninteracting Dirac field at LTE is affected by the PG transformations. Explicit expressions of the mean axial current are also calculated and it is found that even the axial vortical effect conductivity depends on the PG.

Coupling Electronic and Phonon Thermal Transport in Poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) Nanofibers.

The thermal transport of Poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) nanofiber is contributed by the electronic component of thermal conduction and the phonon component of thermal conduction. The relationship between the electrical conductivity and thermal conductivity of these conducting polymers is of great interest in thermoelectric energy conversation. In this work, we characterized the axial electrical conductivities and thermal conductivities of the single PEDOT:PSS nanofibers and found that the Lorenz number L is larger than Sommerfeld value L0 at 300 K. In addition, we found that the L increased significantly in the low-temperature region. We consider that this trend is due to the bipolar contribution of conducting polymers with low-level electrical conductivity and the increasing trend of the electronic contribution to thermal conductivity in low-temperature regions.

Thermal entrance problem for blood flow inside an axisymmetric tube: The classical Graetz problem extended for Quemada's bio-rheological fluid with axial conduction.

The heat-conducting nature of blood is critical in the human circulatory system and features also in important thermal regulation and blood processing systems in biomedicine. Motivated by these applications, in the present investigation, the classical Graetz problem in heat transfer is extended to the case of a bio-rheological fluid model. The Quemada bio-rheological fluid model is selected since it has been shown to be accurate in mimicking physiological flows (blood) at different shear rates and hematocrits. The steady two-dimensional energy equation without viscous dissipation in stationary regime is tackled via a separation of variables approach for the isothermal wall temperature case. Following the introduction of transformation variables, the ensuing dimensionless boundary value problem is solved numerically via MATLAB based algorithm known as bvp5c (a finite difference code that implements the four-stage Lobatto IIIa collocation formula). Numerical validation is also presented against two analytical approaches namely, series solutions and Kummer function techniques. Axial conduction in terms of Péclet number is also considered. Typical values of Reynolds number and Prandtl number are used to categorize the vascular regions. The graphical representation of mean temperature, temperature gradient, and Nusselt numbers along with detail discussions are presented for the effects of Quemada non-Newtonian parameters and Péclet number. The current analysis may also have potential applications for the development of microfluidic and biofluidic devices particularly which are used in the diagnosis of diseases in addition to blood oxygenation technologies.