Melting Heat Research Articles

Heat transfer characteristics in non‐Newtonian fluid flow due to a naturally permeable curved surface and chemical reaction

AbstractIn this research endeavor, Casson fluid flow and melting heat transfer due to a curved nonlinearly stretching sheet are investigated. The sheet is naturally permeable and the flow is considered in a porous medium. For flow in a porous medium, a modified Darcy's resistance term for Casson fluid is considered in the momentum equation. In the energy equation, heat transport characteristics, including viscous dissipation, are taken into account. Mass transport is also studied together with the impact of chemical reaction of higher order. The governing nonlinear partial differential equations of flow, heat, and mass transport are reduced to nondimensional ordinary differential equations using adequate similarity transformations and then solved numerically employing the bvp4c technique and Runge–Kutta fourth‐order method on MATLAB. The impacts of numerous occurring parameters on relevant fields (velocity field, temperature field, and concentration field) are depicted and discussed by plotting graphs. We concluded the curvature parameter, reduces the pace of the flow. The impacts of the stretching index, and melting parameter, are also found to reduce flow and temperature field. Furthermore, we noted that the reaction parameter, and its order, exhibit opposite impacts on the concentration field. Moreover, the numerical values of skin‐friction coefficient and Nusselt number calculated employing bvp4c and Runge–Kutta fourth‐order technique are expressed in tabular mode, and these are found in an excellent match. For validation of the results, skin‐friction coefficient values were computed using the Runge–Kutta fourth‐order technique and bvp4c solver, compared with the existing results, and a good agreement was found.

Magnetic dipole effects on unsteady flow of Casson-Williamson nanofluid propelled by stretching slippery curved melting sheet with buoyancy force

In particular, the Cattaneo-Christov heat flux model and buoyancy effect have been taken into account in the numerical simulation of time-based unsteady flow of Casson-Williamson nanofluid carried over a magnetic dipole enabled curved stretching sheet with thermal radiation, Joule heating, an exponential heat source, homo-heterogenic reactions, slip, and melting heat peripheral conditions. The specified flow's partial differential equations are converted to straightforward ordinary differential equations using similarity transformations. The Runge–Kutta–Fehlberg 4-5th order tool has been used to generate solution graphs for the problem under consideration. Other parameters are simultaneously set to their default settings while displaying the solution graphs for all flow defining profiles with the specific parameters. Each produced graph has been the subject of an extensive debate. Here, the analysis shows that the thermal buoyancy component boosts the velocity regime. The investigation also revealed that the melting parameter and radiation parameter had counterintuitive effects on the thermal profile. The velocity distribution of nanofluid flow is also slowed down by the ferrohydrodynamic interaction parameter. The surface drag has decreased as the unsteadiness parameter has increased, while the rate of heat transfer has increased. To further demonstrate the flow and heat distribution, graphical representations of streamlines and isotherms have been offered.

Magmatic Evolution and Rare Metal Mineralization in Mount El-Sibai Peralkaline Granites, Central Eastern Desert, Egypt: Insights from Whole-Rock Geochemistry and Mineral Chemistry Data

The Ediacaran peralkaline granites, which were emplaced during the post-collisional tectonic extensional stage, have a limited occurrence in the northern tip of the Nubian Shield. In this contribution, we present new mineralogical and geochemical data of Mount El-Sibai granites from the Central Eastern Desert of Egypt. The aim is to discuss their crystallization condition, tectonic setting, and petrogenesis as well as the magmatic evolution of their associated mineralization. Mount El-Sibai consists of alkali-feldspar granites (AFGs) as a main rock unit with scattered and small occurrences of alkali-amphibole granites (AAGs) at the periphery. The AAG contain columbite, nioboaeschynite, zircon and thorite as important rare metal-bearing minerals. Geochemically, both of AFG and AAG exhibit a highly evolved nature with a typical peralkaline composition (A/CNK = 0.82–0.97) and formed in within-plate anorogenic setting associated with crustal extension and/or rifting. They are enriched in some LILEs (Rb, K, and Th) and HFSEs (Ta, Pb, Zr, and Y), but strongly depleted in Ba, Sr, P and Ti with pronounced negative Eu anomalies (Eu/Eu* = 0.07–0.34), consistent with an A-type granite geochemical signature. The calculated TZrn (774–878 °C) temperatures indicate that the magma was significantly hot, promoting the saturation of zircon. The texture and chemistry of minerals suggest that they were crystallized directly from a granitic magma and were later subject to late- to post-magmatic fluids. Both granitic types were most likely generated through partial melting of a juvenile crustal source followed by magmatic fractionation. The lithospheric delamination is the main mechanism which causes uplifting of the asthenospheric melts and hence provides enough heat for crustal melting. The produced parent magma was subjected to prolonged fractional crystallization to produce the different types of Mount El-Sibai granites at different shallow crustal levels. During magma fractionation, the post-magmatic fluids (especially fluorine) contribute significantly to the formation of rare metal mineralization within Mount El-Sibai granites.

Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning

We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.

Melting Heat Transfer on Magnetohydrodynamics-Nanofluid Boundary Layer Flow Past a Stretching Sheet: Thermal Radiation and Viscous Dissipation Effects

The effects of melting heat transfer, thermal radiation, and porous medium on steady, 2-D, viscous, incompressible, magneto hydrodynamic nano-fluid flow concluded a linearly extending sheet in the occurrence of viscous dissipation, as well as first and subsequent order slip effects, were always considered in this numerical research. In this research, appropriate similarity variables were employed to turn the controlling nonlinear partial differentiated equations hooked on a system of linked nonlinear ordinary differential comparisons that are mathematically explained using the Runge-Kutta approach with a firing scheme. The consequence of several pertinent limitations on rapidity profiles, temperature profiles, and attentiveness profiles is graphically explored also thoroughly interpreted. In this work, images and tables were utilized to represent various progressive values of non-dimensionalized parameters, while numerical data was employed to examine variations in skin-friction, heat, and mass transmission charges. The present study of my observation compared with previous studies in a limiting case. A reliable agreement between the numeric values is achieved here. The velocity profiles in this issue decrease as the values of the Suction/Injection fluid parameter as well as the Magnetic field limitation growth. Temperature profiles rise as the impacts of thermophoresis and Brownian motion become stronger. When the value of the Dufour number rises, so do the temperature profiles. Thermophoresis parameter expansions results in enhanced nanoparticle volume concentration distributions, whereas Brownian motion effects produces the opposite effects. As the Soret number parameter increases, so do the concentration profiles. This melting heat transfer study work includes numerous industrial applications, including casting, welding, and magma solidification, permafrost melting and ground thawing, and so on.

Unveiling the Performance of Cu-Water Nanofluid Flow with Melting Heat Transfer, MHD, and Thermal Radiation over a Stretching/Shrinking Sheet.

The use of melting heat transfer (MHT) and nanofluids for electronics cooling and energy storage efficiency has gained the attention of numerous researchers. This study investigates the effects of MHD, mixed convection, thermal radiation, stretching, and shrinking on the heat transfer characteristics of a Cu-water-based nanofluid over a stretching/shrinking sheet with MHT effects. The governing equations are transformed into nonlinear ordinary differential equations and solved numerically using the Keller Box method. To the best of our knowledge, this comprehensive analysis, encompassing all of these factors, including the utilization of a robust numerical method, in a single study, has not been previously reported in the literature. Our findings demonstrate that an increase in the melting parameter leads to an enhanced rate of heat transfer, while an increase in the stretching/shrinking parameter results in a decrease in the rate of heat transfer. Additionally, we present a comprehensive analysis of the influences of all of the mentioned driving parameters. The results are presented through graphical and tabulated representations and compared with existing literature.

Close-contact melting of shear-thinning fluids

This study aims at establishing a model for close-contact melting (CCM) of shear-thinning fluids. We presented a theoretical framework for predicting the variation of liquid melt film thickness and motion of unmelted solid for both Carreau and power-law fluids. We identified the appropriate energy equation considering the convective effect and derived an analytical temperature profile across the liquid film. Using the lubrication approximation, force equilibrium relationships and the corresponding numerical approaches were built. By using laser interferometry and photographic recording methods, we found excellent agreement between numerical solutions and experimental results for Carreau liquids, revealing that the convective effect weakens heat transfer and melting rate. We identified the critical liquid film thickness that determines three situations of CCM in the theoretical model for Carreau fluids. Numerical prediction demonstrated that the CCM of Carreau fluids can be almost equivalent to that of power-law fluids if the initial film thickness is greater than the critical value. Finally, approximate analytical models were developed for both Carreau and power-law models. For the applicability of the approximate analytical solutions, we derived two- and three-dimensional dimensionless phase diagrams of validity range and identified a key dimensionless group $(\varLambda Re)^{4/3}{Re}\left [3\ln (Ste+1)\right ]^{1/3}{Pe}^{-1/3}$ , where $\varLambda$ is dimensionless characteristic time, Re is Reynolds number, Ste is Stefan number and Pe is Peclect number. The reliability of the approximate solutions was verified by comparing with the numerical results. These approximate solutions enable convenient and low-cost computational prediction of the dynamic CCM process of shear-thinning fluids.

Numerical and Machine Learning Approach for Fe3O4-Au/Blood Hybrid Nanofluid Flow in a Melting/Non-Melting Heat Transfer Surface with Entropy Generation

The physiological system loses thermal energy to nearby cells via the bloodstream. Such energy loss can result in sudden death, severe hypothermia, anemia, high or low blood pressure, and heart surgery. Gold and iron oxide nanoparticles are significant in cancer treatment. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. The present study provides a novel implementation of an intelligent numerical computing solver based on an MLP feed-forward backpropagation ANN with the Levenberg–Marquard algorithm to interpret the Cattaneo–Christov heat flux model and demonstrate the effect of entropy production and melting heat transfer on the ferrohydrodynamic flow of the Fe3O4-Au/blood Powell–Eyring hybrid nanofluid. Similarity transformation studies symmetry and simplifies PDEs to ODEs. The MATLAB program bvp4c is used to solve the nonlinear coupled ordinary differential equations. Graphs illustrate the impact of a wide range of physical factors on variables, including velocity, temperature, entropy generation, local skin friction coefficient, and heat transfer rate. The artificial neural network model engages in a process of data selection, network construction, training, and evaluation through the use of mean square error. The ferromagnetic parameter, porosity parameter, distance from origin to magnetic dipole, inertia coefficient, dimensionless Curie temperature ratio, fluid parameters, Eckert number, thermal radiation, heat source, thermal relaxation parameter, and latent heat of the fluid parameter are taken as input data, and the skin friction coefficient and heat transfer rate are taken as output data. A total of sixty data collections were used for the purpose of testing, certifying, and training the ANN model. From the results, it is found that the fluid temperature declines when the thermal relaxation parameter is improved. The latent heat of the fluid parameter impacts the entropy generation and Bejan number. There is a less significant impact on the heat transfer rate of the hybrid nanofluid over the sheet on the melting heat transfer parameter.

Mathematical modeling of unsteady convective flow analysis of water and nano-encapsulated phase change particles in composite enclosure subject to rotation

Free convection heat transfer in water and hybrid particles in an enclosure is studied. A layer of porous material with various thickness and permeability is attached to the enclosure. Both fluid and porous layers rotate with a specific speed. Hybrid particles are formed by a polyurethane (PU) and an N-nonadecane (ND). PU acts as shell and ND goes through a phase change and it capables of preserving and releasing a considerable amount of latent heat. The enclosure movement can be controlled through a rotation speed. The Brinkman-Forchheimer extended Darcy model is used for governing the flow within a fully saturated porous layer. The governing equations for the convective flow and phase change heat transfer, including specific heat capacity and permeability, were introduced and solved by FEM. The impact of the porous thickness, permeability, fusion temperature and rotation speed on the heat capacity ratio, streamline and isotherms structures were investigated. The results showed that a high Darcy number and thin porous thickness were a good candidate for the improvement of average heat transfer rate since reinforcing the melting process and heat transmitting.

Eminence of ferrite particle shapes in stratified nanofluids concerning the melting phenomenon: Lie group and spectral analysis

The current study is being done to determine how the shape factors of NiZnFe2O4 (nickel zinc ferrite) nanosolid particles affect the free convective flow of engine oil (C8H18) based stratified nanofluid over a melting stretchable surface, which play a part in establishing flow patterns and thermal features. NiZn ferrite nanoparticles of needle, platelet, and brick shapes are used to assess the impact of shape factors in the presence of melting phenomena, heat generation/absorption, and viscous dissipation. Optimal solutions are obtained by the spectral local linearization method via Lie group analysis, with an emphasis on residual errors. According to the evaluation, this type of nanofluid is found to have a lower friction factor, entropy, and Bejan number when compared to conventional fluids. In the presence of viscous dissipation, brick-shaped particles are found to have a higher heat transport rate, whereas needle-shaped particles minimize entropy by 58.66%. Suspended ferrite nanoparticles with a melting effect reduce the entropy up to 62.4% and stratified nanofluid with a brick shape has a higher heat transfer rate as compared to ordinary nanofluid. It is also observed that heat absorption produces less heat transport compared to heat generation. This research is found to be useful in many sectors, such as tumor treatments, electromagnetic interfaces (EMI), microwave applications, bone plate surgeries, and aerodynamic extrusion processes.

Research on Optimization Model of Heat Exchange Fin Structure in Energy Storage System

Aiming at the thermodynamic problem of heat transfer fin in heat storage system, the solidification and melting model and thermodynamic conventional model are established by using simulation software, thermodynamic image processing and other methods. MATLABAB, COMSOL and other software are used to program the optimal rectangular fin spacing Angle and the optimal heat exchange fin structure. Firstly, based on the reason that the simulation software can simulate the heat transfer process of phase change material (PCM) in the actual process to the greatest extent, the plane modeling and thermodynamic equation method are used to analyze the distance Angle of the rectangular fin, and the melting solidification model is established, and the optimal solution is obtained. Finally, combined with the analytic hierarchy model and TOPSIS method, the triangular fin structure and rectangular fin structure were compared from three levels, namely, the heat sink area, temperature rise time and PCM maintenance time of different shapes. And create a heat transfer rate of return to more favorably analyze the data and visually present the comparative results.

Synthesis and thermophysical property determination of NaCl-PuCl3 salts

Currently, a knowledge gap exists in the available data and understanding of thermophysical properties relating to fresh fuel salts, especially those containing plutonium. These data are necessary for designing, constructing, and licensing future commercial molten-salt reactors. Thermophysical properties, such as melting temperature, salt stability, density, and heat capacity were ascertained using NaCl-PuCl3 (36 mol% PuCl3) and a more sodium rich composition containing 25 mol% PuCl3. The NaCl-PuCl3 salt mixture was synthesized for this study and contained 63.4 mol% NaCl, 36.3 mol% PuCl3 and was 99.7% pure. Upon heating, the NaCl–PuCl3 eutectic was stable at temperatures up to 800 °C. The onset of melting occurred at 451 ± 3 °C, and the enthalpy of fusion was determined to be 23.0 ± 1.4 kJ/mol. Heat capacity measurements in the liquid phase ranged from 107.7 to 91.3 J/mol.K, with an average value of 104.6 ± 11.4 J/mol.K between 500 and 650 °C. Three independent trials of the molten NaCl-PuCl3 salt found the density to be ρ(T) = 3.8589 – 9.5342·10-4 T(°C). In addition, ab initio molecular dynamic simulations to calculate density and heat capacity values are included.

Characterization by differential scanning calorimetry of thermal storage properties of organic PCMs with operating temperature of 150 °C

The involvement of Phase Change Materials (PCMs) in energy storage systems leads to more sustainable and efficient use of energy. Medium operating temperature (melting point 100–400 °C) find various applications in industrial waste heat recovery and hybrid compressed air - thermal energy storage systems. However, there is still a lack of detailed knowledge in terms of their thermal storage properties that hinders them from being more integrated in industry. In this study, thermal properties such as melting point, enthalpy and heat capacity of three medium temperature PCMs were characterized using Differential Scanning Calorimetry (DSC). The enthalpy-temperature graph for each PCM is presented that contains key information on sensible and latent heat contribution in the total energy storage. The selected organic PCMs are adipic acid with two different purities 99%, 99.5%, and its chemical equivalent PureTemp151® with a melting point of (150.5 ± 0.5 °C) and a latent heat of (230 ± 10 J/g). Furthermore, the effect of heating rate and sample mass in DSC procedures on transition temperatures and enthalpy were evaluated. Finally, thermal performance of PCMs was quantified through 150 cycles of melting and solidification. The tested PCMs show a significant storage capacity and good thermal stability with less than 10 % enthalpy loss.

Significance of melting heat in bioconvection flow of micropolar nanofluid over an oscillating surface

Pharmaceuticals, biological polymer synthesis, eco-friendly uses, sustainable fuel cell innovations, microbial-enhanced extraction of petroleum, biological sensors, biological technology, and continual mathematical modeling refinement are all examples of how bioconvection is applied. This study examines the bio convectional viscoelastic-micropolar nano liquid flow with non-uniform heat sink/source, motile microorganisms that move across a stretched sheet. Thermal radiation and thermal conductivity are also explored. Brownian and thermophoresis diffusion effects are taken into account. The system of a higher partial differential equation is transformed to ODEs by using the appropriate similarity functions. Such reported equations are implemented with the computational tool MATLAB shooting approach using a bvp4c solver. The variations of numerous flow parameters comprise velocity, temperature, concentration, and motile microorganism profile. Various important, interesting transport numbers are numerically and graphically demonstrated with physical justifications. The bouncy ratio parameter reduces the fluid's velocity profile whereas the material parameter increases it. For increased melting parameters, the micro rotation profile improves, but it deteriorated. For the Prandtl number and temperature ratio parameters, the temperature profile is negative. The melting parameter influences the concentration profile. The microorganism’s profile is decreased bioconvective Lewis numbers and is higher for the magnetic parameter. The current model has many features in the manufacturing industries, engineering works, physics, and applied mathematics.

Numerical study on melting process and heat transfer analysis of a multitube combination latent heat storage unit with innovative harpoon-type fins

The heat transfer rate of a coupled system combining a passive residual heat removal system and a latent heat thermal energy storage system is directly related to worker safety in nuclear power plants. To enhance the heat transfer performance of the coupled system, in this study, the melting process of phase change material in the latent heat thermal energy storage system is numerically investigated by inserting innovative harpoon-type fins. A new assessment index is also proposed to evaluate the comprehensive heat transfer performance of fins. More than thirty cases with different harpoon-type fins are designed, and the impacts of various efficient structural parameters of the harpoon-type fin on the melting process are evaluate. The response surface method is used to optimize the structure. The results demonstrated that the handle length and the number of fins significantly improve the heat transfer performance of the harpoon-type fin. The optimal geometrical parameters (arc angle θ = 45°, handle length Lha = 10 mm, fin number Nf = 8, and arc number Na = 1) of harpoon-type fins are obtained. The heat transfer rate of the optimal fin structure is six times that without fins, and the total melting time is shortened by 85.9%. Furthermore, the longitudinal extension of the fins is more important than the complex horizontal extension of fins. The harpoon-type fin not only shows better performance in the coupled system but can also be used in shell-and-tube latent heat thermal energy storage systems.

Solubility and Valence Variation of Ce in Low-Alkali Borosilicate Glass and Glass Network Structure Analysis.

Low-alkali borosilicate glass was used as the immobilization substrate, and Ce was used to replicate the trivalent and tetravalent actinides, in order to create simulated waste glass through melt heat treatment. The valence of Ce and solubility of CeO2 in waste glass were studied as well as its network structure and thermal and chemical stability. The solubility of Ce in waste glass was examined by XRD and SEM. The network structure was examined by Raman spectroscopy. The valence of Ce was determined by X-ray photoelectron spectroscopy. Thermal analysis and product consistency (PCT) were employed to determine the thermal and chemical stability of waste glasses. The results show that the solubility of cerium in low-alkali borosilicate glasses is at least 25.wt.% and precipitates a spherical CeO2 crystalline phase when it exceeds the solid solution limit; Ce is immobilized in the glass by entering the interstices of the glass network. Depolymerization and the transition from [BO3] to [BO4] occurs when CeO2 doping levels rise. About 60 percent of Ce4+ is converted to Ce3+, and the thermal stability of glass rises then falls with the increase of CeO2. All samples exhibit strong leaching resistance, with the average mass loss of Ce at 28 days being less than 10-4 gm-2d-1.

Thermo-economic assessments on building heating by a thermal energy storage system with metal foam

Due to the intermittency and discontinuity of solar energy, thermal energy storage (TES) using phase change materials (PCMs) is generally required to ensure stable operation in solar heating systems (SHS) during winter. This paper presents the design of a TES unit with different horizontal metal foam filling ratios (60%–100%), and simulations of thermal characteristics, such as complete melting time and heat storage capacity by numerical method. Based on the heating demands of an office building in Xi'an, TES units are combined in parallel and economic indexes are calculated based on static evaluation method, including initial investment and investment payback period. Novelty, the contribution of gradient microstructure to the phase transition process is evaluated from thermophysical properties and economy. Results show that the TES unit with a filling ratio of 90% possesses the shortest complete melting time of 5310 s, which is 87.56% shorter than that of a TES unit with pure PCM. Finally, economic assessments of the engineering application of the partially filled metal foam structure are carried out, and it is determined that the SHS with the TES system of 90% filling ratio requires the least number of 548 TES units, with a payback period of three heating seasons.

A novel method for modeling the phase change of iron ore particles in the cohesive zone of a blast furnace

Cohesive zone plays a vital role in the stable operation of a blast furnace (BF), yet the complex phase change process of iron ore particles in this zone is still not well understood. In this study, a novel one-dimensional (1D) unsteady phase change model was developed to elucidate the heat transfer and melting mechanisms of iron ore particles. After model validation, the effects of several key operating parameters (e.g., particle diameter, gas velocity, initial temperature) on the phase change behavior of iron ore particles were analyzed, and the joint effect of multiple parameters was discussed. The results show that larger-sized iron ore particles possess lower specific surface areas, which in turn reduces their convective heat absorption capacity. Consequently, the distance from the solid-liquid phase interface to the particle surface increases, thereby slowing down the movement of the phase interface and prolonging the melting duration of the particles. Increasing the gas velocity and the initial temperature does not have a significant impact on reducing the duration of the complete melting process. Under the specified conditions, it is observed that increasing the gas velocity by 3-fold and 9-fold results in a reduction of the melting duration by 2.4% and 8.3%, respectively. Elevating the initial temperature of iron ore particles results in a decrease in the core-to-surface temperature difference, a slower heating rate, and a shorter duration to achieve melting. Among the factors affecting the melting process, the particle diameter is found to be the most significant in terms of the liquid phase precipitation, mushy zone thickness, and core-to-surface temperature difference of iron ore particles.

Design and performance of the Hotrod melt-tip ice-drilling system

Abstract. We introduce the design and performance of an electrothermal ice-drilling system designed to insert a temperature sensor cable into ice. The melt tip is relatively simple and low-cost, designed for a one-way trip to the ice–bed interface. The drilling system consists of a melt tip, umbilical cable, winch, interface, power supply, and support items. The melt tip and the winch are the most novel elements of the drilling system, and we make the hardware and electrical designs of these components available open-access. Tests conducted in a laboratory indicate that the melt tip has an electrical energy to forward melting heat transfer efficiency of ∼35 % with a theoretical maximum penetration rate of ∼12 m h−1at maximum 6.0 kW power. In contrast, ice-sheet testing suggests the melt tip has an analogous heat transfer efficiency of ∼15 % with a theoretical maximum penetration rate of ∼6 m h−1. We expect the efficiency gap between laboratory and field performance to decrease with increasing operator experience. Umbilical freeze-in due to borehole refreezing is the primary depth-limiting factor of the drilling system. Enthalpy-based borehole refreezing assessments predict refreezing below critical umbilical diameter in ∼4 h at −20 ∘C ice temperatures and ∼20 h at −2 ∘C. This corresponds to a theoretical depth limit of up to ∼200 m, depending on firn thickness, ice temperature, and operator experience.

Analysis of radiative MHD Carreau nanofluid flow with melting heat transfer and variable thermal conductivity

AbstractIn this work, we present the impacts of melting heat transfer phenomena on the steady, laminar, incompressible, two‐dimensional magnetohydrodynamic (MHD) Carreau nanofluid flow towards the stretching sheet. Additionally, in energy equation thermal radiation and variable thermal conductivity effects are also taken into consideration. By using similarity variables, governing non‐linear partial differential equations (PDEs) of the Carreau nanofluid flow model are transformed into dimensionless non‐linear ordinary differential equations (ODEs). Numerical solutions are then investigated and the results are illustrated through graphs and tables showing parameters effect on velocity, temperature, and concentration profiles of the fluid and on physical quantities including skin friction coefficient, Nusselt and Sherwood numbers, respectively. From the analysis, it is found that boosting melting heat transfer parameter leads to increasing behavior in velocity and concentration distributions, while the opposite trend is noticed for temperature distribution. Numerical results are found in close agreement and are accurate by carrying out its comparison with previous results for skin friction coefficient with different magnetic parameters while keeping other parameter values constant.