Solution Of Heat Transfer Research Articles

An Approximate Solution for Heat Transfer in the Entrance Region of Laminar Newtonian Pipe Flow

The study of the simultaneously developing pipe flow requires facing nonlinear systems of partial differential equations. In this framework, the aim of this paper is to demonstrate that the integral method can be an effective procedure to obtain analytic-approximate solutions that are easy to handle while allowing the recovery of a satisfactory accordance with the exact solution. To prove the above statement this paper will present a comparison between the approximate solution and the corresponding numerical solution in the entrance region of Newtonian pipe flow. Third-kind thermal boundary conditions are included, while velocity and temperature profiles at the inlet are assumed uniform. Numerical results demonstrate that the proposed approximate solution is quite accurate and readily implemented, both in terms of developing velocity and temperature profiles. Moreover, the expected functional dependence on the main parameters of the problem at hand is retained. As a consequence, the developing Fanning friction coefficient and Nusselt curves are satisfactory and accurate for different thermal boundary conditions at the wall.

Dual Solutions of Two-Dimensional Hybrid Nanofluid Flow and Heat Transfer Past a Porous Medium Permeable Shrinking Sheet with Influence of Heat GenerationAbsorption and Convective Boundary Condition

In this study, the dual solutions of two-dimensional hybrid nanofluid flow and heat transfer past a porous medium permeable shrinking sheet with influence of heat generation/absorption and convective boundary condition were examined using the bvp4c solver with the MATLAB computational framework. The utilization of two-dimensional hybrid nanofluid flow and heat transfer in the presence of a porous medium permeable shrinking sheet, considering the effects of heat generation/absorption and convective boundary conditions, has wide-ranging applications in industries such as cooling systems, aerospace, chemical engineering, biomedical applications, energy systems, microfluidics, automotive thermal management, industrial drying, and nuclear reactor cooling, etc. These applications employ the improved thermal characteristics of hybrid nanofluids and the efficient heat control offered by porous media and convective boundary conditions. The governing partial differential equations (PDEs) are transformed into a collection of higher-order ordinary differential equations (ODEs) together with their corresponding boundary conditions. These equations are subsequently shown both numerically and graphically. The main objective of this inquiry is to examine the relationship between the solid volume fraction of copper and the permeability parameter of the porous medium, specifically focusing on the values of f''(0) and - (0) according to the suction effect. The current research has also integrated the temperature and velocity profile of a hybrid nanofluid flow, which corresponds to the influence of porous medium permeability, heat generation/absorption, and convective boundary condition. Dual solutions are acquired by certain combinations of parameters. Non unique solutions are obtained when the critical point reaches , for suction effects. Increasing the intensity of heat generation absorption and convective boundary condition leads to a more pronounced temperature profile and thicker boundary layer.

Approximate analytical and numerical investigation of Oseen-type forced convection around a sphere in a low Reynolds number slip flow

Convective heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated using Oseen’s theory. The size of the sphere is assumed to be small enough so that the temperature jump condition of dilute gas dynamics is valid on the sphere surface. Approximate analytical formulations are presented for the mean Nusselt number, the local Nusselt number and the temperature field. The presented formulations outperform the existing analytical solutions for the Oseen-type heat transfer around the sphere for both no-slip and slip flows. The new formulations do not diverge by increasing the Reynolds number and are capable of predicting acceptable results even up to Reynolds numbers beyond the validity of the Oseen’s theory. While the existing asymptotic solutions only give the mean Nusselt number, the proposed solutions additionally yield the local Nusselt number and the temperature field. A numerical solution of Oseen’s equation is also conducted for comparison. Based on the results presented, recommendations are made on the use of various formulations to achieve accurate results.

Numerical solutions for unsteady laminar boundary layer flow and heat transfer over a horizontal sheet with radiation and nonuniform heat Source/Sink

This paper investigates the unsteady laminar boundary layer flow and heat transfer over a horizontal sheet subjected to radiation and a nonuniform heat source/sink. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and solved via the bvp4c numerical method. The key findings indicate that increasing the unsteadiness parameter leads to a reduction in both velocity profiles and heat flux, while higher values of the Prandtl number reduce thermal boundary layer thickness. In contrast, the radiation and magnetic parameters enhance the temperature profile within the boundary layer. The study offers new insights into the effects of flow parameters on boundary layer behaviour, validated through table and graphical comparisons with existing literature. These findings provide practical approaches for optimizing heat transfer systems in engineering applications.

Heat transportation of 3D chemically reactive flow of Jeffrey nanofluid over a porous frame with variable thermal conductivity

Nanofluids with variable thermal conductivity can potentially bring about a transformative impact in various industries. They offer adaptive and efficient heat transfer solutions that can adjust to changing conditions and specific requirements. The insertion of nanoparticles into the base fluid significantly changes its properties, affecting thermal conductivity and viscosity. The primary objective of this paper is to analyze the heat transfer rate and three-dimensional bio-convective flow of a non-Newtonian Jeffrey nanofluid across a porous surface with variable thermal conductivity. The investigation also considers the impacts of thermophoresis, Brownian motion, and the Lorentz force. The combine impact of thermal radiation and motile microbes also incorporated in the current study. To model these phenomena, we employ the boundary layer approximation to derive a system of partial differential equations (PDEs). These PDEs are subsequently simplified into more manageable ordinary differential equations (ODEs) using the similarity variables. The numerical analysis is performed via the finite difference approach, which consists of a three-stage Lobatto scheme using MATLAB package. Additionally, important engineering parameters under different constraints-like skin friction, Nusselt number, and Sherwood number—are given in a thorough manner using tabular and graphical representations. The results of this study demonstrate significant enhancements in various aspects, including thermophoresis, Brownian motion, and thermal boundary layer thickness are demonstrated through graphically and in the form of tables. As the thermal radiation parameter increases, the temperature profile rises accordingly. This enhancement in the temperature profile is directly attributable to the higher value of the radiation parameter, which results in a physical increase in temperature. These improvements are attributed to a reduction in viscous forces and an increase in the Brownian diffusion coefficient. This research advances the understanding of non-Newtonian thermally radiative flow with variable thermal conductivity, elucidating the complex behavior of such fluids and providing valuable insights for engineering applications.

Asymptotic solutions for heat transfer and stresses in functionally graded porous sandwich pipes subjected to nonuniform pressures and thermal loads

In this work, thermomechanical behaviors of temperature-dependent (TD) functionally graded porous (FGP) sandwich pipes subjected to nonuniform pressures and thermal loads are studied. Because the material properties are variable across the wall of the pipe, seeking exact solutions for the pipe is almost impossible. We use a slice model where the pipe is partitioned into plenty of annular slices and each slice is assumed to have uniform material properties. First, the nonlinear heat transfer along the pipe wall thickness is obtained by introducing an iterative procedure. Then, by using the Fourier series, the mechanical problem is decomposed into axisymmetric and nonaxisymmetric parts. Both the parts can be treated by the state space method and transfer matrix method, and then the superposition principle is used to obtain the displacement and stress distributions. The model results are in good consistency with those obtained from the numerical simulation and those reported in the literature. Finally, an FGP sandwich pipe is considered to discuss the effects of the temperature dependence of material properties (TDMP), power-law index, porosity, and pressure distribution on its thermomechanical behaviors.

A Mathematical and Analytical Solution for MHD Boundary Layer Flow and Heat Transfer of a Nanofluid Over a Stretching Sheet Using the Homotopy Analysis Method

A Mathematical and Analytical Solution for MHD Boundary Layer Flow and Heat Transfer of a Nanofluid Over a Stretching Sheet Using the Homotopy Analysis Method

A comparative analysis of ammonia and supercritical carbon dioxide in horizontal microchannels

Supercritical carbon dioxide (sCO2) and ammonia (NH3) can be used as coolants in high power-density microelectronics. sCO2 at the micro scale provides enhanced heat transfer solutions for a range of microelectronics cooling applications·NH3 can also potentially provide appropriate cooling solutions as it has favorable thermophysical properties at high pressure, and it can be used as an energy carrier as it contains Hydrogen atoms. Near its critical and pseudocritical condition sCO2 exhibits abrupt changes in its thermophysical properties and at similar pressures liquid NH3 too has adequate properties that make it a good coolant. While sCO2 is non-toxic, NH3 is a toxic substance and should only be used in closed loop micro heat exchangers.The current study compares the convective heat transfer performance of supercritical carbon dioxide (sCO2) and ammonia for microchannel cooling. A total of 144 numerical cases inside a square microchannel of hydraulic diameter of 200 µm with a total length of 52 mm and a heated length of 50 mm at constant surface temperatures in laminar flow conditions were examined. Two scenarios were investigated, in one the inlet mass flux was kept constant at 100, 150, and 200 kg/m2s, and in the second the pressure drop across the microchannel was maintained at 200, 400, and 600 Pa. Both scenarios were investigated at pressures of 8 and 10 MPa and at surface temperatures of 32, 40, 50, 60, 70, and 80 °C. In all cases the inlet temperature of both fluids was kept at 21 °C. At the same mass flux, NH3 yielded a higher average heat transfer coefficient (havg) but at the same pressure drop, sCO2 resulted in higher havg at certain surface temperatures. The havg for NH3 didn’t show significant variation but for sCO2 it showed significant change with surface temperature, and this was due to the significant change in the thermophysical properties of sCO2. The havg showed a mixed behavior with respect to the pumping power. The coefficient of performance (COP) was as high as 600,000 for sCO2 and it was significantly higher than that for NH3. Near the pseudocritical region, the COP for sCO2 witnessed a significant improvement, more than double, for 8 MPa compared to 10 MPa.

A Novel Fast Wavenumber Selection Scheme for Line-by-Line Monte Carlo Simulations of High Temperature Gases

Abstract Implementing line-by-line absorption spectra in the Monte Carlo method provides a benchmark solution for radiative heat transfer in participating media. It is, however, a computationally demanding calculation, and therefore its application is limited to small and medium-scale cases. In gas mixtures, one of the most time-consuming parts is the wavenumber selection for each emission bundle (aka photon). Due to interdependency of spectral emission of individual species, trial-and-error is needed to obtain the emission wavenumber of species. Doing trial-and-error with tight convergence threshold through large set of data increases the simulation time. This paper presents a novel scheme to select the wavenumber by adding a new dataset which circumvents the need for trial-and-error. The performance of the new scheme is exhibited in three different test cases containing CO2, H2O, and CO. An excellent agreement was observed between the results of the new and old schemes. Compared to the previously published hybrid selection scheme, the wavenumber selection is around seven times faster using the current scheme.

A Comprehensive Evaluation of Recent Studies Investigating Nanofluids Utilization in Heat Exchangers

This comprehensive review critically examines recent research concerning the application of nanofluids in heat exchangers. The utilization of nanofluids, which are colloidal suspensions of nanoparticles in a base fluid, has garnered significant attention in enhancing heat transfer performance. Various studies have explored the potential benefits and challenges associated with incorporating nanofluids into heat exchanger systems. Through a systematic analysis of recent literature, this review assesses the effectiveness of nanofluids in improving heat transfer efficiency and overall performance of heat exchangers. Key parameters such as nanoparticle concentration, size, and type are thoroughly evaluated to understand their influence on heat transfer characteristics. Additionally, factors such as stability, flow behavior, and thermal conductivity enhancement are scrutinized to provide a comprehensive understanding of nanofluid behavior in heat exchangers. The review also addresses potential limitations and areas requiring further investigation to optimize the utilization of nanofluids in heat exchanger applications. By synthesizing recent findings, this review aims to contribute to the advancement of knowledge in the field of heat exchanger technology and nanofluid applications. Ultimately, the insights provided in this review offer valuable guidance for researchers and engineers seeking to enhance heat transfer processes through the implementation of nanofluid-based heat exchangers. Nanofluids offer advantages like enhanced thermal conductivity and tailored properties, promising optimized heat exchanger designs, leading to energy efficiency and reduced costs. However, challenges remain, such as nanoparticle dispersion and cost-effectiveness, necessitating further research for refinement. Interdisciplinary collaboration is crucial for advancing nanofluid applications, fostering innovation to meet demands for sustainable heat transfer solutions.

Peristaltic transport with multiple solutions of heat and mass transfer using modified Buongiorno nanofluid model over tapered channel with long wave‐length at small Reynolds number

AbstractThis research paper aims to investigate the peristaltic transport of a nanofluid (NF) in a tapered asymmetric channel. Initially, the governing equations for the balance of mass, momentum, temperature, and volume fraction for the NF using Reiner–Philippoff (RP) based NF are formulated. Subsequently, these equations are employed to analyze long wavelength and small Reynolds number scenarios. The numerical results for various flow features are thoroughly examined and discussed. Dual solutions have been examined for some factors. So, stability assessment is implemented to find stable solution. Novelty of the existing is to investigate the peristaltic motion of Buongiorno's NF model and its stability which has not investigated in the previous literatures. It has been demonstrated that modifying the RPF parameter leads to a transition in the fluid's velocity, changing it from a dilatant liquid to a Newtonian fluid and from Newtonian to pseudoplastic. The findings indicate that the temperature curves rise as Brownian motion and thermophoretic factors increase, while they decrease as the Prandtl number increases. Furthermore, a concise mathematical and graphical analysis is carried out to examine the impact of each key parameter on the flow characteristics.

Energy and exergy analysis of a long-term nonlinear dynamic roll bond PVT solar collector model under Tunisian (North Africa) climatic conditions

Roll-bond type PVT modules drew little attention while offering a higher energy exchange area and an efficient heat transfer solution. Furthermore, comparative studies including exergetic assessment on PVT systems are very limited in the literature. In this paper, a novel and detailed nonlinear dynamic roll bond PVT model is performed under real-world weather conditions that provide reasonable and realistic system performance. By incorporating local solar, thermal, exergy, and electrical models based on five diode parameters, a thorough analysis is conducted. Likewise, a unique, rigorous exergy comparison between PV, thermal, and roll bond PVT systems is conducted. Results reveal that there appears to be a direct relationship between wind velocity and changes in ambient temperature which affect exergy efficiency. Higher irradiance and lower wind speeds lead to increased thermal losses, which lower the electrical exergy efficiency of the PV and PVT solar collectors.The exergy analysis reveals that a PVT system outperforms PV + ST, and findings show that for thermal and electrical parts, the yearly average efficiencies are 33.7 % and 12.27 %, respectively. Findings enable a fast and an accurate assessment of fill factor (FF), which is temperature-dependent, over the course of a year’s worth of PVT collector operation.

Exact solution for conjugate heat transfer within a solar receiver tube: A comprehensive analysis

This study presents exact solutions for the phenomenon of conjugate heat transfer occurring within a solar receiver tube. The investigation focuses on three distinct configurations: (a) tubes with negligible wall thickness, (b) thin-walled tubes, and (c) thick-walled tubes. The primary objective is to offer precise mathematical representations for the distribution of temperature, as well as numerical values of local and average Nusselt numbers. Furthermore, the study delves into the examination of limiting cases to enhance the understanding of the problem at hand and validating the outcomes. The derived solutions are also utilized to conduct a comprehensive analysis of the specific practical scenario involving the flow of molten salt in both Alloy 625 and stainless steel solar receiver tubes. Inspection of the configurations presented in this study demonstrates that the circumferential conduction heat transfer in the tube wall helps to distribute the heat more evenly along the circumference and mitigate the occurrence of localized hot spots.

Heat Transfer Application of Nanofluids and Testing of Thermal Conductivity

In response to the growing demand for more efficient heat transfer technologies in various industrial processes, the development of nanofluids has emerged as a promising solution. Traditional heat transfer fluids like mineral oil, ethylene glycol, and water have relatively low thermal conductivities compared to solids, limiting the compactness and efficiency of heat exchangers. Nanofluids, which are created by suspending ultrafine metallic or nonmetallic solid powders in base fluids, exhibit enhanced thermal properties due to the superior thermal conductivities of solid materials. This paper reviews the preparation, thermal conductivity measurement, and influencing factors of nanofluids, with a focus on thermal conductivity as the primary driver for improved heat transfer. The preparation of nanofluids involves either a one-step or two-step method, with the two-step method being more commonly used for oxide nanoparticles (NPs) such as Al2O3, ZnO, MgO, TiO2, and SiO2. The study discusses stabilization techniques like ultrasonication and magnetic force agitation to ensure homogeneous suspension and long-term stability of the nanofluids. The thermal conductivity measurements are conducted using short hot wire (SHW) and transient hot wire (THW) techniques, with considerations of the nonsteady-state nature and potential error sources. The research underscores the importance of rigorous experimental design and accurate data analysis to address the complexities and variability in thermal conductivity measurements, ultimately contributing to the advancement of nanofluid technologies for efficient heat transfer solutions.

Potential of 3D Printing for Heat Exchanger Heat Transfer Optimization—Sustainability Perspective

In just a few short years, the additive manufacturing (AM) technology known as 3D printing has experienced intense growth from a niche technology to a disruptive innovation that has captured the imagination of mainstream manufacturers and hobbyists alike. The purpose of this article is to introduce the use of 3D printing for specific applications, materials, and manufacturing processes that help to optimize heat transfer in heat exchangers, with an emphasis on sustainability. The ability to create complex geometries, customize designs, and use advanced materials provides opportunities for more efficient and stable heat transfer solutions. One of the key benefits of incremental technology is the potential reduction in material waste compared to traditional manufacturing methods. By optimizing the design and structure of heat transfer components, 3D printing enables lighter yet more efficient solutions and systems. The localized manufacturing of components, which reduces the need for intensive transportation and associated carbon emissions, can lead to reduced energy consumption and improved overall efficiency. The customization and flexibility of 3D printing enables the integration of heat transfer components into renewable energy systems. This article presents the key challenges to be addressed and the fundamental research needed to realize the full potential of incremental manufacturing technologies to optimize heat transfer in heat exchangers. It also presents a critical discussion and outlook for solving global energy challenges through innovative incremental manufacturing technologies in the heat exchanger sector.

[formula omitted]-Functions for fields of series- and parallel-connected boreholes with variable fluid mass flow rate and reversible flow direction

A new methodology is developed for the calculation of g-functions for the simulation of geothermal bore fields in non-stationary conditions. The g-functions are able to represent the variations of fluid mass flow rate and reversible flow direction, and model the effect of these variations on the long-term ground temperature response. The thermal model is constructed by coupling an axially-discretized finite line source solution for the ground heat transfer, a thermal resistance circuit model for the interior of the boreholes, as well as connectivity relations between parallel- and series-connected boreholes. Simulation experiments show that the new g-functions are required for the accurate prediction of fluid temperatures in series-connected boreholes with variable mass flow rate and reversible flow direction. A simulation of a borehole thermal energy storage system of 144 boreholes over a period of 20 years shows a maximum absolute error of 0.65 °C. The new g-functions thus extend the simulation capabilities of g-functions to borehole thermal energy storage systems.

Analytical Solution for MHD Casson Nanofluid Flow and Heat Transfer due to Stretching Sheet in Porous Medium

The feature of having a surface that can stretch has garnered attention in numerous industrial and engineering fields because of its advantages. Nevertheless, most fluid mechanics simulations for stretchable surfaces have predominantly relied on numerical solutions, with a notable lack of theoretical investigations into this matter. Consequently, the current research aims to contribute a theoretical exploration of heat transfer and boundary layer flow for Casson nanofluid on a linearly stretching sheet, considering the existence of porosity and magnetic field effects. Two distinct types of water-based nanofluids containing aluminium oxide and silicon dioxide are examined. By employing similarity transformations, the governing momentum and energy equations undergo transformation and subsequent analytical resolution using Laplace transformations. The resulting solutions are graphically presented to examine the influence of key parameters on temperature and velocity distribution. The analysis indicates that heat transfer is improved by the inclusion of nanoparticles, porosity, and a magnetic field. However, the velocity distribution slows down as a result of higher nanoparticle volume fraction, porosity, and magnetic field imposition.

A new analytical method for transient heat conduction in composite disks applied to thermal plug and abandonment of oil wells

A new hybrid method for transient heat conduction problems is developed and applied to simulate a Plug and Abandonment (P&A) operation of oil wells. An oil well is approximated by concentric disks in a one-dimensional configuration, which allows for use of polar coordinates. The application of the Separation of Variables Method (SVM) is used as the analytical framework for the solution of the conductive heat transfer arising from a volumetric heat source located in the center of the disks. The SVM is able to solve only time-independent boundary conditions. However, using the Duhamel's theorem, the solution determined with the SVM can be used to achieve the solution when both time-dependent boundary conditions and internal heat generation are prescribed. Lastly, for verification purposes, a commercial software that solves the transient temperature field by means of numerical procedures, providing reliability to the analytical method proposed in this work.

Effects of cross-sectional shape on flow and heat transfer of the laminar flow of supercritical carbon dioxide inside horizontal microchannels

Supercritical carbon dioxide (sCO2) flow at the micro scale provides an excellent heat transfer solutions for a range of microelectronics cooling applications. The cross-sectional shape of the microchannel (in combination with the abruptly changing thermophysical properties of sCO2) affects the heat transfer and flow characteristics, but these effects are not well understood at constant wall temperatures as most of the previous studies were performed at constant surface heat fluxes. Current study numerically investigated, using CFD, the effects of different cross-sectional shapes, such as circle, equilateral triangle, semi-circle, and square, in zero gravity (space) and in terrestrial conditions, at constant wall temperatures.In all cases, the hydraulic diameter of the microchannel was 100 μm, the total length was 27 mm, and the heated length was 25 mm. A total of 216 cases were analyzed to predict the effects of surface temperature ranging from 310 to 330 K, pressures ranging from 8 to 10 MPa, and Reynolds numbers from 100 to 500 on the heat transfer and flow. It was revealed that the microchannel with triangular cross-section has the highest heat transfer rate, highest mass flow rate, and lowest pressure drop both in zero gravity and in terrestrial conditions. The total surface heat transfer rate for the triangular microchannel was about 49% higher than the circular microchannel at a pressure of 8 MPa, around 53% higher at 9 MPa, and about 55% higher at 10 MPa. However, the average surface heat transfer coefficient displayed a complex behavior, and it depends on the combination of surface temperature, Reynolds number, and operating pressure. The surface heat transfer rate and pressure drop were increased for all shapes at terrestrial conditions, emphasizing that the effects of buoyancy cannot be neglected. Overall, this study revealed a complex behavior of the flow of sCO2 inside microchannels of different cross-sectional shapes, and the triangular cross-section performed better than other shapes.

Series Solutions of Three-Dimensional Magnetohydrodynamic Hybrid Nanofluid Flow and Heat Transfer

Hybrid nanofluids have many real-world applications. Research has shown that mixed nanofluids facilitate heat transfer better than nanofluids with one type of nanoparticle. New applications for this type of material include microfluidics, dynamic sealing, and heat dissipation. In this study, we began by placing copper into H2O to prepare a Cu-H2O nanofluid. Next, Cu-H2O was combined with Al2O3 to create a Cu-Al2O3-H2O hybrid nanofluid. In this article, we present an analytical study of the estimated flows and heat transfer of incompressible three-dimensional magnetohydrodynamic hybrid nanofluids in the boundary layer. The application of similarity transformations converts the interconnected governing partial differential equations of the problem into a set of ordinary differential equations. Utilizing the homotopy analysis method (HAM), a uniformly effective series solution was obtained for the entire spatial region of 0 < η < ∞. The errors in the HAM calculation are smaller than 1 × 10−9 when compared to the results from the references. The volume fractions of the hybrid nanofluid and magnetic fields have significant impacts on the velocity and temperature profiles. The appearance of magnetic fields can alter the properties of hybrid nanofluids, thereby altering the local reduced friction coefficient and Nusselt numbers. As the volume fractions of nanoparticles increase, the effective viscosity of the hybrid nanofluid typically increases, resulting in an increase in the local skin friction coefficient. The increased interaction between the nanoparticles in the hybrid nanofluid leads to a decrease in the Nusselt number distribution.