{"title":"MHD Casson Nanofluid Flow over a Stretching Rotating Disk with Heat Source and Spatially Varying Magnetic Field","authors":"Talha Anwar , Qadeer Raza , Tahir Mushtaq , Bagh Ali , Ehsanullah Hemati","doi":"10.1016/j.ijft.2025.101422","DOIUrl":"10.1016/j.ijft.2025.101422","url":null,"abstract":"<div><div>This paper investigates the steady magnetohydrodynamic (MHD) flow and heat transfer of a Casson nanofluid over a stretching, rotating disk in the presence of a spatially varying magnetic field and internal heat source. The model incorporates the Buongiorno nanofluid framework, which accounts for nanoparticle motion due to Brownian diffusion and thermophoresis, and includes velocity, thermal, and concentration slip conditions at the disk surface. Unlike traditional studies assuming a uniform magnetic field, the present work considers a magnetic field that decays exponentially away from the disk surface, providing a more realistic representation of applied magnetic fields in practical systems such as electromagnetic processing and rotating machinery. Additionally, the influence of an internal heat generation term is included in the energy equation to simulate thermal sources within the fluid. By applying similarity transformations, the governing nonlinear partial differential equations are reduced to a system of coupled ordinary differential equations. These equations are solved numerically using the bvp4c function in the Matlab computer language. The effects of various physical parameters such as magnetic field strength and gradient, slip coefficients, Casson fluid parameter, and heat source intensity are systematically explored. The results reveal that increasing the magnetic field strength or the heat source significantly enhances the thermal boundary layer, while velocity profiles are suppressed near the disk due to magnetic damping. The presence of multiple slips and the Casson fluid parameter further alter the flow and thermal behavior, making the system tunable for thermal management applications.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101422"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nisha Chouhan , Reema Jain , K. Loganathan , S. Eswaramoorthi
{"title":"Heat and mass transmission in Maxwell nanofluid flow over an exponential stretchable surface with swimming of motile gyrotactic microorganisms","authors":"Nisha Chouhan , Reema Jain , K. Loganathan , S. Eswaramoorthi","doi":"10.1016/j.ijft.2025.101466","DOIUrl":"10.1016/j.ijft.2025.101466","url":null,"abstract":"<div><div>The flow of nanofluid across an exponential stretchable surface becoming a growing topic in past few decades due to its numerous usages in industrial and engineering areas. Particularly, glass blowing, polymer extrusion, wire drawing, hot rolling, annealing, etc. This communication mainly focuses on the flow of Maxwell nanofluid via an exponential stretchable surface with magnetic impact and heat consumption. Thermophoresis and Brownian motion are also considered with the existence of heat radiation and fluid dissipation in a two dimensional model with gyrotactic microorganisms. The nonlinear governing models are changed into an ordinary differential models by incorporating the appropriate translation variables. The remodeled equations are numerically computed by utilizing the bvp4c approach in MATLAB. The impact of the physical features on velocity, temperature, nanofluid concentration, and microorganisms profiles, as well as the skin friction coefficient, Nusselt, Sherwood and motile density numbers are evaluated. Further, findings revealed that the fluid velocity diminishes when enriching the values of the magnetic and material parameters. The thermophoresis parameter causes the nanofluid temperature and concentration profiles to develop. The microorganisms profile declines when enriching the Peclet and Lewis numbers. The radiation parameter improves the heat and mass transference rates. The motile density number develops for greater quantity of the microorganism difference parameter with the presence of the Peclet number.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101466"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Carbon emission reduction potential calculation method based on rapid selection of carbon emission factors and time series analysis","authors":"Zhibin Yan , Xuwei Xia , Shuang Zhang , Dongge Zhu","doi":"10.1016/j.ijft.2025.101463","DOIUrl":"10.1016/j.ijft.2025.101463","url":null,"abstract":"<div><div>The current calculation method struggles to ensure data integrity and consistency and overlooks the combined effects of other influencing factors, leading to results that fail to fully reflect the actual carbon emission reduction situation. Therefore, a method for calculating carbon emission reduction potential based on rapid selection of carbon emission factors and time series analysis is proposed. A comprehensive and systematic carbon emission inventory is established, carbon emission coefficients are accounted for, carbon emission intensity is calculated, and a real-time carbon emission calculation model is constructed. Using the autoregressive distributed lag model from time series analysis, a model for predicting energy consumption and industrial output based on electricity consumption is developed. Multiple methods for selecting energy carbon emission factors are introduced, the most reasonable carbon emission factor is selected, a carbon emission efficiency evaluation model is constructed, and the carbon reduction potential is calculated. Experimental results indicate that the carbon emissions per 10,000 yuan of output value obtained by the proposed method remain below 0.8 t, demonstrating the highest emission reduction potential across all years. The carbon emission factor remains lower than 65, and the carbon emission efficiency exceeds 0.8, reaching a maximum of 0.98.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101463"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Ehsan Ullah , Syed Tauseef Saeed , Najla A. Mohammed , Muhammad Idress , Muhammad Nauman Aslam , Ilyas Khan , Osama Oqilat , Muhammad Sabaoon Khan
{"title":"Prandtl ternary nanofluid flow with MHD, Porosity, and thermal effects over a 3D stretching surface with convective boundary conditions","authors":"Muhammad Ehsan Ullah , Syed Tauseef Saeed , Najla A. Mohammed , Muhammad Idress , Muhammad Nauman Aslam , Ilyas Khan , Osama Oqilat , Muhammad Sabaoon Khan","doi":"10.1016/j.ijft.2025.101451","DOIUrl":"10.1016/j.ijft.2025.101451","url":null,"abstract":"<div><div>This comprehensive numerical study of three-dimensional Prandtl ternary ferrofluid flow over a stretching surface considers the combined effects of Darcy–Forchheimer drag, activation energy, thermal radiation, Brownian motion, thermophoresis, heat generation/absorption, porous media, mass diffusivity, and magnetohydrodynamics (MHD). Ferrofluid is created by dispersing copper (Cu), iron oxide (<span><math><mrow><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>), and cobalt ferrite (<span><math><mrow><mi>C</mi><mi>o</mi><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>) nanoparticles in a water-based Prandtl fluid in order to enhance thermal conductivity and magnetic permeability. The model includes radiative and non-Fourier heat conduction for realistic thermal representation, while the Darcy–Forchheimer approach characterises linear and nonlinear resistance in porous structures. Convective boundary conditions are used to replicate realistic heat exchange at the surface.</div><div>The governing partial differential equations of mass, momentum, energy, and species concentration are reduced by similarity transformations into a system of nonlinear ordinary differential equations. For computational accuracy, the shooting technique is employed to numerically solve these equations. The study looks at the parametric impacts of radiation, heat source/sink, Schmidt number, activated energy, magnetic field strength, porosity, Forchheimer number, Brownian motion, and thermophoresis. In addition to assessments of skin friction, Nusselt number, and Sherwood number, the distributions of temperature, velocity, and concentration are examined using tabular and graphical results.</div><div>The results show that thermal radiation and thermophoresis improve thermal dispersion, but greater porosity and magnetic intensity reduce velocity because of greater resistance. Because of finite mass diffusivity, concentration falls with increasing Schmidt numbers and activation energy. For engineering systems incorporating magnetic nanofluids and porous media, this work offers insightful information on transport phenomena. These systems have applications in materials processing, thermal management, and biomedical engineering.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101451"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Prabu , Shajar Abbas , Inamullah Inam , Mustafa Bayram , Barno Abdullaeva , Afnan Al Agha , Hakim AL Garalleh , Ibrahim Mahariq
{"title":"Cattaneo–Christov model for Marangoni convection in Casson fluid with thermal radiation and activation energy under dual-phase heat transfer","authors":"D. Prabu , Shajar Abbas , Inamullah Inam , Mustafa Bayram , Barno Abdullaeva , Afnan Al Agha , Hakim AL Garalleh , Ibrahim Mahariq","doi":"10.1016/j.ijft.2025.101413","DOIUrl":"10.1016/j.ijft.2025.101413","url":null,"abstract":"<div><div>This study investigates the effect of local thermal non-equilibrium (LTNE) conditions on the flow of Casson fluid under elastic deformation along a stretched boundary. The Cattaneo–Christov flux framework is used to model thermal and mass diffusion, incorporating non-classical effects of thermal and concentration relaxation phenomena. Furthermore, the model accounts for thermal radiation, activation energy, and an internal heat source, offering a more comprehensive representation of energy transfer in non-Newtonian fluid systems. These physical effects are particularly relevant in technical applications that require precise heat transfer control between fluid and solid phases, such as heat exchangers, geothermal systems, and thermal control devices. The model is also applicable in industrial processes that involve viscoplastic or yield-stress fluids, such as polymer extrusion, oil recovery, and food processing. By applying similarity transformations, the governing partial differential equations are reduced to a set of coupled ordinary differential equations, which are numerically solved using MATLAB’s bvp4c solver. The results reveal that increasing the interphase heat transfer coefficient <span><math><mrow><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>)</mo></mrow></math></span> from 1.0 to 5.0 causes a 23.7% reduction in the fluid-phase temperature and a 31.4% reduction in the solid-phase temperature at a fixed location. Furthermore, the presence of thermal radiation (<span><math><mrow><mi>R</mi><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span>) and internal heat generation (<span><math><mrow><mi>Q</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></math></span>) amplifies this cooling effect by an additional 12.5% compared to the case without these effects. These findings emphasize the critical role of the LTNE parameters and energy transport mechanisms in optimizing thermal performance in engineering systems.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101413"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial: Thermal power cycles and optimization","authors":"Parth Prajapati , Bertrand Delpech , Vivek Patel","doi":"10.1016/j.ijft.2025.101420","DOIUrl":"10.1016/j.ijft.2025.101420","url":null,"abstract":"<div><div>The special issue on Thermal Power Cycles and Optimization presents a collection of cutting-edge research and insightful reviews that advance the understanding and application of energy systems. This issue encompasses a broad spectrum of topics, including heat engines, combined heat and power systems, refrigeration and air conditioning, and the integration of renewable energy sources with conventional power cycles. Emphasis is placed on thermodynamic analysis, heat transfer mechanisms, and environmental and economic considerations in energy generation. The contributions collectively underscore the importance of optimizing thermal systems to enhance efficiency, reduce emissions, and support sustainable energy development. This editorial provides an overview of the thematic focus, key findings, and future directions highlighted by the articles in this issue.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101420"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145568796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmed Abed Al-Kadhem Majhool , Noor M. Jasim , Sara Falih Kareem , Mujtaba A. Flayyih , Faris Alqurashi
{"title":"Optimum blending hydrogen ratio in spray combustion to reduce emissions of nitrogen oxides","authors":"Ahmed Abed Al-Kadhem Majhool , Noor M. Jasim , Sara Falih Kareem , Mujtaba A. Flayyih , Faris Alqurashi","doi":"10.1016/j.ijft.2025.101425","DOIUrl":"10.1016/j.ijft.2025.101425","url":null,"abstract":"<div><div>This study examined the effects of adding hydrogen to flammable liquid fuel droplets on emissions. It was found that an optimal mixing ratio with hydrogen can reduce the amount of NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> in the reaction zone, which is the area where the primary combustion reactions occur. N-pentane is burnt in air enriched with different amounts of hydrogen, and the effects of the amount of hydrogen in the air on the combustion and emission parameters are investigated numerically. The combustion is modelled with the PDF/mixture fraction, and standard two-equation turbulence models and thermal NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> models are used for this modelling. The determination of the optimum H<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> blending ratio is evaluated after the estimation results. It is evident that the addition of H<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> led to an increase in spray flame temperatures. As a result, the addition of H<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> increases the combustion performance of n-pentane. The emissions evaluation results show that a blending ratio of 20% H<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> reduces CO emissions at the combustion’s reaction zone and also results in a decrease in the mixture fraction. There is an increase in NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> emissions due to the increase in spray flame temperatures. Combustion under air conditions containing 20% H<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> by volume resulted in the highest temperature levels reaching 2130 K, while the reduced NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> levels decreased to approximately 11.3%. The thermal NO<span><math><msub><mrow></mrow><mrow><mi>x</mi></mrow></msub></math></span> model, when combined with the combustion model, provides a sufficient level of agreement with the experimental data.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101425"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Esmaeilisafa, M. Gholinia, D.D. Ganji, M.Gorji Bandpy
{"title":"Thermo-fluid analysis of bio-inspired fish scale fins and eco-friendly H2O/GAGNPs nanofluid for CPU cooling: A CFD-CCD hybrid approach","authors":"M. Esmaeilisafa, M. Gholinia, D.D. Ganji, M.Gorji Bandpy","doi":"10.1016/j.ijft.2025.101474","DOIUrl":"10.1016/j.ijft.2025.101474","url":null,"abstract":"<div><div>This research investigates the efficiency of a micro heat sink featuring bio-inspired flow-disturbing structures modeled after fish scales. The micro heat sink consists of 12 rows of fins with a fish scale design, placed on a heat source such as a central processing unit (CPU) to control the temperature. The channel flow is laminar, steady, and incompressible. In addition, a kind of nanoparticle-containing liquid called gallic acid combined with graphene nanoplatelets (GNPs) has been used as a new type of nanofluid (GAGNPs /H<sub>2</sub>O). The governing equations were solved in three dimensions using the finite volume method in ANSYS-FLUENT, incorporating structure-fluid coupling. The results show: The micro heat sink geometry was modified from a simple model to designs inspired by gar, Cyprinus carpio, and salmon scales, the maximum temperature of the CPU is reduced about 3.5, 5.7, and 9.23 % respectively. The minimum acquired exergy is about 2.48W for simple model with GAGNP/H<sub>2</sub>O nanofluid: 0.1 % wt and Reynolds number <em>Re</em>=1500. The maximum acquired exergy was also recorded for the geometry of the micro heat sink with the salmon scale design at about 11.44 W (about 4.6 times the minimum value). By modifying the micro heat sink geometry from the simple model to the salmon fish scales, the uniformity index decreases by about 17.78 % and the thermal resistance index decreases about 22.05 %. The second-order model of data analysis for predicting convective heat transfer coefficient and maximum surface temperature in different geometries of micro heat sink is reported based on the Response Surface Method (RSM).</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101474"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145520094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Investigations on heat transfer in turbulent free surface and submerged jets","authors":"Vivek Mathew Jose","doi":"10.1016/j.ijft.2025.101500","DOIUrl":"10.1016/j.ijft.2025.101500","url":null,"abstract":"<div><div>This paper details the outcomes derived from numerical studies carried out on submerged air jets and free surface water jets striking on a horizontal surface. The cooling capabilities of a water jet supplemented with Alumina nanoparticles are also examined. The normalized distance from the nozzle to the target (Z/D) ranges from 2 to 12, with the Reynolds number (Re) varying from 4000 to 23000 and the particle volume fraction spanning from 0 to 1 %. The optimal Z/D for a free surface water jet is 2, while for a submerged air jet, it is 6. Within the stagnation region of the free surface jet, the Nusselt number (Nu) increases radially, peaking at about r/D ≈ 0.7. However, this increase becomes trivial at higher Re. Compared to the submerged jet, the local Nu for the free surface jet is markedly greater. In free surface jet, the jet speed is sustained as it flows from the exit of the nozzle. The velocity gradient near the surface is greater at low Z/D, which accounts for the increased wall shear stress observed at lower Z/D. The maximum enhancement in Nuo is 15 % when the volume fraction is increased from 0 to 1 %.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101500"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145614333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of shear rate-dependent viscoelastic mucociliary flow in mucus hypersecretion with thermal and concentration aspects","authors":"Hameed Ashraf , Tariq Ali , Talha Anwar , Imran Siddique , A.M. Siddiqui","doi":"10.1016/j.ijft.2025.101431","DOIUrl":"10.1016/j.ijft.2025.101431","url":null,"abstract":"<div><div>Thermal and concentration aspects in analyzing mucociliary transport is essential in understanding the mechanisms behind airway diseases caused by mucus hypersecretion in human airways. A mathematical model proposed by Ashraf et al. (2024) is used for the hypersecretion scenario. The airway ciliary and peri ciliary layers are formed when goblet cells secrete a substantial amount of mucus, blocking the airway channel. The shear rate-dependent viscoelastic fluid is used to better characterize the mucus rheology. The established system of nonlinear partial differential equations is addressed for approximate series solutions through the Adomian decomposition method. The analysis clarifies that both the velocity of mucus and the temperature rise as the relaxation time and pressure gradient at the airway entrance increase. The concentration decreases with the increase in mass diffusivity ratio while it increases with the increase in Schmidt number, Soret number, and pressure gradient at the airway entrance. Moreover, a comparison of the current results with the findings in existing literature reveals that shear rate-dependent viscoelastic fluid demonstrates better dynamic behavior in hypersecretion scenarios during mucociliary clearance. The Adomian decomposition method’s series solutions are validated by comparing them with numerical solutions obtained using the finite difference method.</div></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":"30 ","pages":"Article 101431"},"PeriodicalIF":0.0,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}