[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85156-en":3,"doc-seo-85156-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85156,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Flow and Heat Transfer Characteristics of Forced Convection Past an Isoflux Circular Cylinder in Galinstan for Reynolds Numbers up to 600","A numerical investigation addresses steady forced convection heat transfer from an isoflux circular cylinder immersed in the liquid metal Galinstan. Streamfunction, vorticity, and energy equations are solved using a fourth-order compact finite difference scheme in cylindrical coordinates (FOCS–CC) coupled with a stable pseudotime iteration (PTI). Reynolds number effects (1 ≤ Re ≤ 600) are studied at Pr = 0.025. Grid independence and validation against published average Nusselt number and drag confirm reliability. Results connect higher Re with stronger separation, enlarged wake, enhanced downstream transport, and improved convective heat transfer, and yield a new empirical correlation with R2 = 0.99939.","arXiv :2607 .09922v1 [physics .flu-dyn] 10 Jul 2026  \nFlow and Heat Transfer Characteristics of Forced Convection Past an Isoflux Circular Cylinder in Galinstan for Reynolds Numbers up to 600  \nDipjyoti Nath  \nFaculty of Science, Assam down town University, Guwahati, Assam, India Email: [dipjyoti.nath@adtu.in](dipjyoti.nath@adtu.in), [dipjyotinath997@gmail.com](dipjyotinath997@gmail.com) (Corresponding Author)  \nAbstract  \nA numerical investigation of steady forced convection heat transfer from an isoflux circular cylinder immersed in the liquid metal Galinstan is presented. The governing streamfunction, vorticity, and energy equations are solved using a fourth-order compact finite difference scheme in cylindrical coordinates (FOCS–CC) coupled with a stable pseudotime iteration (PTI) technique. The influence of the Reynolds number (1 ≤ Re ≤ 600) on the flow and heat transfer characteristics is systematically investigated for Galinstan with a Prandtl number of Pr = 0 .025. The performance and accuracy of the proposed scheme are first established through grid independence studies and validation against previously published numerical results for the average Nusselt number and total drag coefficient over a range of Reynolds numbers. Excellent agreement with the available literature confirms the reliability and robustness of the present formulation. The effects of Reynolds number (1 ≤ Re ≤ 600) on the flow and thermal fields are examined through streamline patterns, isotherm distributions, and local Nusselt number variations. The results reveal that increasing the Reynolds number promotes flow separation, enlarges the wake region, intensifies downstream thermal transport, and significantly enhances convective heat transfer from the cylinder surface. Furthermore, a new empirical correlation for the average Nusselt number is proposed for Galinstan fluid over the Reynolds number range 1 ≤ Re ≤ 600, exhibiting excellent agreement with the numerical data with a coefficient of determination of R2 = 0 .99939.  \nKeywords—Forced convection, Circular cylinder, FOCS–CC, isoflux thermal boundary condition, PTI  \n1 Introduction  \nThe study of forced convection heat transfer around circular cylinders is of considerable practical importance because of its widespread use in thermal engineering systems.  \nHeat transfer from circular cylinders has been investigated through both analytical and experimental studies by Khan et al. (2006), Grosh and Cess (1958), and Ishiguro et al.(1976) . Subsequently, numerous numerical and experimental investigations have focused on forced convection heat transfer from an isothermal circular cylinder. Notable contributions include the works of Dennis and Chang (1970), Fornberg (1980), Tritton (1959), Dennis et al. (1968), Baranyi (2003), Erturk and Gokcol (2018), and Abdelhady and Wood (2019), who examined the problem over a broad range of Reynolds numbers and flow conditions.  \nFor the isoflux thermal boundary condition, Ahmad (1996) employed a finite difference method with a hybrid differencing scheme to study forced convection heat transfer for 100 ≤ Re ≤ 500 at Pr = 0 .7. Later, Khan et al. (2005) applied the Von Kármán– Pohlhausen integral boundary layer approximation to analyse heat transfer from circular cylinders subjected to both isothermal and isoflux boundary conditions by solving the coupled momentum and energy equations. This problem was subsequently revisited by Bharti et al. (2007), who utilised the QUICK discretization scheme to investigate the ranges 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. Furthermore, Paramane and Sharma (2010) investigated forced convection heat transfer from an isoflux circular cylinder using the finite volume method for 20 ≤ Re ≤ 160 at Pr = 0 .7. Sufyan et al. (2015) analysed flow and forced convection heat transfer past a circular cylinder with both isothermal and isoflux thermal boundary conditions using the finite volume method based on the SemiImplicit Method for Pressure-Linked Equa","cbCaioemdXJWiAm4","https://ap.wps.com/l/cbCaioemdXJWiAm4","pdf",1205604,1,17,"English","en",105,"# Abstract\n# 1 Introduction\n## Forced convection around circular cylinders\n## Isoflux boundary condition studies\n## Fourth-order compact schemes and PTI approach\n## Galinstan and motivation for Reynolds-number range","[{\"question\":\"What method is used to solve the governing equations for the forced convection problem?\",\"answer\":\"The study solves streamfunction, vorticity, and energy equations using a fourth-order compact finite difference scheme in cylindrical coordinates (FOCS–CC) coupled with a stable pseudotime iteration (PTI) technique.\"},{\"question\":\"Which physical parameters are varied, and what are their ranges?\",\"answer\":\"The Reynolds number is varied from 1 to 600, while Galinstan is considered with Prandtl number Pr = 0.025.\"},{\"question\":\"What trends are reported when Reynolds number increases?\",\"answer\":\"Increasing Reynolds number promotes flow separation, enlarges the wake region, intensifies downstream thermal transport, and significantly enhances convective heat transfer from the cylinder surface.\"}]",1784201441,43,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"flow-and-heat-transfer-characteristics-of-forced-convection-past-an-isoflux-circular-cylinder-in-galinstan-for-reynolds-numbers-up-to-600","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/flow-and-heat-transfer-characteristics-of-forced-convection-past-an-isoflux-circular-cylinder-in-galinstan-for-reynolds-numbers-up-to-600/85156/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What method is used to solve the governing equations for the forced convection problem?","Question",{"text":75,"@type":76},"The study solves streamfunction, vorticity, and energy equations using a fourth-order compact finite difference scheme in cylindrical coordinates (FOCS–CC) coupled with a stable pseudotime iteration (PTI) technique.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which physical parameters are varied, and what are their ranges?",{"text":80,"@type":76},"The Reynolds number is varied from 1 to 600, while Galinstan is considered with Prandtl number Pr = 0.025.",{"name":82,"@type":73,"acceptedAnswer":83},"What trends are reported when Reynolds number increases?",{"text":84,"@type":76},"Increasing Reynolds number promotes flow separation, enlarges the wake region, intensifies downstream thermal transport, and significantly enhances convective heat transfer from the cylinder 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