Bench mark solutions to natural convection heat transfer problem around a horizontal circular cylinder
High-accuracy bench mark solutions are presented for the natural convection flow around a horizontal circular cylinder with uniform surface temperature. In the past two decades, several approximate and numerical solutions to this problem have been reported in the literature. However, owing to limitations of (i) computer running time (CPU time) and (ii) resolution of the solution methodology, no exact bench mark solution has been presented to date. A large computational domain is inevitably necessitated in the case of small Rayleigh numbers. A thin boundary layer forms when the Rayleigh number increases, thereby requiring high resolution in the vicinity of the cylinder surface. Both of these features make it difficult to obtain exact bench mark solutions. These difficulties were overcome by adopting a high-accuracy fourthorder finite difference method and a coordinate transformation technique. The present bench mark solutions are accurate to at least three decimal places for small Rayleigh numbers (e.g. Ra = 10 3 and 10 4 ) and will be quite useful as standard comparison solutions to which many numerical solutions can be compared. Further, typical isotherms, streamlines, vorticities, local Nusselt numbers, tangential and radial velocities and temperature distributions were clarified in detail.
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