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We consider a model CHT problem consisting of linear advection\u2013diffusion and heat equations, coupled at an interface through the continuity of temperature and heat flux. We employ high-order summation-by-parts finite-difference operators in conjunction with simultaneous-approximation-terms (SATs) in curvilinear coordinates for spatial derivatives, combined with first- and second-order time discretization, and extrapolation in time at the interface. Energy stability is maintained by carefully defining SAT parameters at the interface. A range of coupling parameters are explored to identify those that yield a stable scheme and a step-wise approach for choosing SAT parameters that result in stability is given. The effectiveness of the method is demonstrated through numerical experiments in a two-dimensional model problem on rectangular domain with curvilinear grids. The proposed approach enables the development of high-order conditionally-stable partitioned solvers suitable for general geometries.<\/jats:p>","DOI":"10.1007\/s10915-026-03462-x","type":"journal-article","created":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T07:27:20Z","timestamp":1789543640000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Finite-Difference Summation-by-Parts Conditionally Stable Partitioned Algorithm for Conjugate Heat Transfer Problems"],"prefix":"10.1007","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5657-4810","authenticated-orcid":false,"given":"Sarah","family":"Nataj","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David C.","family":"Del Rey Fern\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Brown","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rajeev","family":"Jaiman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,16]]},"reference":[{"issue":"2","key":"3462_CR1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1080\/713855861","volume":"26","author":"AS El-Karamany","year":"2003","unstructured":"El-Karamany, A.S.: Boundary integral equation formulation in generalized thermoviscoelasticity with rheological volume and density in material having temperature-dependent properties. 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