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"Advances in Heat Transfer" is designed to fill the information gap between the regularly scheduled journals and university level textbooks, allowing for in-depth review articles on a broader scope than is allowable in either journals or texts. This work: reviews recent work on melt lubrication at the interface between two solid parts, one of which is at its melting point; employs variational principle with vanishing parameter in the study of linear and nonlinear transient heat conduction through bodies of finite length; reviews heat transfer in porous media and its rapidly growing body of literature; emphasizes recent developments in handling complex geometry, treating wide flow speed variations, yielding accurate solutions, and producing results efficiently as illustrated throughout with many examples; and, discusses unsteady convective situations which are generated in response to the time-dependent boundary conditions on the surface walls of a container, and its practical industrial applications.