Analytical study of thermal spreading resistance in curved-edge heat spreader

• Heat spreading/conduction equation is derived in general curvilinear coordinates.
• Maxwell transform is used to map the geometry of curved-edge heat spreader.
• Thermal spreading resistance of a curved-edge heat spreader is calculated.

Because pieces of microelectronic devices are made in a wide variety of scales and shapes, heat must flow through them in spreading or constriction forms. Two heat flow conditions are primarily responsible for thermal spreading resistance: heat flowing from one solid to another with different cross-sectional areas (the primary focus of past studies); and heat flowing through a conductive solid with variable cross-sectional area. In this study, both conditions are considered simultaneously. The equation governing heat spreading is derived in the general curvilinear coordinate system. The Maxwell coordinate system is used as a special case to map the irregular geometry from Cartesian coordinates to the boundary-fitted curvilinear coordinate system. Temperature distribution and spreading resistance are then estimated by solving the equation governing heat conduction. A generalized thermal resistance is then introduced to evaluate the impact of variable cross-sectional area and heat source length on heat spreading. Finally, the effects of heat source length and the Biot number on spreading resistance are investigated.