Three dimensional temperature field in a conducting sphere due to an arbitrarily located split ring heating source

• We model 3-D asymmetric heat conduction due to a thin split ring heater in a sphere.
• We use integral methods with Green's functions.
• We present an almost analytical solution which is elegant and we cherish them.
• We show it is still possible to solve complex problems analytically without immediate recourse to numerical techniques.
• We have shown interdisciplinary approach by using ideas from electrostatics to heat transfer problems.

Thermal control of spacecrafts plays an important role in space missions. In the design stage the preliminary thermal analysis of the spacecraft requires an estimate of the conductive thermal resistance between the various spacecraft components. With this in mind, the fully three dimensional problem of determining the thermal field in a conducting sphere with an asymmetric split ring current carrying heating source is resolved in an analytical or almost analytical form, implying either a closed form solution or utmost expressions involving a simple numerical integration. This has immediate application for evaluation of thermal resistance in spacecrafts. Green's function integral techniques are used. Comparisons are made with series solutions and also with purely numerical solutions to contrast the simplicity and highlight the elegance of the present method. Parametric studies reveal expected behavior.