The Temperature Field Around a Spherical Ridge or Trough in a Plane

An analytical solution, which describes the temperature field around a single spherical particle partly embedded in a plane or around a trough making an arbitrary contact angle with a plane, is presented here. The temperature distributions for three cases are studied: the temperature distribution around a conducting bowl or trough, the temperature distribution around a non-conducting bowl or trough present in a conducting plane, and the temperature profile around a conducting bowl or trough conducting heat toward a sink at infinity. The normalized heat flux distribution on the plane and particle is presented. The various incremental resistances caused by a single and a dilute planar random array of truncated spherical particles are also derived.