The thermal response of a metal slab to a class of radially dependent heat inputs

✍ Scribed by Stickler, David C.

• Publisher: Springer
• Year: 1964
• Tongue: English
• Weight: 566 KB
• Volume: 14
• Category: Article
• ISSN: 0003-6994
• DOI: 10.1007/bf00382251

✦ Synopsis

The t e m p e r a t u r e fields are deduced for an infinite m e t a l slab of finite thickness p r o d u c e d b y a h e a t flux i n p u t which depends on t h e radial eoordinate. The formal solution is o b t a i n e d b y means of t r a n s f o r m techniques.

Several r e p r e s e n t a t i o n s of t h e Green's function are o b t a i n e d as weil as two a p p r o x i m a t e representations. One of these a p p r o x i m a t i o n s converges well for t i m e large t h e o t h e r for t i m e small.

A small t i m e a s y m p t o t i c expansion is given for i n p u t flux densities which satisfy certain s m o o t h n e s s requirements.

Two inputs have been considered in detail. Orte is the uniform spot and the other is the Gaussian. An extension of the results o b t a i n e d b y O o s t e rk a m p a) has been o b t a i n e d along w i t h an estimate of the validity.