Stability of non-isothermal flow in channels—III. Temperature-dependent power-law fluids with heat generation

✍ Scribed by Y.T. Shah; J.R.A. Pearson

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 579 KB
• Volume: 29
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(74)80173-9

✦ Synopsis

The simplified lubrication type model used in Parts I and II of this work? on the flow of temperature dependent power-law fluids in channels is here extended to take account of heat generation.

It is found that the steady unidirectional flow solution, for the case of flat plates forming a channel of uniform length, leads to a relation between pressure drop P and mean velocity V that can display two ranges of V for which dP/dV < 0. One of these is associated with the physical mechanism investigated earlier, that of initially hot fluid flowing into a cold channel where generation is unimportant; the second, and often distinct, range relates to the interaction between heat generation and heat transfer and is relevant at much larger values of V.

The stability of this unidirectional flow to small disturbances is then investigated. Once again it is found that all regions for which dP/dV < 0 lie within the unstable part of operating space. In particular, this means that whatever the inlet temperature of the fluid, and whatever the channel wall temperature, there will always be some value of V above which the unidirectional flow is unstable.