Analytical solutions of heat transfer for laminar flow in rectangular channels

• Autorzy: Rybiński W. , Mikielewicz J.
• Języki publikacji: EN

Abstrakty

EN

The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

Słowa kluczowe

EN

analytical solution; heat transfer; rectangular channel; laminar flow; fully developed

PL

rozwiązanie analityczne; wymiana ciepła; kanał prostokątny; przepływ laminarny

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2014
• Tom: Vol. 35, no. 4
• Strony: 29--42
• Opis fizyczny: Bibliogr. 5 poz., il.

Twórcy

autor

Rybiński W.

• The Szewalski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gdańsk, Poland

autor

Mikielewicz J.

• The Szewalski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gdańsk, Poland

Bibliografia

• [1] Shah R.K., London A.L.: Laminar Flow Forced Convection in Ducts. Academic Press, New York 1978.
• [2] Kays W.M., Crawford M.E.: Convective Heat and Mass Transfer. McGraw-Hill, New York 1993.
• [3] Kandlikar S.G., Garimella S., Li D., Colin S., King M.R.: Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier Ltd., Oxford 2006.
• [4] Hartnett J.P., Kostic M.: Heat transfer to Newtonian and non-Newtonian fluids in rectangular ducts. Adv. Heat Transfer, 19(1989), 247–356.
• [5] Papautsky I., Mohanty S., Ameel T., Frazier A.B.: Effects of rectangular microchannel aspect ratio on laminar friction constant. In: Proc. of SPIE Conference on Microfluidic Devices and Systems, Santa Clara 1999, 147–159.

Uwagi

EN

This work has partially been funded from a National Project POIG.01.01.02-00-016/08 Model agroenergy complexes as an example of distributed cogeneration based on a local rene wable energy sources.