Forced Convection and MHD Effect of Non-Ewtonian Fluids Along a Pipe
Abstract
In this paper, the forced convection heat transfer of incompressible, Power law Non-Newtonian fluids through two-dimensional circular pipes in the presence of an external uniform magnetic field was considered. Moreover, momentum and energy equations are solved using a finite volume method and a simple algorithm. Two cases of the thermal boundary condition, a constant temperature and a constant heat flux at the wall, are investigated. The viscous and Joule dissipations are taken into account in the energy equation. Moreover, the influence of the magnetic field and flow behavior index (n) on the velocity distribution, the friction factor, and the Nusselt numbers is discussed. Also, the influence of the viscous and Joule dissipations on the Nusselt numbers is investigated. The results show that the magnetic field has a damping effect on the flow for all values of n. By increasing n, the maximum fluid velocity and friction factor will increase. Increasing n increases maximum fluid velocity and friction factor. Increasing the Hartmann number decreases maximum fluid velocity and increases the friction factor. Also, the increment in the Brinkman number decreases the value of the Nusselt number for all Hartmann numbers and n.
Keywords:
Magnetohydrodynamic flow, Forced convection, Power-law fluid, SIMPLE algorithmReferences
- [1] Min, T., Choi, H. G., Yoo, J. Y., & Choi, H. (1997). Laminar convective heat transfer of a Bingham plastic in a circular pipe—II. Numerical approach hydrodynamically developing flow and simultaneously developing flow. International journal of heat and mass transfer, 40(15), 3689–3701. https://doi.org/10.1016/S0017-9310(97)00004-5
- [2] Hossain, M. A. (1992). Viscous and Joule heating effects on MHD-free convection flow with variable plate temperature. International journal of heat and mass transfer, 35(12), 3485–3487. https://doi.org/10.1016/0017-9310(92)90234-J
- [3] Jha, B. K. (2001). Natural convection in unsteady MHD Couette flow. Heat and mass transfer, 37(4), 329–331. https://doi.org/10.1007/PL00013295%0A%0A
- [4] Sayed-Ahmed, M. E., & Attia, H. A. (2000). MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity and Hall effect. International communications in heat and mass transfer, 27(8), 1177–1187. https://doi.org/10.1016/S0735-1933(00)00204-9
- [5] Sayed-Ahmed, M. E., & Attia, H. A. (2005). The effect of Hall current on magnetohydrodynamic flow and heat transfer forBingham fluids in a rectangular duct. Canadian journal of physics, 83(6), 637–651. https://doi.org/10.1139/p05-006
- [6] Attia, H. A. (2006). Hall effect on the flow of a dusty bingham fluid in a circular pipe. Turkish journal of engineering & environmental sciences, 30(1). https://openurl.ebsco.com/EPDB%3Agcd%3A2%3A2736082/detailv2?sid=ebsco%3Aplink%3Ascholar&id=ebsco%3Agcd%3A21183349&crl=c&link_origin=scholar.google.com
- [7] Ahmed, M. E. S. (2006). Numerical solution of power law fluids flow and heat transfer with a magnetic field in a rectangular duct. International communications in heat and mass transfer, 33(9), 1165–1176. https://doi.org/10.1016/j.icheatmasstransfer.2006.06.003
- [8] Holman, J. P. (1996). Heat transfer. McGraw hill college. https://www.scribd.com/doc/52043947/Heat-Transfer-J-P-Holman
- [9] Patankar, S. (2018). Numerical heat transfer and fluid flow. CRC press. https://doi.org/10.1201/9781482234213
- [10] Skelland, A. H. P., & Flow, N. N. (1967). John wiley and sons inc. New york, 72–74. https://books.google.nl/books/about/Non_Newtonian_Flow_and_Heat_Transfer.html?id=-07xAAAAMAAJ&redir_esc=y