Steady‐state solutions of Buoyancy‐assisted internal flows using a fast false implicit transient scheme (FITS)

Abstract

A fast false implicit transient scheme FITS is developed to predict the two-dimensional steady-state solutions of buoyancy-assisted laminar internal flows. This new scheme uses the control volume based on power law technique in conjugation with the alternating direction implicit (ADI) and the successive grid refinement (SGR) procedures to solve the transient vorticity and energy transport equations. The ADI procedure allows the power law, which gives an excellent approximation to the exact 1-D solution, to be applied locally in one-dimensional sense for each sweep in the co-ordinates' directions. This in turn increased the solution accuracy and hence permits the use of a larger time increment. As a result a remarkable increase in the convergence rate to steady-state is achieved. The final solution is obtained by successively refining the grid as the solution advances in time. The efficiency of FITS is verified by comparing the present predictions with three steady-state benchmark solutions: natural convection of a heat generating fluid in a rectangular enclosure, natural convection inside a cavity with two isothermal walls, and a vertical buoyancyassisted laminar backward-facing step flow.KEY WORDS Buoyancy-assisted laminar internal flows False implicit transient scheme Steady-state solutions

Natural convection in partially cooled tilted cavities

“…Based on these results, a mesh size of 40× 40 has been adopted for all the cases completed in the present study. As shown previously by El-Refaee et al [9], further increase of the mesh size did not significantly change the final steady state results for 10 5 5 Ra5 10 7 . The steady state solution is assumed to be converged when the variation of the Nusselt number between two consecutive time steps is B 0.1%.…”

“…Further applications include determining thermal losses in shop refrigerators. The fast false implicit transient scheme (FITS) as described by El-Refaee et al [9] is modified to solve the 2D derived variables governing equations. Solutions are obtained for a range of values of the cavity aspect ratio (15 AR5 4), sink-source ratio (1/4 B SRB 1) and tilting angle ( − 90°5 h5 0°) at Rayleigh numbers Ra= 10 5 and 10 7 .…”

Non-Darcian Effects on Buoyancy-Induced Heat Transfer in a Partially Divided Square Enclosure with Internal Heat Generation

“…Figure 3 illustrates an excellent comparison between our results and the streamlines and isotherms contours by El-Refaee et al (1996) and Churbanov and Vabishchevich (1994). Table 1 illustrates an excellent comparison of minimum and maximum values of the stream function and temperature between the present results and the numerical results found in the literature (El-Refaee et al 1996;Churbanov and Vabishchevich 1994;Khanafer and Chamkha 1998). An additional verification on the accuracy of the present numerical code is displayed in Table 2 and Fig.…”

“…Comparison of the streamlines and isotherms between the present results and that ofEl-Refaee et al (1996) andChurbanov and Vabishchevich (1994) (Ra = 6.4 × 10 5 , Pr = 7.0) assuming isothermal boundaries (T = T C )…”

Numerical investigation and recurrence plot analysis of pulsating magnetohydrodynamic mixed convection over a backward facing step

“…The numerical code is first checked against the benchmarked results of backward facing step reported in the literature [3,10,13,15,22]. Table 2 shows the results of the reattachment length divided by step height at Reynolds number of 100 for expansion ratio of 2.…”