Steady two-dimensional laminar free convection between isothermal vertical plates including entrance flow effects has been numerically investigated. The full elliptic forms of the Navier-Stokes and energy equations are solved using novel inlet flow boundary conditions. Results are presented for Prandtl number Pr = 0.7, Grashof number range 50 ≤ Grb ≤ 5×104, and channel aspect ratios of L/b = 10, 17, 24. New phenomena, such as inlet flow separation, have been observed. The results cast doubt on the validity of previous elliptic solutions. Comparisons with the approximate boundary-layer results show that a full elliptic solution is necessary to get accurate local quantities near the channel entrance.
A numerical and experimental investigation of free convection from vertical, isothermal, parallel-walled channels has been undertaken to explore the heat transfer enhancement obtained by adding adiabatic extensions of various sizes and shapes. Investigations were carried out for air (Pr= 0.7) over a wide range of wall heating conditions. In all cases, the adiabatic extensions were able to increase heat transfer. The increase varied from 2.5 at low Ra* to 1.5 at high Ra*. The experimental and numerical results are in excellent agreement. A single correlation accounting for the channel aspect ratio Lh/b, expansion ratio, B/b, modified Rayleigh number, Ra* and heated length ratio, Lh/L is presented.
Heat transfer by free convection in air from isothermal horizontal surfaces heated and facing upward has been experimentally studied by using a Mach-Zehnder interferometer. The local and the average heat-transfer coefficients and the temperature distributions were determined in the range of Gr Pr from 1.9 × 106 to 1.7 × 108. Measurements were compared with available experimental and theoretical results. Periodical flow instabilities caused random changes, which could reach +45 and −35 percent of mean values in the local Nusselt number and +23 and −15 percent of mean value in the average Nusselt number. The nature of the free convection flow over the heated surface and the separation of the boundary layer were inferred from these random changes in the local and average Nusselt numbers.
This is a two-part study of two-dimensional laminar natural convection heat transfer in a divided vertical channel. The divided channel consists of an isothermal dividing plate located on the center line of a vertical channel formed by two isothermal walls. The study examines the effect of Rayleigh number, plate-to-channel length ratio, vertical plate position, and plate thickness on the heat transfer rate from the channel walls, the dividing plate, and the channel as a whole. In Part I, solutions to both the full elliptic and parabolic forms of the Navier–Stokes and energy equations are obtained for Prandtl number Pr = 0.7 (air). Positioning the plate at the bottom of the channel was found to give the highest average Nusselt numbers for the plate and channel. Dividing plate average Nusselt numbers as much as two times higher than the isolated plate Nusselt number were predicted numerically. Experimental measurements and data correlations for the divided channel are presented in Part II of this paper.
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