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.
An interferometric study has been conducted on two-dimensional laminar natural convection heat transfer in an isothermal vertical divided channel. Interferograms were obtained for air and a plate-to-channel length ratio of Lp/Lc= 1/3. Data are presented for the dividing plate located at the bottom (Li/Lc = 0) and top of the channel (Li/Lc=2/3). Comparisons of local and average Nusselt numbers are made with the numerical predictions from Part I. Although the experimental average Nusselt numbers are typically about 10 percent lower than the numerical results, the general trends of the data are in good agreement. Average Nusselt number correlation equations are presented.
A Mach-Zehnder interferometer was employed to determine the three-dimensional temperature field, and the circumferential and average Nusselt numbers for laminar flow of air in the entrance region of an isothermal horizontal tube where the velocity and the temperature profiles were developing simultaneously. The influence of free convection due to buoyancy on forced convection heat transfer was investigated. The Reynolds numbers ranged from 120 to 1200, the Grashof numbers ranged from 0.8 × 104 to 8.7 × 104, and the ratio L/D was varied from 6 to 46. The free convection increases, substantially, the average Nusselt number, by up to a factor of 2.0 from the analytical predictions, which account for forced convection only, near the tube inlet. Far from the tube inlet the free convection tends to decrease the average Nusselt number below the analytical predictions.
Steady two-dimensional laminar natural convection heat transfer from isothermal horizontal and inclined open cavities of rectangular cross section has been investigated experimentally using a Mach-Zehnder interferometer and numerically by a finite difference technique. Experimental results are presented for Prandtl number, Pr = 0.7, Rayleigh numbers from 104 to 5 × 105, cavity aspect ratios, A (or h/w) = 0.25, 0.5, and 1.0, and inclination angles (or angles of rotation about the longitudinal axis), θ = 0, 30, 45, and 60 deg to the horizontal. The numerical model uses a relaxation technique to solve the governing elliptic, partial differential equations. Numerical results are presented for the range of Rayleigh number, 103 ≤ Raw ≤ 5 × 105, θ = 0 and 45 deg, and A = 1. Flow and temperature patterns, velocity and temperature profiles, and local and average heat transfer rates are presented. Flow recirculation with two counterrotating convective rolls developed in the cavity at Ra ≥ 105. The inclination of the cavity induced flow entrainment, causing flow separation at the lower corner and flow reattachment at the upper corner of the aperture opening except in shallow cavities, A < 0.5, where the flow reattachment occurred on the base of the inclined cavity. For all Ra numbers, the first inclination of the cavity from the horizontal caused a significant increase in the average heat transfer rate, but a further increase in the inclination angle caused very small increase in heat transfer rate. However, for every angle of inclination considered, the average heat transfer rate increased significantly as Ra was increased. The equation of the form Nu = mRan, where 0.018 ≤ m ≤ 0.088 and 0.325 ≤ n ≤ 0.484, correlates the experimental and numerical results satisfactorily for the range of Ra, 104 ≤ Ra ≤ 5 × 105 and of θ, 0 ≤ θ ≤ 60 deg. The present experimental and numerical results are in good agreement with the results reported in the literature.
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