Local Grashof Number Research Articles

Flow Visualization Studies on Vortex Instability of Natural Convection Flow Over Horizontal and Slightly Inclined Constant-Temperature Plates

Flow visualization experiments were performed in a low-speed wind tunnel to study vortex instability of laminar natural convection flow along inclined isothermally heated plates having inclination angles from the horizontal of θ = 0, 5, 10, 15 and 20 deg. The temperature difference between plate surface and ambient air ranged from ΔT = 15.5 to 37.5°C and the local Grashof number range was Grx = 1.02×106 to 2.13×108. Three characteristic flow regimes were identified as follows: a two-dimensional laminar flow, a transition regime for developing longitudinal vortices, and a turbulent regime after the breakdown of the longitudinal vortices. Photographs are presented of side and top views of the flow and of cross-sectional views of the developing views of the developing secondary flow in the postcritical regime. Instability data of critical Grashof number and wavelength are presented and are compared with the theoretical predictions from the literature.

Natural convection on horizontal, inclined, and vertical plates with variable surface temperature or heat flux

An analysis is performed to study the flow and heat transfer characteristics of laminar free convection in boundary layer flows from horizontal, inclined, and vertical flat plates in which the wall temperature T w ( x) or the surface heat flux q w ( x) varies as the power of the axial coordinate in the form T w ( x) = T ∞ + ax n or q w = bx m . The governing equations are first cast into a dimensionless form by a nonsimilar transformation and the resulting equations are then solved by a finite-difference scheme. Numerical results for fluids with Prandtl numbers of 0.7 and 7 are presented for three representative exponent values under each of the nonuniform surface heating conditions. It has been found that both the local wall shear stress and the local surface heat transfer rate increase as the angle of inclination from the horizontal γ increases or as the local Grashof number increases. An increase in the value of the exponent n or m enhances the surface heat transfer rate, but it causes a decrease in the wall shear stress. Correlation equations for the local and average Nusselt numbers are obtained for the special cases of uniform wall temperature (UWT) and uniform surface heat flux (UHF). Comparisons are also made of the local Nusselt numbers between the present results and available experimental data for the UHF case, and a good agreement is found to exist between the two.

Effects of flow inertia on vertical, natural convection in saturated, porous media

An analytical study is made for the effect of flow inertia on vertical, natural convection in saturated, porous media. Within the framework of boundary-layer approximations, Forchheimer's model was transformed into a set of non-similar equations. Effects of flow inertia are measured and examined in terms of the dimensionless inertia parameter ξ = Gr x Fo x where Gr x is the local Grashof number of determined by the bulk properties of saturated porous media, and Fo x is a new dimensionless parameter governed by the microstructure of porous matrix. The non-similar solutions are presented and discussed for two types of flow: (1) the uniform heat flux surface; and (2) plane plume flows. Results show that thermal boundary layer in the non-Darcy regime is thicker than the corresponding pure-Darcy flow. In addition, the local wall heat fluxes for the first case and the maximum temperature gradient for the second case decrease with increasing ξ.

Free Convective Heat Transfer in a Liquid-Filled Vertical Annulus

An experimental study of convective heat transfer in liquid-filled vertical annulus of radius ratio κ = 5.338 has been conducted for the height-to-gap width ratio A = 0.5, 1, and 1.5. By using water, heptane, and ethylene glycol as the test fluids, a Rayleigh number range of 8 × 106 < Ra < 3 × 1010, and a Prandtl number range of 4 < Pr < 196 have been covered. Curvature effects on the temperature field are significant and result in a lower effective sink temperature for the boundary layer on the isothermally heated inner wall. The Nusselt number Nu thus increases with radius ratio κ. However, the slope of ln (Nu) versus ln (κ) curve is not a constant, and decreases with an increase in κ. The effect of Prandtl number is weak. In the laminar flow regime, the Nusselt number is weakly dependent on the aspect ratio when Nu and Ra are considered in terms of the annulus height L. The start of laminar flow regime is delayed with an increase in radius ratio. For A = 0.5, κ = 5.338, the critical Grashof number is GrL = 7 × 104, which decreases with an increase in A. Turbulence is initiated when the local Grashof number Grx ≃ 4 × 109.

Natural convection over a vertical flat plate due to absorption of thermal radiation

Heat transfer by simultaneous free convection and radiation in a participating fluid has received some attention during the past few years. However most of the previous work has been focussed on gases. The present work investigates the problem of combined radiation and natural convection in liquids. Analysis are given for an optically thick cold fluid layer adjacent to a non-emitting and non-reflecting radiation-transmitting plate. The external surface of the plate is subjected to heat loss to surroundings. The governing differential equations are transformed to a dimensionless form where the solution becomes dependent on the following parameters: the plate absorpitivity,αp; the dimensionless distance along the plate,ζ; the fluid Prandtl number,Pr; and dimensionless heat loss coefficient to surrounding,Nc. A local non-similar technique is adopted to obtain solutions atPr=6.5 and at a wide range ofαp,ζ, andNc. The results showed that both velocity and temperature are non-similar and they are greatly affected by the value ofαp whenζ is small. At large values of f the effect ofαp diminishes and for a plate without heat loss the velocity becomes similar, i.e. independent of C The heat loss from the external surface of the plate causes the maximum temperature of the fluid to depart far from the plate. The results also showed that for plates without heat loss the local heat transfer coefficient from the plate depends on the local Grashof number to the power 0.185.

Local Nonsimilarity Solution of Free Convection Flow and Heat Transfer from an Inclined Isothermal Plate

The effect of the angle of inclination on free convection flow and heat transfer from an isothermal surface is analyzed by the local nonsimilarity method of solution. An inclination parameter ξ as obtained from the analysis is tan γ/4 (Grx/4)1/4, where γ is the angle of inclination measured from the vertical and Grx is the local Grashof number, based on the component of the gravity vector along the surface. Numerical solutions of the equations are obtained for Prandtl numbers of 0.1, 0.7, 6 and 275. Results show an appreciable effect of ξ on the velocity field, and practically none on the temperature field, except for very large angles of inclination from the vertical or for very small values of the Prandtl number. In the limiting case of very large Prandtl number, ξ has no effect either on the velocity or the temperature field.

Natural convection with mercury in a uniformly heated vertical channel during unstable laminar and transitional flow

AbstractExperimental heat transfer correlations were determined for natural convection in mercury in a uniformly heated vertical channel with width‐to‐height ratios varying from 0.25 to infinity (the single plate limit). Local modified Grashof numbers varied between 108 and 1011. Temperature and velocity profiles were obtained for these same channel configurations and local Grashof numbers. Instantaneous velocity plots indicate the range of conditions studied to proceed from unstable laminar flow well into the transition regime. Heat transfer results are in good agreement with earlier results reported for stable laminar flow which were limited to values of modified Grashof number less than 109.

Laminar Natural Convection About Vertical Plates With Oscillatory Surface Temperature

The characteristics of laminar natural convection about a vertical plate with periodically changing surface temperature have been studied by the finite-difference method. The effects of the amplitude and period of the surface temperature oscillation on the instantaneous and time-average Nusselt numbers, temperature and velocity profiles are demonstrated by several examples. High amplitude and a large range of frequency of the oscillation were considered in these examples. The time-wise variation of the fluid temperature in the inner region adjacent to the surface produces back heat flow at high amplitude, high frequency, and at high local Grashof number.

An experimental study of the transition of natural convection flow adjacent to a vertical surface

Events in transition were measured in water, in terms of mean and fluctuating temperature, thermal region thickness and a thermal transition factor. Anemometer measurements were also made. A distinct “thermal” transition mechanism was found. It began downstream of the first signs of velocity field transition. In this delayed region the mean temperature and disturbance quantities gradually assume their turbulent form. In addition, our data indicate that transition events are not accurately predictable solely in terms of the local Grashof number. These first results indicate that the local amount ofconvected thermal energy is a much better correlator of the transition region location, as well as of other less salient features of transition. A re-examination of previously published data on transition supports this finding.

Combined forced and free-convection over thin needles

The problem of laminar combined forced and free-convection heat transfer from a vertical thin needle in a variable external stream is considered. The similarity solutions for needles with isothermal walls and needles with uniform wall heat fluxes have been obtained. For a given value of the needle size, the flow and heat transfer behaviours are similar to those encountered with flat plates. The Nusselt number and the skin-friction coefficients increase with decreasing needle sizes for assigned values of Prandtl number, local Reynolds number, and local Grashof number.

Natural convection from isothermal flat surfaces

Local heat-transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters. Experiments were carried out for different temperature differences in heating and cooling, and with inclinations varying from the horizontal “facing upwards” position, through the vertical position, to the horizontal “facing downwards” position. The results are presented in terms of local Nusselt number as a function of the local Grashof number “tangential component”. All runs were in the range accepted as that of laminar boundary layer flow. However, under certain conditions when the normal velocity component of the air is directed away from the surface, separated flow is indicated along the trailing part of the surface, well before turbulence sets in in the boundary layer. Separation starts at a certain point along the surface. This point is nearer to the leading edge the higher the temperature difference, and the larger the inclination of the surface to the vertical. In a separation region, the flux density is uniform. In all other regions the results agreed closely with established theories of laminar boundary layer flow. A leading adiabatic section, used in some of the experiments, did not affect the results. An appendix gives relations recommended for engineering calculations.

Steady laminar natural convection plumes above a horizontal line heat source

The extensive past publication concerning the calculation of the behavior of laminar natural convection plumes above energy sources contains numerous elements of uncertainty and confusion concerning proper variables, boundary conditions, and governing equations. This paper, for the first time, states the problem in simplest variables, resolves various apparent redundancies in boundary conditions, and indicates the optimum way to formulate this boundary value problem. Results of numerical calculations are given in terms of the present simple formulation for a wide range of values of Prandtl number, some not having been treated before. Results of experiments with plumes are included to emphasize the various properties of plume flow and to indicate that the large thickness of the boundary region in the range of stable laminar plumes (i.e. at relatively low local Grashof numbers) should encourage the calculation of higher order approximations of the flow.

The Effect of Blowing or Suction on Heat Transfer by Free Convection from a Vertical Flat Plate

The effect of blowing or suction on free convection heat transfer about a vertical flat plate is analyzed by an approximate method by using the integral formulas for momentum and energy equations. There are similar solutions, if the surface temperature distribution is expressed by the equation Tw=T∞+Axn (x : distance from leading edge, A and n : constants, T∞ : temperature in quiescent ambient fluid) and the blowing or suction rate distribution is proportional to x(n-1)/4. Approximate similar solutions found under these conditions may be applied for any exponent n (0gng1) in a power law surface temperature distribution and the gases for any Prandtl number, if the blowing or suction Reynolds number is restricted within the following ranges. At n=0 [numerical formula] At n=1 [numerical formula] where ν is the kinematic viscosity of fluid and Grx denotes the local Grashof number at the position x.

The Effect of Blowing and Suction on Heat Transfer by Free Convection from a Vertical Flat Plate

The effect of suction and blowing on free convection heat transfer along a vertical flat plate is analysed by an approximate method by using the integral formulas for momentum and energy equations. There are similar solutions, if the surface temperature distribution is expressed by the equation Tω=T∞+Axn (x : distance from leading edge, A, n : constant, T∞ : temperature at quiescent ambient fluid) and the blowing and suction rate distributions are proportional to x(n-1)/4. Approximate similar solutions under these conditions may be applied for any exponent n(0≨n≨1) in a power law temperature distribution and the gases for any Prandtl number, if the blowing and suction Reynolds number is restricted within the following range. at n=0 [numberical formula] at n=1 [numberical formula] where ν is the kinematic viscosity of fluid and Grx denotes the local Grashof number at the position x.

Experiments of Free-Convection Heat-Transfer from a Vertical Cylinder Submerged in Liquids

Free convection was experimented with two kinds of vertical cylinders (the one was about 12 cm in height and the other was about 35 cm in height) submerged in water or ethylene-glycol. For laminar heat transfer, it was proved that the Ostrach's theoretical solution was right within the equal accuracy of measuring instruments, and that the authors's and Yamagata-Kawano's theoretical treatments were right on selections of physical constants, and of effective values of surface temperature and fluid temperature. For the turbulent heat-transfer, especially the relation between local Nusselt number and local Grashof number could be measured through improvement of the heating device. The following relations were found for ethylene-glycol ; [numerical formula] Similar relations to the above would be obtainable for other fluids. Heat-transfer coefficients of a vortex street zone are little different from these of laminar flow. Boundary layer temperature distributions measured with a thermocouple showed only the characteristics of flow pattern, that is laminar, vortex street, or turbulent.