Showing papers on "Nusselt number published in 1971"
TL;DR: In this paper, the authors presented solution methods of convective heat transfer problems which take into account heat propagation in the solid in contact with a moving fluid, referred to as the solution of conjugated problems.
145 citations
TL;DR: Condensate film thickness and Nusselt number on axisymmetric vertical plates and cylinders, correcting for variable gravity and body form as discussed by the authors, were calculated on axismmetric cylinders.
Abstract: Condensate film thickness and Nusselt number on axisymmetric vertical plates and cylinders, correcting for variable gravity and body form
143 citations
TL;DR: In this article, an analytical and experimental results for a fully developed laminar flow in a curved channel with a square cross section are obtained under the condition of a constant wall heat flux.
97 citations
TL;DR: In this article, an expression for the eddy diffusivity in the turbulent boundary layer near a smooth wall for fluids of high Prandtl number is obtained from emperical considerations.
81 citations
TL;DR: In this paper, a theoretical method for obtaining the exact solution to the problem of thermal entry region heat transfer which takes into account both transverse nonuniformity in the velocity field and axial conduction was described.
Abstract: A theoretical method is described for obtaining the exact solution to the problem of thermal entry region heat transfer which takes into account both transverse non-uniformity in the velocity field and axial conduction. To allow for the effect of upstream conduction, the fluid temperature was taken to be uniform at × = – ∞, and the first 20 eigenvalues and the corresponding eigenfunctions were determined separately for the heated and adiabatic regions. Both the temperatures and temperature gradients were then matched at × = 0 by constructing a pair of orthonormal functions from the nonorthogonal eigenfunctions.
Nusselt numbers calculated for pipe flow subject to the boundary condition of uniform wall heat flux show virtually perfect agreement with those reported recently by Hennecke, who solved the governing partial differential equation numerically. To illustrate its general applicability, the present method was further employed to analyze the corresponding problem in parallel-plate channel flow, for which no solution has hitherto been reported.
79 citations
TL;DR: In this paper, a straight circular pipe rotating around an axis perpendicular to its own axis, there occurs a secondary flow caused by Coriolis force, by which the flow resistance and the heat-transfer rate are increased.
77 citations
TL;DR: In this paper, the authors determined the solutions of the energy equation which satisfy certain fundamental boundary conditions, and these fundamental solutions can be superposed to satisfy a wide variety of boundary conditions.
63 citations
TL;DR: In this paper, the effects of free convection on laminar flow of water in horizontal circular tubes having essentially constant heat flux at the tube wall were investigated and a visual and quantitative study was performed utilizing electrically heated glass tubing.
61 citations
TL;DR: In this paper, the incompressible thermal boundary layer equations for a vertical tube open at both ends and heated at the wall were solved by a finite difference method for conditions of constant wall temperature and constant wall heat flux.
51 citations
Abstract: The problem of heat transfer at high Peclet number Pe from a sphere freely rotating in a simple shear field is considered theoretically for the case of small shear Reynolds numbers. It is shown that the present problem is in many respects similar to that of heat transfer past a freely rotating cylinder which was recently solved by Frankel & Acrivos (1968). By taking advantage of the close analogy between these two problems, an approximate method of solution is developed according to which the asymptotic Nusselt number for Pe → ∞ is 9, i.e. 4½ times its value for pure conduction. As in the corresponding case of the cylinder, the fact that the asymptotic Nusselt number is independent of Pe results from the presence of a region of closed streamlines which completely surrounds the rotating sphere.
48 citations
TL;DR: In this paper, numerical integration of the rigid-boundary Boussinesq equations in two and three space dimensions is investigated by numerical integration with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number.
Abstract: The finite‐amplitude Benard convection problem is investigated by numerical integration of the rigid‐boundary Boussinesq equations in two and three space dimensions. Solutions are obtained for a wide range of Prandtl numbers and at moderate Rayleigh numbers for which the flow is observed to approach a two‐dimensional steady state. Detailed quantitative comparisons are made with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number and to determine the effect of changing cell size on the heat transport. The three‐dimensional model shows good evidence of being able to yield realistic values of the cell wavelength, while the two‐dimensional models yield wavelengths that are much too short. These results strongly suggest that the increase in wavelength is determined by a three‐dimensional transient process, while the convection tends to a two‐dimensional steady state. The increase in cell size is shown to be responsible for a substantial part of the discrepancy between previous theoretical‐numerical and experimental determinations of Nusselt number. It also provides a plausible explanation for the experimentally observed dependence of heat transport on Prandtl number.
TL;DR: In this paper, two experimental studies of the melt spinning of fibers have been carried out using low-density polyethylene and polystyrene, and the relationship between the fiber kinematics and drawdown force was studied using the concept of a non-Newtonian elongational viscosity and a nonlinear integral theory of viscoelastic fluids.
Abstract: Two experimental studies of the melt spinning of fibers have been carried out using low-density polyethylene and polystyrene First, isothermal spinning experiments were carried out and the relationship between the fiber kinematics and drawdown force was studied The data were correlated by using the following two methods: (1) the concept of a non-Newtonian elongational viscosity and (2) a nonlinear integral theory of viscoelastic fluids In the second experiment, the spinline temperature profile of a monofilament fiber being pulled down from a spinneret through stagnant air was measured and the heat transfer coefficient computed A correlation between the local Nusselt number and a fiber Reynolds number was obtained An integral boundary layer analysis of forced convection heat transfer from a descending fiber was carried out
TL;DR: In this paper, a simple relation, based on the Prndtl mixing length theory, is proposed for the variation of the turbulent Prandtl number within the viscous layer, which gives temperature distributions that are in good agreement with the experimental data in the region of constant shear stress.
Abstract: : Experimental investigations of total temperature and Mach number distributions in turbulent boundary layers have been performed in the Mach number range from 1.75 to 4.5, using a newly developed combined temperature and pressure probe. The measurements carried out so far have been used to reanalyze the process of heat transport by calculating the turbulent Prandtl number distribution throughout the boundary layer. The results show an increase of the turbulent Prandtl number close to the surface, thus indicating that the turbulent transport of heat decreases more rapidly towards the wall than the turbulent transport of momentum. A simple relation, based on the Prndtl mixing length theory, is proposed for the variation of the turbulent Prandtl number within the viscous layer. This relation gives temperature distributions that are in good agreement with the experimental data in the region of constant shear stress. (Author)
TL;DR: In this article, a temperature probe system was developed to measure the radial temperature profile of polymer flowing in a rod die and a method to systematically correct the conduction and the frictional shear effects were developed.
Abstract: A temperature probe system to measure radial temperature profile of polymer flowing in a rod die and a method to systematically correct the conduction and the frictional shear effects were developed. Experimental data obtained on a 1-1/2-inch extruder using a blow molding compound show that both conduction and frictional shear heating effects are significant in melt temperature measurement and that the radial temperature profiles of the melt in the rod die are influenced by the RPM of the screw and the die-wall temperature.
The reliability of the temperature data obtained was compared with the solution obtained from the equations of motion and energy. A good agreement between the predicted versus experimental temperature profile exists. For this polymer system, the relationship between local Nusselt number and the velocity parameter could be adequately described with the theory of Van LeeuWen.
TL;DR: In this paper, a widely applicable solution for convective mass or heat transfer in concentrated assemblages of spherical drops, bubbles or solid particles has been obtained by employing the methods of the boundary layer theory.
TL;DR: In this paper, a finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction, and the velocity profile is fully developed and flow in a tube and between parallel plates is studied.
Abstract: A finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction. The velocity profile is fully developed and flow in a tube and between parallel plates is studied. Local and average Nusselt numbers and mixing temperatures are presented as a function of the Peclet number. A criterion is also established which proves useful for predicting the conditions under which axial conduction may be ignored.
TL;DR: In this article, a simplified Nusselt number based on superposed free and forced convection for air for a horizontal cylinder in which the forced and free convection forces act in the same direction is considered.
Abstract: An analytical correlation of superposed free and forced convection for air for a horizontal cylinder in which the forced convection and free convection forces act in the same direction is considered. A simplified method by which the ordinary formulas for forced convection and for free convection can be used together to give the Nusselt number is presented. The method proposed herein can easily be modified to work for other combinations of free and forced flow systems. The method, therefore, may have wide application because standard formulas for simple systems are easily combined to obtain formulas which are valid for complicated systems.
TL;DR: In this article, the authors present a mathematical analysis of thermal convection in a cylinder which rotates about its vertical axis and determine the Nusselt number for the top and bottom cylinder surfaces.
TL;DR: In this article, the finite element method of solution to a partial differential equation, and the associated numerical procedure, are outlined and applied to a convection heat transfer problem, which consists of determining the temperature distribution and the axial variation of the local Nusselt number for a fluid of constant physical properties.
TL;DR: In this article, a simple theory of the probe behavior was formulated and checked by experimental measurements over a substantial range of operating conditions, and the results revealed that in the interpretation of experimental data the validity of some assumptions usually made is strongly dependent upon seemingly minor features of probe construction and operation.
Abstract: A vacuum sweeper probe of a type introduced by previous investigators was evaluated for use in the study of heat and mass transfer during evaporation. A simple theory of the probe behavior was formulated and checked by experimental measurements over a substantial range of operating conditions. The results revealed that in the interpretation of experimental data the validity of some assumptions usually made is strongly dependent upon seemingly minor features of probe construction and operation. Errors as large as 200% were encountered when the gas flow distribution in the probe was not symmetrical. Consequently, some results now in the literature are open to question.
To test the technique and theory as well as to introduce a subsequent study of the effect of monolayers on evaporation, the evaporation rate from a clean water surface was measured over a temperature range of 2° to 22°C. The role of natural convection was clearly reflected in the increase of Nusselt number as the water bulk temperature passed through the density inversion at 4°C. A relation between Nusselt and Rayleigh numbers was determined and found to be consistent with earlier results of others.
TL;DR: In this paper, the authors made estimates of the rate of heat and mass transfer by molecular streaming, diffusion, convection and radiation during crystal growth in a pressure-pulling system.
TL;DR: In this article, the reduction in evaporation from a water substrate and the accompanying change in heat transport through the water induced by monolayers of cetyl alcohol and stearic acid were investigated.
Abstract: The reduction in evaporation from a water substrate and the accompanying change in heat transport through the water induced by monolayers of cetyl alcohol and stearic acid are investigated. Evaporation resistance of the monolayer and Nusselt number in the water are determined at 2° to 22°C. The evaporation resistance increases with increasing surface pressure of the monolayer. In the presence of natural convection in the water, the Nusselt number decreases during monolayer compression. This reduction is larger than could be expected just from the lowered evaporative heat flux and the resulting reduction in the Rayleigh number. It may be due to a change in the surface hydrodynamic characteristics caused by the monolayer.
TL;DR: In this paper, the steady laminar viscous hypersonic flow of an electrically conducting fluid in the region of the stagnation point of an insulating blunt body in the presence of a radial magnetic field is studied by similarity solution approach, taking into account the variation of the product of density and viscosity across the boundary layer.
Abstract: In this paper, the steady laminar viscous hypersonic flow of an electrically conducting fluid in the region of the stagnation point of an insulating blunt body in the presence of a radial magnetic field is studied by similarity solution approach, taking into account the variation of the product of density and viscosity across the boundary layer. The two coupled non-linear ordinary differential equations are solved simultaneously using Runge-Kutta-Gill method. It has been found that the effect of the variation of the product of density and viscosity on skin friction coefficient and Nusselt number is appreciable. The skin friction coefficient increases but Nusselt number decreases as the magnetic field or the total enthalpy at the wall increases.
TL;DR: In this article, the Spalding-Patankar numerical integration procedure was applied to the case of heat transfer from an air-cooled disc rotating close to a stationary casing.
TL;DR: In this article, a new correlation was presented to describe heat and mass transfer at large Prandtl or Schmidt numbers to power law fluids in fully developed turbulent flow in a pipe, and the resulting expression for the Stanton number differs from earlier semi-empirical correlations in that it is based on a continuous eddy viscosity distribution from the wall to the center of the pipe and contains no adjustable parameters to be determined from heat transfer data.
Abstract: A new correlation is presented to describe heat and mass transfer at large Prandtl or Schmidt numbers to power law fluids in fully developed turbulent flow in a pipe. The resulting expression for the Stanton number differs from earlier semiempirical correlations in that it is based on a continuous eddy viscosity distribution from the wall to the center of the pipe and contains no adjustable parameters to be determined from heat transfer data. Nusselt numbers determined by the new correlation are in excellent agreement with data on heat transfer to both pseudoplastic and dilatant fluids.
TL;DR: In this paper, a method for integrating numerically the equations of motion for a compressible free shear layer developing from a boundary-layer profile of arbitrary shape is presented, where Sutherland's law is used to determine the coefficient of viscosity and the Prandtl number is taken as 0.72.
Abstract: A method is presented for integrating numerically the equations of motion for a compressible free shear layer developing from a boundary-layer profile of arbitrary shape. Sutherland's law is used to determine the coefficient of viscosity and the Prandtl number is taken as 0.72. Calculated results are reported for free-stream Mach numbers ranging from 0 to 10 and for stagnation-enthalpy ratios ranging from 0 to 5.0. The effects of varying the initial boundary-layer profile and of a discontinuity in temperature at the origin are also studied. The results include graphs showing the development of dividing-streamline velocity, of local Nusselt number, and of dividing-streamline location.
TL;DR: In this paper, approximate equations are developed which allow one to calculate the boundary-layer,thickness, velocity, and Nusselt numbers for the boundary layer in the presence of the non-uniform electric field.
Abstract: A thermal boundary layer is established by heating a vertical plate in a dielectric liquid. An alternating voltage is applied between the heated plate and another plate which is not parallel to the heated plate. This voltage produces a non-uni- form electric field which in turn produces electrical forces acting on the gradients in dielectric permittivity which result from the temperature gradients. These electrical forces alter the boundary layer. In this paper approximate equations are developed which allow one to calculate the boundary-layer,thickness, velocity, and Nusselt numbers for the boundary layer in the presence of the non-uniform electric field. Numerical calculations show that the heat-transfer coefficient can be either increased or decreased by the non-uniform field, depending on whether the field is strongest at the top or bottom of the plates and also on the field strength. Experiments were performed which demonstrate the change in heat transfer caused by the non-uniform field.
TL;DR: In this paper, the effects of the ratio of the Sherwood and Nusselt numbers Sh Nu, reaction order, n, and volume change coefficient, σ, on the region of instability for catalytic exothermic reactions are examined.