Showing papers on "Nusselt number published in 1968"
TL;DR: In this paper, an analytical attempt is made to understand the non-equilibrium interaction between thermal radiation and laminar free convection in terms of a heated vertical plate in a stagnant radiating gas.
125 citations
TL;DR: In this article, the problem of heat and mass transfer from small spheres and cylinders freely suspended in a shear flow is considered in the limit of Reynolds number Re → 0, and asymptotic formulas are derived which relate the Nusselt number Nu to the Peclet number Pe → 0.
Abstract: The problem of heat and mass transfer from small spheres and cylinders freely suspended in a shear flow is considered in the limit of Reynolds number Re → 0. Asymptotic formulas are derived which relate the Nusselt number Nu to the Peclet number Pe in the limit Pe → 0, and for the case of the cylinder, Pe → ∞. At high Pe, the Nusselt number is found to approach a constant value, whereas, at low Pe it is shown to increase with Pe12 for the sphere and with —(log Pe)−1 for the cylinder. These results indicate the existence of a fundamental difference at high Pe between the shear flow problem studied here and the corresponding classical problem of uniform flow at infinity.
116 citations
TL;DR: In this article, an analysis is made of unsteady laminar heat transfer in a duct with periodically varying inlet temperature and time and space-dependent wall temperature, where wall temperature variation is not specified in advance, but rather, is dynamically determined by a balance of the heat transfer rate and the energy storage.
74 citations
TL;DR: In this article, the set of ordinary differential equations governing free convection boundary layer flow past an isothermal semi-infinite vertical flat plate is solved for large Prandtl numbers by means of the method of matched asymptotic expansions.
Abstract: The set of ordinary differential equations governing free convection boundary layer flow past an isothermal semi-infinite vertical flat plate is solved for large Prandtl numbers by means of the method of matched asymptotic expansions. The analysis leads to an expression for heat transfer which contains the Prandtl number explicitly and which is very accurate for sufficiently large values of the Prandtl number. On the other hand the analysis also has qualitative assets. Before choosing the mathematical method of solution, the physical aspects of the large Prandtl number free convection boundary layer are investigated. The mathematical solution serves to enlarge our understanding of the physical implications of a free convection boundary layer in a large Prandtl number fluid.
71 citations
TL;DR: In this paper, the influence of the turbulence intensity, the scale of turbulence, and the position of the support, on the average heat transfer from spheres to an air stream was reported. But the authors did not consider the effect of crossflow support on the heat transfer.
64 citations
TL;DR: In this article, an expansion for the Nusselt number is given up to and including the term of order R 2 for the case R < 1, where the Prandtl number is of order unity.
Abstract: The present paper deals with the temperature field past an isothermal sphere. Acrivos & Taylor (1962) have obtained results for the case R [les ] 1 with no restriction on the Prandtl number. The results of the present paper are for the case R < 1 in which the Prandtl number is of order unity. An expansion for the Nusselt number is given up to and including the term of order R2.
58 citations
TL;DR: In this article, a laminar flow field and temperature field in a pipe rapidly rotating around a perpendicular axis are analyzed theoretically, by assuming velocity and temperature boundary layers along the pipe wall.
53 citations
TL;DR: In this article, a mathematical scheme for obtaining the exact thermal-entry-region temperature solutions for laminar flow (Poiseuille's parabolic velocity profiles) heat transfer subject to significant axial conduction and the boundary condition of the third kind was devised.
50 citations
TL;DR: In this paper, it was shown that the Nusselt number for liquid metals in the Reynolds number range 3 × 104 to 3 × 105 is distorted by a superimposed free convection effect up to Reynolds numbers of at least 50000.
47 citations
TL;DR: In this article, a semi-empirical analogy between heat and momentum transfer was used to estimate heat transfer rates for flows of dilute polymer solutions which exhibit drag reduction, which is limited to the range of Prandtl numbers larger than one and smaller than fifty.
39 citations
TL;DR: In this paper, an iterative numerical technique was used to calculate the Nusselt number and the structure of the roll for Rayleigh numbers between 2000 and 22 000 and for Prandtl numbers of 0.5, 1, 2, 6.8, and 200.
Abstract: Results are reported of calculations of the Nusselt number for steady two‐dimensional laminar convection in a thin fluid layer between parallel conducting plates. An iterative numerical technique is used to calculate the Nusselt number and the structure of the roll for Rayleigh numbers between 2000 and 22 000 and for Prandtl numbers of 0.5, 1, 2, 6.8, and 200. Comparison with results at Prandtl numbers of 6.8 and ∞ obtained by other investigators using different techniques show good agreement. Discussion is included of the factors affecting accuracy: (1) the zone size in a finite‐difference mesh, (2) the number of iteration cycles, and (3) extrapolation from a sequence of meshes to zero zone size. The conclusion is that extrapolation from a pair of grids using 20 and 30 zones per length scale can yield 1% accuracy over the ranges of parameters considered.
TL;DR: In this article, an analysis is presented which extends the analogy between energy and momentum transport for turbulent pipe flow of purely viscous fluids to include drag reducing, non-Newtonian fluids.
Abstract: An analysis is presented which extends the analogy between energy and momentum transport for turbulent pipe flow of purely viscous fluids to include drag reducing, non-Newtonian fluids. The correlation by Meyer is used to predict friction factor and sublayer thickness for the drag reducing fluids. The use of the friction factor correlation with the heat transfer analogy makes it possible to predict heat transfer rates from simple measurements of pressure drop and flow rate for the drag reducing fluids. Some recent experimental data for two effective drag reducing fluids and for water are compared with the predicted heat transfer rates, and the mean deviation in Nusselt number is found to be +8.5% for all of the data. The heat transfer analysis predicts a reduction in Nusselt number accompanying a reduction in friction factor for a given Reynolds number and for Prandtl numbers greater than 1.
TL;DR: In this paper, the thermal entrance region for a steady, constant-property, uniform laminar flow of an electrically conducting fluid in a constant cross-section, parallel-plate channel with isothermal, electrically nonconducting walls is presented.
TL;DR: In this article, a theoretical analysis of conduction through and free convection from a tapered, downward-projecting fin immersed in an isothermal quiescent fluid is presented.
Abstract: A theoretical analysis of conduction through and free convection from a tapered, downward-projecting fin immersed in an isothermal quiescent fluid is presented. The problem is solved by assuming quasi-one-dimensional heat conduction in the fin and matching the solution to that of the convection system, which is treated as a boundary layer problem. For an infinite Prandtl number, solutions are derived which take the form of a power law temperature distribution along the fin. The effect of this power (n) on heat transfer, drag, and the corresponding boundary layer profiles is discussed. It is shown that n is independent of the fin profile and dependent on a single nondimensional group χ. The theoretical results for infinite Prandtl number are compared with corresponding results derived from previous work using a Prandtl number of unity. The effect of Prandtl number on the determination of n and consequently the fin effectiveness is found to be extremely small. The results of an experimental program are also presented. These consist of temperature profiles and the n — χ relation for different fin geometries and surrounding fluids. Comparison with the theoretical predictions reveals good agreement.
TL;DR: In this article, an asymptotic solution for the temperature distribution at high Peclet number in a doubly-connected, laminar, incompressible flow field consisting entirely of closed streamlines was developed.
TL;DR: In this paper, an approximate method is proposed to predict Nusselt number for turbulent flow in a tube with an arbitrary axially varying heat flux distribution, and the predicted results by the proposed method were examined experimentally with air for uniform heat flux.
TL;DR: In this article, a numerical method is used to solve the heat transfer equations for laminar flow in ducts of rectangular cross section with simultaneously developing temperature and velocity profiles, both for constant wall temperature and for constant heat input per unit length of the duct.
Abstract: A numerical method is used to solve the heat transfer equations for laminar flow in ducts of rectangular cross section with simultaneously developing temperature and velocity profiles, both for constant wall temperature and for constant heat input per unit length of the duct. Like the solutions for a fully developed velocity profile, the Nusselt number for each aspect ratio is found to increase from a limiting value at large distances from the entry plane to a maximum at the entry plane. The results also show a strong effect of the Prandtl number on the heat transfer coefficients with uniform and fully developed velocity profiles representing the upper and lower limits respectively. Comparisons are made with analytical solutions for circular ducts and parallel plates and with experimental data.
TL;DR: In this article, the nonlinear, partial differential equations defining free convection boundary-layer flow along a vertical, flat, subliming, nonreacting surface were solved by means of a similarity transformation and a numerical method of asymptotic iteration through the boundary layer.
TL;DR: In this article, the problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls and extended to the cases of large suction and large injection at the wall.
Abstract: The problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls. In [6] the heat transfer problem of a discontinuous change in wall temperature was solved. In the present paper the solution of Terrill for small suction at the walls is revised and the whole problem is extended to the cases of large suction and large injection at the walls. It is found that, for all values of the Reynolds number R, the limiting Nusselt number Nu
∞ increases with increasing R.
01 Jan 1968
TL;DR: Adiabatic tube flow at low Reynolds number turbulence and heat transfer characteristics in thermal entrance and downstream regions as mentioned in this paper was shown to have high heat transfer properties in thermal entry and downstream region.
Abstract: Adiabatic tube flow at low Reynolds number turbulence and heat transfer characteristics in thermal entrance and downstream regions
TL;DR: In this paper, a theoretical investigation of the combustion characteristics of a monopropellant droplet during its heat-up period was made, and it was found that the Sherwood number was greater than the Nusselt number throughout the heatup period.
01 Sep 1968
TL;DR: In this article, a numerical analysis is made of incompressible transient turbulent flow heat transfer between two parallel plates when there is a step jump in space along the channel in wall heat flux or wall temperature.
Abstract: A numerical analysis is made of incompressible transient turbulent flow heat transfer between two parallel plates when there is a step jump in space along the channel in wall heat flux or wall temperature. The variation of the fluid velocity and effective diffusivity over the channel cross section are accounted for. The fluid is assumed to have a fully-developed turbulent velocity profile throughout the length of the channel. The thermal responses of the system are obtained by solving energy equation for air by a digital computer. The results are presented in graphical forms. The stability of the finite difference solution is studied and condition for the stability of the difference solution is derived. A method is given to obtain velocity distributions from the distribution of turbulent eddy diffusivity of momentum. Variations of Nusselt numbers are obtained as a function of time and space. Steady-state values are also given and compared with the published results.
TL;DR: In this article, the authors present the recovery factors corresponding to most of the cases considered by Mirels and calculate the recovery enthalpy for the boundary layer, which is useful to obtain a Nusselt number.
Abstract: T Note is mainly concerned with the numerical data for the frictional stress and heat-transfer rate at the wall obtained from previous theoretical investigations" of laminar shock-induced boundary layers and their reduction to convenient forms of wall-friction coefficient and Nusselt number. To obtain a Nusselt number it is useful to know the recovery enthalpy for the boundary layer, and, in this aspect, the published data are incomplete. In particular, in Mirels's work, heat-transfer data are given, but no data for recovery factor are provided. Therefore, the recovery factors corresponding to most of the cases considered by Mirels have been calculated and are presented in the present Note.
01 Feb 1968
TL;DR: In this article, the effect of free-stream turbulence on stagnation-point heat transfer from circular cylinders in cross-flow was analyzed on an IBM 1130 digital computer for a wavelength equal to 5/3 times the neutral wavelength for the flow.
Abstract: : Calculations were performed using a mathematical model to show the effect of free-stream turbulence on stagnation-point heat transfer from circular cylinders in cross-flow. The calculations were performed on an IBM 1130 digital computer for a wavelength equal to 5/3 times the neutral wavelength for the flow. This wavelength was obtained from experimental mass transfer results. The Prandtl numbers used in the computations were 0.70, 2.70, 2.85, 3.00, 7.00 and 100, and the amplitude parameter A had the range 0.0(0.5)3.0. The results of the calculations show that the mean heat transfer at the stagnation point increases with Prandtl number for each value of the amplitude parameter used in the calculations, and that the largest increase occurred for a Prandtl number equal to 100. A method is proposed on how to relate the amplitude parameter A to free-stream turbulence intensity. For a Prandtl number of 2.85, a comparison is made between heat transfer results of the model and experimental mass transfer results. The agreement between results is found to be satisfactory. (Author)
TL;DR: In this article, the heat transfer problems of uniform wall temperature and uniform heat flux at wall are solved for small suction Reynolds numbers, and the Nusselt number, with increasing Reynolds number, increases for case (i) and decreases for (ii).
Abstract: The steady laminar flow of an incompressible, viscous, and electrically conducting fluid between two parallel porous plates with equal permeability has been discussed by Terrill and Shrestha [6]. In this paper, using the solution of [6] for the velocity field, the heat transfer problems of (i) uniform wall temperature and (ii) uniform heat flux at wall are solved. For small suction Reynolds numbers we find that the Nusselt number, with increasing Reynolds number, increases for case (i) and decreases for (ii).
TL;DR: In this paper, the Graetz problem for turbulent flow between parallel plates with an n-th order reaction on one wall has been solved, and mixing cup concentrations were obtained for a range of Reynolds numbers of 30000-70000, Schmidt numbers 0·2-1·0, reaction orders of 1·0-2·0 and reaction rate constants from zero to infinity.
TL;DR: In this article, the authors examined the integrations of two-dimensional convection between rigid horizontal boundaries performed by the author and others for small Rayleigh numbers, for a Prandtl number of unity, and for a fundamental wavelength of twice the height.
Abstract: Numerical integrations of two‐dimensional convection between rigid horizontal boundaries performed by the author and others for small Rayleigh numbers, for a Prandtl number of unity, and for a fundamental wavelength of twice the height, are examined closely to see if they reproduce the experimental result that NR = aR − b, where N is the Nusselt number and R the Rayleigh number. If only one mode of convection were present, this linear law would be obeyed. The presence of higher modes in the calculations causes NR to gradually increase faster than the linear law as R increases. It is concluded that the discrete transitions of Malkus are not associated with instability of higher vertical modes when the convection is forced to be two dimensional with a fixed maximum horizontal wavelength.
TL;DR: Nusselt numbers correlated for entrance section heat transfer from helium, argon and nitrogen plasma jets in circular tubes as discussed by the authors were correlated for the transfer of heat from a circular tube.
Abstract: Nusselt numbers correlated for entrance section heat transfer from helium, argon and nitrogen plasma jets in circular tubes
TL;DR: In this article, the effect of the Reynolds number and Hartmann number on the fluid temperature during a transient varies greatly depending on their initial and steady state values, in some cases the peak transient temperature can be orders of magnitude greater than either the initial or steady state value.
Abstract: Unsteady-state, laminar, forced-convection heat transfer of an electrically conducting fluid subjected to a transverse magnetic field, flowing through a horizontal parallel plate channel has been analytically investigated for the short circuit condition using the method of characteristics. The transient is caused by a step change in the axial pressure gradient or magnetic field. Both the entrance region and fully developed heat-transfer regions were considered for a fluid with constant wall temperature. The velocity profile was assumed uniform throughout the channel at any instant of time for the purpose of calculating convective heat transfer only, but the temperature profile distribution depends 011 both the axial and transverse linear coordinates. Numerical computations were carried out which indicate that the effect of the Reynolds number and Hartmann number on the fluid temperature during a transient varies greatly depending on their initial and steady-state values. In some cases, the peak transient temperature can be orders of magnitude greater than either the initial or steadystate value.