Showing papers on "Nusselt number published in 1970"
TL;DR: In this paper, local heat transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters, and the results were presented in terms of local Nusselt number as a function of the local Grashof number "tangential component".
111 citations
TL;DR: For any Prandtl number and for arbitrary vertical temperature or heat flux distribution at the cylinder surface, local heat transfer coefficients are represented non-dimensionally by the following approximate formulae as mentioned in this paper.
90 citations
TL;DR: In this article, an analysis of axial conduction in the wall bounding a fluid in laminar flow is developed to determine the effects of the conduction on heat transfer with Poiseuille Couette flow between parallel plates.
79 citations
01 Jan 1970
TL;DR: A submitted manuscript is the author's version of the article upon submission and before peer-review as mentioned in this paper, and the final published version features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
65 citations
TL;DR: In this article, the Nusselt number was shown to be in excellent agreement with the theoretically derived asymptotic expression,, for Peclet numbers in excess of 100.
Abstract: Heat transfer from a cylinder placed symmetrically in a constant shear field is considered experimentally for low values of the shear Reynolds number, but for Peclet numbers Pe as large as 2000. With the cylinder held stationary, the experimentally obtained Nusselt number Nu is found to be in excellent agreement with the theoretically derived asymptotic expression, , for Peclet numbers in excess of 100. In contrast, with the cylinder rotating at a speed corresponding to zero torque, the Nusselt number becomes effectively independent of the Peclet number for Pe > 70. This surprising behaviour, predicted theoretically by Frankel & Acrivos (1968), results from the presence of a region consisting entirely of closed streamlines which surrounds the freely rotating cylinder.
60 citations
TL;DR: In this paper, a simple model of this process is examined wherein the fiber is treated as a continuous infinite circular cylinder issuing steadily from an orifice and penetrating a fluid environment of infinite extent, and assuming that the fibre is maintained at a uniform temperature, a method is developed for finding the local Nusselt number by means of the Karman-Pohlhausen integral technique.
55 citations
TL;DR: In this paper, a hemispherical bubble, attached to a plate, is surrounded by an initially quiescent and isothermal liquid, and a thermal gradient over the bubble surface results.
Abstract: A hemispherical bubble, attached to a plate, is surrounded by an initially quiescent and isothermal liquid. By suddenly heating the plate, a thermal gradient over the bubble surface results. Because surface tension is temperature dependent, tangential stresses arise at the bubble surface. The liquid is viscous, and motion in the liquid phase begins. Such motion is an example of thermocapillary flow. This problem, besides being of interest from a fundamental point of view, is of possible concern in the design of space vehicles capable of storing cryogenic fluids for long periods of time in a weightless condition.
Solutions to the problem are developed by numerical treatment of the governing equations. Flow and temperature fields, which depend upon the Prandtl and Marangoni numbers, were obtained for Prandtl numbers 1 and 5 and Marangoni numbers from 0 to 100,000.
Results show that liquid is pulled toward the intersection of the bubble and the plate, then flows around the bubble surface, and leaves the bubble as a jet. The extent of the jet increases with increasing Marangoni number and decreases with increasing Prandtl number.
Thermocapillary flow increases heat transfer (Nusselt number) over that obtained from conduction, but the increase is modest. The Nusselt number increases with the Marangoni number and is insensitive to the Prandtl number. At a Marangoni number of 40,000, the local Nusselt number was increased by a factor of 2. In order for thermocapillary flow to become a dominant heat transfer mechanism, the Marangoni number must exceed 100,000.
55 citations
TL;DR: In this article, it was shown that the fractional increase in heat transfer coefficient due to the presence of solids was always less than the increase in the friction factor, and further evidence that turbulence is suppressed by the particles, particularly when the duct is small and Re is large.
Abstract: This paper is a sequel to two earlier studies of friction (I)† and eddy diffusion (2) carried out for the same flow conditions as in the present study of heat transfer. Heat was transferred to an upward flowing suspension of 0-40 μ zinc particles in pipes of 1, 2 and 3 in bore. The solids/gas flow rate was in the range 0 < Ws/Wg< 17 and the pipe Reynolds number in the range 3·5 × 104< Re < 105.It was found that the fractional increase in heat transfer coefficient due to the presence of solids was always less than the increase in the friction factor. Minimum values of both these parameters are often observed in the range 1 < Ws/Wq< 2·5. This paper gives further evidence that turbulence is suppressed by the particles, particularly when the duct is small and Re is large; in this case the wall Nusselt number, Nus, is markedly reduced below the value when gas flows alone. However, when the pipe is large and Re is low, Nus can be substantially higher than the value for gas alone. In this case the suspension is ...
53 citations
TL;DR: In this paper, the stability of convective flow in a rotating fluid layer for rigid boundary conditions is investigated and the critical Taylor number above which the only stable two-dimensional flow becomes unstable is calculated as a function of the Prandtl number.
53 citations
TL;DR: In this article, the authors presented the computed friction factors and Nusselt numbers of the sinusoidal geometry for several aspect ratios and Biot numbers (or wall reaction rates).
45 citations
TL;DR: In this article, the transition from turbulent to laminar regime as consequence of high heating rates for internal convective flow was discussed, noting roles of Nusselt numbers and friction factors.
Abstract: Transition from turbulent to laminar regime as consequence of high heating rates for internal convective flow, noting roles of Nusselt numbers and friction factors
TL;DR: In this paper, film condensation heat flux measurements have been made on a vertical surface at film Reynolds numbers below the critical values for ripple formation, and the average heat flux values for air-steam mixtures were divided by those computed from the Nusselt theory for pure vapor at the same difference between vapor and surface temperature.
TL;DR: In this article, exact temperature solutions and theoretical Nusselt curves were obtained for thermal-entry-region heat transfer for laminar flow through concentric annuli, subject to a step jump in wall heat flux at z = 0.
TL;DR: In this paper, the effect of fin geometry and temperature on the respective heat transfer coefficients for the upper, vertical, and lower edges of fin arrays has been clarified, and empirical formulas for the respective average Nusselt numbers are obtained.
Abstract: As a sequel to the previous report of this series, the author has this time taken up the fin-edge as one component surface composing a fin array and experimentally studied natural convection heat transfer from the fin-edges in air. The effect of fin geometry and temperature on the respective heat transfer coefficients for the upper, vertical, and lower edges of fin arrays has been clarified. Furthermore, empirical formulas for the respective average Nusselt numbers are obtained. It is found that the heat transfer coefficients for the lower and vertical edges show fairly high values, e.g. 20∼30kcal/m2hr°C.
TL;DR: In this article, the authors measured the rate of change of apparent weight of melting ice spheres and found that the traditional correlation format of Nusselt number against Rayleigh number is satisfactory only for bulk temperatures above 7°C.
Abstract: Experimental results have been obtained for heat transfer to melting ice spheres by measuring the rate of change of apparent weight. It is found that the traditional correlation format of Nusselt number against Rayleigh number is satisfactory only for bulk temperatures above 7°C. Average Nusselt numbers obtained from the sphere experiments are closely related to previous theoretical work with vertical flat plates.
TL;DR: In this article, it was shown experimentally that a corona discharge established on a heated wire immersed in a cooler gas enhances heat transfer from the wire to the gas, ostensibly by disrupting the boundary layer about the wire.
TL;DR: In this article, a free convection between two vertical coaxial cylinders was studied by solving the governing transport equations as an initial value problem, and the coupled, nonlinear, partial differential equations were converted into a set of difference equations by use of an alternating-direction implicit finite-difference numerical scheme.
Abstract: Free convection between two vertical coaxial cylinders was studied by solving the governing transport equations as an initial-value problem. The coupled, nonlinear, partial differential equations were converted into a set of difference equations by use of an alternating-direction implicit finite-difference numerical scheme. Twenty-four different combinations of Prandtl and Grashof numbers, and height to annular spacing ratios were used to characterize the problem. The results are presented primarily in the form of contour maps for the steady-state isotherms and streamlines.
For Rayleigh numbers greater than 5 × 103, a fully developed boundary-layer flow was found to exist in the cavity. The interior region of the annulus was found to be thermally stratified and to possess a nearly uniform vertical temperature gradient, with a unicellular flow pattern being generated.
With Rayleigh numbers of 5 × 104 and greater, it was found that the flow patterns could not be properly described with a grid spacing of 1/10. The variation of the steady-state mean Nusselt number with Prandtl and Rayleigh numbers and with geometric ratios was also investigated.
TL;DR: In this paper, the problem of determining the heat transfer in fully developed turbulent flow of a non-gray radiating gas in a circular tube was considered and the effects of radiation on the temperature profile and the Nusselt number were reported.
TL;DR: In this paper, heat transfer and wall friction predictions for quasi-developed strongly heated turbulent pipe flow, using mixing length model, were made using a mixing length-based model for convex flow.
Abstract: Downstream heat transfer and wall friction predictions for quasi-developed strongly heated turbulent pipe flow, using mixing length model
TL;DR: In this article, the laminar swirling flow in the hydrodynamic entrance region of a circular pipe is treated in the framework of boundary layer theory, the solutions being obtained by means of an extended form of the finite difference method invented by Leigh and Terril.
Abstract: Treated in this paper is the laminar swirling flow in the hydrodynamic entrance region of a circular pipe, in which the entering flow has uniform axial-and linearly varying tangential-velocity components The analysis is carried out within the framework of the boundary layer theory, the solutions being obtained by means of an extended form of the finite difference method invented by Leigh and Terril the following results are obtained from the analysis: (1) The entrance length is significantly increased by the presence of swirl at the entrance section (2) The additional pressure drop based on the center-line pressure at the entrance section is considerably decreased as the swirl is increased (3) If the wall temperature is constant, the local Nusselt number is increased by a few percent at a certain distance downstream from the entrance section when Prandtl number is taken as 072 (4) The damping coefficients of the swirl show an exponential decay shortly after the entrance section However, in the immediate neighbourhood of the entrance section, the damping of the swirl is a little faster than the exponential decay
01 Apr 1970
TL;DR: Heat transfer in turbulent boundary layer with strong favorable pressure gradients and blowing as mentioned in this paper, where the boundary layer is covered by a boundary layer of turbulent boundary layers with favorable pressure gradient.
Abstract: Heat transfer in turbulent boundary layer with strong favorable pressure gradients and blowing
Journal Article•
TL;DR: In this paper, local flow and heat transfer characteristics in a seven tube bundle helically wrapped with wires of circular cross section are obtained computationally and presented for a Reynolds number range of 8,000 to 100,000.
Abstract: Local flow and heat transfer characteristics in a seven tube bundle helically wrapped with wires of circular cross section are obtained computationally and presented. Regions of sweeping and mixing flows and hot spots are identified from the local characteristics. Parametric investigations with varying outer diameter ratio (D/d = 3.93, 4.24 and 4.54), helical pitch ratio (P/d = 9.09, 18.18 and 30.30) and triangular pitch ratio (Pt/d = 1.28, 1.32 and 1.36) are presented for a Reynolds number range of 8,000 to 100,000. The average friction factors and Nusselt numbers show highest values for D/d = 3.93, P/d= 9.09 and Pt/d =1.36. The variation of thermal hydraulic performance ratio against the mass flow rate provides an optimum geometry for the design of heat exchanger with seven tube bundle.
TL;DR: In this article, the interaction of radiation with convection in an absorbing and emitting boundary layer is investigated by means of the integral method, and closed form solutions are obtained for the Nusselt number.
TL;DR: In this article, the heat transfer by free convection from a heated 60° vee-corrugated plate to a cooled flat plate placed above it has been studied, with the cold flat plate and the vees horizontal.
TL;DR: In this article, an analytical solution for the turbulent entrance region problem with a stepfunction heat flux distribution was obtained, where necessary eigenvalues, eigenfunctions, and series coefficients were evaluated from the characteristic equation by the method of Runge-Kutta.
01 Jun 1970
TL;DR: In this article, an experimental rotating wickless heat pipe apparatus was designed and machined, which includes a rotating heat pipe assembly, test stand, spray cooling assembly, safety shielding, and instrumentation.
Abstract: : An experimental rotating wickless heat pipe apparatus was designed and machined. The apparatus includes a rotating heat pipe assembly, test stand, spray cooling assembly, safety shielding, and instrumentation. A revised condensing limit for the operation of the rotating heat pipe was obtained by modifying Ballback's Nusselt film condensation theory to include the effects of a thermal resistance in the condenser wall and in the condenser outside surface cooling mechanism. Approximate results, obtained for half-cone angles of 1, 2, and 3 degrees, show that less heat can be removed than originally predicted by Ballback, and that the outside heat transfer coefficient can significantly alter the condensing limit. An improved Nusselt theory was developed which applies for all half-cone angles, and which includes the effects of the thermal resistances in the condenser wall and in the condenser outside surface cooling mechanism. This formulation led to a second-order non-linear differential equation for the film thickness which was numerically integrated using a free-overfall boundary condition at the condenser exit. Results obtained for a half-cone angle of 0 degrees are substantially less than the results obtained from the approximate solution for half-cone angles of 1, 2, and 3 degrees.
TL;DR: In this article, a point matching method in terms of a series containing Bessel functions has been used to obtain a solution by point matching in a vertical regular polygonal ducts.
Abstract: Laminar combined free and forced convection through vertical regular polygonal ducts has been studied. All fluid properties are considered constant, except variation of density in the buoyancy term. Heat flux is considered uniform in the flow direction while in the transverse direction two wall conditions have been considered; Case 1—uniform circumferential wall temperature, and Case 2—uniform circumferential heat flux. A solution by point matching method in terms of a series containing Bessel functions has been obtained. Nusselt numbers, local heat flux, local shear stress, and pressure drop have been investigated. The condition of Case 1 results in higher Nusselt number values compared to the condition of Case 2. However, these differences in Nusselt number diminish as the number of sides of the polygon are increased. In each case at higher values of the Rayleigh number, the Nusselt number is less sensitive to the number of sides. When Nusselt numbers against number of sides are considered, in Case 1, the Nusselt numbers reach asymptotic value at lower number of duct sides compared to Case 2. At low values of buoyancy effect, in Case 1, the maximum circumferential heat flux results at the centre of the wall, while at higher values of the same, the local heat flux becomes uniform over a substantial portion of the wall. Under Case 1 buoyancy effect increases the heat flux ratio at the duct corners. In three-sided polygon at higher values of the buoyancy parameter the maximum shear stress is no longer incident at the wall center. As the number of sides is increased, however, the maximum shear stress again takes place at the wall center. The Case 1 produces higher shear stress values near the wall center, while the Case 2 produces higher shear stress values near the duct corner. When the buoyancy parameter is high and the number of sides is not large, Case 2 results in higher values of pressure drop parameter compared to Case 1.
TL;DR: In this paper, the Nusselt number in terms of the Grashof and Prandtl number was determined for free-burning arcs in air at pressures from 0.019 to 1.0 atm and high currents from 190 to 400 A.
Abstract: The measured characteristic curves for free‐burning arcs in air at pressures from 0.019 to 1.0 atm and high currents from 190 to 400 A are presented. The experimental results show that the characteristic curves are flat (E = const) at these high currents. Characteristic arc dimensions were determined from arc photographs. The results show the arc diameter to be proportional to I12. Heated solid cylinder heat transfer ideas are applied to the free‐burning arc data and the functional form for the Nusselt number in terms of the Grashof and Prandtl number is determined.
TL;DR: In this article, the equations of motion and energy are solved numerically for fully developed laminar flow of a power law fluid in a vertical pipe with constant heat flux at the wall.
Abstract: The equations of motion and energy are solved numerically for fully developed laminar flow of a power law fluid in a vertical pipe with constant heat flux at the wall. Density is assumed to be the only temperature dependent physical property of the fluid. Temperature profiles, velocity profiles, and Nusselt numbers are presented as functions of the power law exponent and the ratio of the Grashof number divided by the Reynolds number.