The influence of an abrupt convergence on heat transfer in circular ducts

The effect of an abrupt convergence on the local heat transfer coefficient at the entrance of a uniformly heated straight pipe has been investigated. Experiments were carried out with water for Reynolds numbers from 200 to 2000, and for Prandtl numbers 4 and 6. The experimental values of the local Nusselt number are considerably lower than expected and strongly Reynolds number dependent in the region near the inlet, whereas they become comparatively high further downstream. This behaviour is discussed in connection with the hypothesis of the occurrence of a separated flow at the inlet section of the pipe. These and several previous experiments, covering turbulent and transitional flows, have been considered and summarised to obtain a general view of the effect of this geometrical configuration on heat transfer     

Finite element solutions of laminar flow and heat transfer of air in a staggered and an in-line tube bank

A finite element method is used to solve the full Navier-Stokes and energy equations for the problems of laminar flow and heat transfer characteristics of air around three isothermal heated horizontal cylinders in a staggered tube bank and around four isothermal heated horizontal cylinders in an in line tube bank. The variations of surface shear stress, pressure and Nusselt number are obtained over the entire cylinder surface, including the zone beyond the separation point. The predicted values of total drag, pressure drag and friction drag coefficients, average Nusselt number, and the plots of velocity flow fields and isotherms are also presented.     

Heat transfer in tube assemblies under conditions of laminar axial,transverse and inclined flow

This paper considers laminar flow heat transfer in tube assemblies. The main interest is focused on the virtually unexplored cases of heat transfer under conditions of fully-developed flow inclined to the axes of the tubes and of purely transverse developing flow. The limiting cases of purely axial or purely transverse fully-developed flow are also examined. In all cases, the thermal boundary condition on the tubes is constant heat flux. Governing differential equations are expressed in terms of curvilinear-orthogonal coordinates and solved using finite-differences. Results are compared with available theoretical and experimental data. The effect of the transverse component of the flow on the temperature distribution is found to remain very strong even in nearly-axial flows and therefore considerably higher heat transfer coefficients are exhibited by a nearly-axial flow than a purely axial one.     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

Numerical prediction for laminar forced convection heat transfer in parallel-plate channels with streamwise-periodic rod disturbances

A numerical study has been performed for the periodically fully-developed flow in two-dimensional channels with streamwise-periodic round disturbances on its two walls. To accurately describe the round disturbance boundary condition, a body fitted grid was used. The flow and heat transfer have been studied in the range of Reynolds number, Re=50–700, and Prandtl number Pr=0.71. The influences of disturbance parameters and Reynolds number on heat transfer and friction have been investigated in detail. Some of the solutions have been examined using both steady and unsteady finite difference schemes; and the same results have been obtained. The results show that different flow patterns can occur with different deployments of the disturbances. With appropriate configuration of the disturbances, the Nusselt number can reach a value four times greater than in a smooth channel at the same condition, with the penalty of a much greater pressure drop. On the other hand, if the disturbances are not deployed properly, augmentation of heat transfer cannot be acquired. © 1998 John Wiley & Sons, Ltd.     

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

The influence of an abrupt convergence on heat transfer in circular ducts: a theoretical assessment

This is a theoretical assessment of the postulation made by Barozzi et al, of separation in laminar flow in a circular duct caused by an abrupt entry. Using sets of data supplied by Barozzi, predictions have been made using a program developed by Collins. The effects of viscosity variation with temperature, and of natural convection, are quantified for the flow of water in a vertical tube. The results are consistent with the discussion of Barozzi et al, and tend to confirm the presence of a definite abrupt entry effect     

The effects of viscous dissipation on laminar heat transfer to power law Ruids in tubes

This work is concerned with laminar heat transfer in circular tubes to power law fluids with temperature-dependent rheological properties. Basic equations governing the problem under consideration are derived including effects of viscous dissipation but neglecting internal heat generation. The derived equations are solved numerically by means of finite-difference scheme and for the boundary conditions of constant wall temperature. The results are presented in form of graphs and compared to the computations carried out by other authors. A very good agreement is stated. The present work is intended to be an extension of the paper which has been recently published by Krishnan and Sastri [5].

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Der Einfluß viskoser Dissipation auf die Wärmeübertragung bei laminarer Rohrströmung von Ostwald-de Waele Flüssigkeiten

Zusammenfassung In dem vorliegenden Beitrag wird die Wärmeübertragung bei laminarer Rohrströmung von denjenigen nicht-Newtonschen Flüssigkeiten untersucht, die dem Potenzansatz nach Ostwald-de Waele gehorchen. Es werden Grundgleichungen für den zu behandelnden Vorgang hergeleitet, unter besonderer Berücksichtigung viskoser Dissipation sowie der Temperaturabhängigkeit rheologischer Parameter des strömenden Mediums. Der Einfluß innerer Wärmequellen wird hingegen vernachlässigt. Zur numerischen Lösung der hergeleiteten Differentialgleichungen wird die Methode der finiten Differenzen eingesetzt, unter der Voraussetzung, daß die Temperatur der Rohrwand unverändert bleibt (Randbedingungen erster Art). Die gewonnenen Ergebnisse wurden graphisch dargestellt sowie mit den von anderen Autoren erarbeiteten Resultaten verglichen. Es wurde dabei eine recht gute Übereinstimmung festgestellt. Der hier vorliegende Beitrag soll als eine Verallgemeinerung des Aufsatzes [5] gehalten werden, der neulich in dieser Zeitschrift von Krishnan und Sastri veröffentlicht wurde.

     

Conjugate heat transfer in thermally developing laminar flow with viscous dissipation effects

In this study, thermally developing laminar forced convection in a pipe including viscous dissipation and wall conductance is investigated numerically. The constant heat flux is assumed to be imposed at the outer surface of the pipe wall. The finite volume method is used. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. The dependence of the results on the Brinkman number and the dimensionless thermal conductivity are shown. The viscous heating effect on the wall is shown. Significant viscous dissipation effects have been observed for large Br.     

Slip-flow heat transfer in a microchannel with viscous dissipation

Forced convection flow in a microchannel with constant wall temperature is studied, including viscous dissipation effect. The slip-flow regime is considered by incorporating both the velocity-slip and the temperature-jump conditions at the surface. The energy equation is solved for the developing temperature field using finite integral transform. To increase β_v Kn is to increase the slip velocity at the wall surface, and hence to decrease the friction factor. Effects of the parameters β_v Kn, β, and Br on the heat transfer results are illustrated and discussed in detail. For a fixed Br, the Nusselt number may be either higher or lower than those of the continuum regime, depending on the competition between the effects of β_v Kn and β. At a given β_v Kn the variation of local Nusselt number becomes more even when β becomes larger, accompanied by a shorter thermal entrance length. The fully developed Nusselt number decreases with increasing β irrelevant to β_v Kn. The increase in Nusselt number due to viscous heating is found to be more pronounced at small β_v Kn.     

Finite element solution of heat and mass transfer flow with Hall current, heat source, and viscous dissipation

The aim of the paper is to investigate the effect of heat and mass transfer on the unsteady magnetohydrodynamic free convective flow with Hall current, heat source, and viscous dissipation. The problem is governed by the system of coupled non-linear partial differential equations whose exact solution is difficult to obtain. Therefore, the problem is solved by using the Galerkin finite element method. The effects of the various parameters like Hall current, Eckert number, heat source parameter, Prandtl number, and Schmidt number on the velocity components, the temperature, and the concentration are also examined through graphs.     

Numerical simulation for laminar flow and heat transfer of gas in rectanglar micropassages with constant wall heat flux

Theoretical investigations were performed on the developed laminar flow and convective heat transfer characteristics for incompressible gases flow through rectanglar micropassages with constant wall heat flux. Mathematical models were proposed for considering the change in viscosity and thermal conductivity of gas in the wall-adjacent region from the kinetic theory. The dimensionless velocity distribution and corresponding pressure drop, the dimensionless temperature distribution and corresponding heat transfer characteristics were both simulated numerically, and the results were compared to other report simulations [10–12] with brief discussions.     

Peripheral variation of heat transfer under pool boiling on tubes

Boiling heat transfer measurements on a tube designed to yield the peripheral variation of heat transfer coefficient without interfering with the nucleation site density are presented. A variation of up to 25% around the tube is found with a maximum at the base. High speed cine photography was used to estimate the variation of mean bubble layer thickness and mean velocities with angle. An iterative heat balance around the periphery indicated a voidage decrease from about unity at the base to 0.3–0.6 at 90°     

Numerical analysis of the transient conjugated heat transfer in a circular duct with a power-law fluid

We treat numerically in this paper, the transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluids is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the transverse and longitudinal heat conduction effects are taken into account. The numerical results for the temporal evolution of the average temperature of the tube wall, _av, is plotted for different nondimensional parameters such as conduction parameter, , the aspect ratios of the tube, and ₀ and the index of power-law fluid, n.     

Effect of streamwise structures on heat transfer in a hypersonic flow in a compression corner

Coefficients of heat transfer to the surface in a laminar hypersonic flow (M _∞ = 21) over plane and axisymmetric models with a compression corner are presented. These coefficients are measured by an infrared camera. The parameters varied in the experiments are the angle of the compression corner and the distance to the corner point. Characteristics of the flow with and without separation in the corner configuration are obtained. The measured results are compared with direct numerical simulations performed by solving the full unsteady Navier-Stokes equations. Experiments with controlled streamwise structures inserted into the flow are described. A substantial increase in the maximum values of the heat-transfer coefficient in the region of flow reattachment after developed laminar separation is demonstrated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 112–120, July–August, 2009.     

Numerical prediction of laminar flow and heat transfer characteristics in a tube fitted with regularly spaced twisted-tape elements

By numerically solving the Navier-Stokes and energy equations in their three-dimensional parabolic form, the friction and heat transfer characteristics are predicted for laminar flow in a circular tube fitted with regularly spaced twisted-tape elements that are connected by circular rods. The predictions have agreed closely with the experimental data for water. It is shown that a strong L/D effect is associated with the configuration under consideration. By extending the predictions outside the range of experimental data, it is found that considerably enhanced thermohydraulic performance is achievable by increasing the number of turns on the tape elements, by reducing the connecting rod diameter, and at high fluid Prandtl numbers.     

Three-dimensional laminar flow and heat transfer in the entrance region of trapezoidal ducts

The laminar convective flow and heat transfer in a duct with a trapezoidal cross-sectional area are studied numerically. The governing equations are solved numerically by a finite volume formulation in complex three-dimensional geometries using co-located variables and Cartesian velocity components. Details of the numerical method are presented. The accuracy of the method was also established by comparing the calculated results with the analytical and numerical results available in the open literature. The Nusselt numbers are obtained for the boundary condition of a uniform wall temperature whereas the friction factors are calculated for no-slip conditions at the walls. The asymptotic values of the Nusselt numbers, friction factors. incremental pressure drops, axial velocity and momentum rate and kinetic energy correction factors approach the available fully developed values. Various geometrical dimensions of the cross-section are considered.     

Effects of viscous dissipation on heat transfer in an oscillating flow past a flat plate

Theoretical investigation has been carried out of laminar thermal boundary layer response to harmonic oscillations in velocity associated with a progressive wave imposed on a steady free stream velocity and convected in the free stream direction. Series solutions are derived both to velocity and temperature field and the resulting equations are solved numerically. The functions affecting the temperature field are shown graphically for different values of Prandtl number. It is observed that there is more reduction in the rate of heat transfer for P _r<1 and a rise in the rate of heat transfer for P _r>1 due to the presence of oscillatory free-stream.Nomenclature u, v velocity components in the x and y direction - x, y Cartesian coordinate axes - t time - U, U ₀ instantaneous value of and mean free stream velocity - density of fluid - kinematic viscosity - T, T _w, T temperature of the fluid, wall and free stream fluid - c _p specific heat at constant pressure - thermal diffusivity - amplitude of free stream velocity - frequency - _p non-dimensional temperature (T–T /T _w–T ) - P _r Prandtl number (c _p/K) - E _c Eckert number (U ₀ ² /c _p(T _w–T )) - a parameter ( ) - ₀ boundary layer thickness of the oscillation of a harmonic oscillation of frequency ( ) - ordinary boundary layer thickness ( ) - time-averaged, time-independent external velocity - A, B, C, D, E, K, L, M, N, P functions used in expansion for u and - Nu Nusselt number (hx/k) - T _w–% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8V4rqqrFfpeea0Jc9yq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepGe9fr-xfr-x% frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcadaGcaa% qaaiaadAhacaWG4bGaai4laiqadwfagaqeaaWcbeaakiaacMcaaaa!3CA6!\[(\sqrt {vx/\bar U} )\] - k thermal conductivity     

Effects of slip,viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.