Fluid-to-Fluid Conjugate Heat Transfer for a Vertical Pipe—Internal Forced Convection and External Natural Convection

1980 ◽  
Vol 102 (3) ◽  
pp. 402-407 ◽  
Author(s):  
E. M. Sparrow ◽  
M. Faghri
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Forced Convection ◽  
Wall Temperature ◽  
Bulk Temperature ◽  
Vertical Pipe ◽  
Uniform Wall Temperature ◽  
Uniform Wall

An analysis is made of the interactive heat transfer problem involving forced convection flow in a vertical pipe and natural convection boundary layer flow external to the pipe. Both flows are laminar. Solutions of the conservation equations for mass, momentum, and energy were obtained numerically by an iterative scheme which deals successively with the internal and external flows. Remarkably rapid convergence was achieved by adopting a procedure whereby information is transferred between the two flows via heat transfer coefficients rather than via the wall or bulk temperatures or the heat flux. Results are presented for the axial distributions of the internal and external Nusselt numbers, of the wall temperature, and of the bulk temperature of the internal flow—all as a function of three parameters. It was found that at any (dimensionless) axial station, the pipe Nusselt number is insensitive to the parameters and is bounded between the values for uniform wall temperature and uniform wall heat flux. On the other hand, the external natural convection Nusselt number is highly sensitive to the parameters and departs substantially from the standard uniform wall temperature results.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

Condensation of Flowing Vapor on a Horizontal Tube—Numerical Analysis as a Conjugate Heat Transfer Problem

1984 ◽  
Vol 106 (4) ◽  
pp. 841-848 ◽  
Author(s):  
H. Honda ◽  
T. Fujii
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Flux Density ◽  
Wall Temperature ◽  
Heat Flux Density ◽  
Tube Wall ◽  
Horizontal Tube ◽  
Uniform Wall

Condensation of flowing vapor on a horizontal tube is numerically analyzed under given conditions of vapor and coolant. Besides the usual boundary layer concept, some approximations are introduced for the determination of shear stress at the vapor-liquid interface. The conjugation of the two-phase boundary layer equations and the heat conduction equation within the tube wall is achieved by using an iterative scheme at the outer surface of the tube wall. The solution thus obtained reveals the effects of vapor velocity, tube material, heat transfer of coolant side, etc., upon circumferential distributions of temperature, heat flux density, and Nusselt number at the outer tube surface. Also the solution compared well with available experimental results for the wall temperature distribution and average Nusselt number. The heat transfer characteristics of steam and refrigerant vapors resemble those of the tubes with uniform wall heat flux density and uniform wall temperature, respectively.

Effect of viscous dissipation on forced convection for laminar flow through a straight regular polygonal duct using BEM method

2018 ◽  
Vol 28 (1) ◽  
pp. 220-238 ◽  
Author(s):  
Tomasz Janusz Teleszewski ◽  
Slawomir Adam Sorko
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Wall Temperature ◽  
Bulk Temperature ◽  
Brinkman Number ◽  
Content Type ◽  
Flow Through

Purpose The purpose of this paper is to investigate the effect of the viscous dissipation of laminar flow through a straight regular polygonal duct on forced convection with constant axial wall heat flux with constant peripheral wall temperature using the boundary element method (BEM). Design/methodology/approach Both the wall heating case and the wall cooling case are considered. Applying the velocity profile obtained for the duct laminar flow and the energy equation with the viscous dissipation term is solved exactly for the constant wall heat flux using the BEM. The numerical values are obtained by means of a computer program, written by the authors in Fortran. The results of the BEM approach are verified by analytic models. Nusselt numbers are obtained for flows with a different number of sides of a regular polygonal duct and Brinkman numbers. Findings When the difference in temperature between the wall temperature and the fluid bulk temperature changes the sign, then the functions of the Nusselt number with the Brinkman number generated some singularities (BrqLs). For the Brinkman number referring to the total wall linear power, with the increasing value of the number of sides of a regular polygonal duct, BrqLs decreases in the range of 3 ≤ n < ∞. If the BrqL < BrqLs, it is possible to note that, in general, the Nusselt number is higher for cross-sections having a lower value of the number of sides of a regular polygonal duct. For BrqL > BrqLs, this rule is reversed. Originality/value This paper illustrates the effects of viscous dissipation on laminar forced convective flow in regular polygon ducts with a different number n of sides. A compact relationship for the Nusselt number vs the Brinkman number referring to the temperature difference between the wall temperature and the fluid bulk temperature and the Brinkman number, which is based on the total wall linear power, have been proposed.

CFD-Aided Simulation of Frost Growth Inside a Narrow Duct With Uniform Wall Temperature Variation

2014 ◽  
Author(s):  
Masoud Darbandi ◽  
Ehsan Asgari ◽  
Morteza Hajikaram ◽  
Gerry E. Schneider
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Growth Rate ◽  
Temperature Variation ◽  
Wall Temperature ◽  
Uniform Wall Temperature ◽  
Boundary Location ◽  
Uniform Wall ◽  
Semi Empirical ◽  
Frost Growth

In this paper, we study the frost formation and growth at the walls of a duct with uniform wall temperature variation. The simulation is performed for laminar flow regime considering suitable semi-empirical models incorporated with computational fluid dynamics (CFD) method. The frost growth is considered to be normal to the duct surface. Since the duct aspect ratio is high, we perform our simulations in two-dimensional zones. To simulate the frost layer properly, we solve both the energy and mass balance equations implementing some semi-empirical correlations on the frost side. At this stage, we suitably predict the required heat flux value at the solid boundary and the heat transfer coefficient, which are required to be used in the CFD calculations in the next stage. So, next is to use the CFD tool to calculate the required heat transfer parameters at the air side. Since the frost growth is performed locally along the wall, the achieved frost growth rate can be applied at any specific location independently. We also investigate the effects of various environmental parameters on the frost growth rate. The current achieved results are verified by comparing them with previous available experimental data. After verification the numerical algorithm, we investigate the frost growth in a duct with uniform wall temperature variation. We assume that the variation of temperature would be gradually and uniform with time. We eventually present the effects of different parameters affecting the frost growth along the duct surface. One significant contribution of this work is to address the effects of inlet boundary location on the frost growth. In this regard, the inlet boundary is placed initially at real entrance and then at a location far upstream of the real entrance. We evaluate the effect of this boundary location on frost thickness. The use of CFD is unavoidable in this study because we need its capability to compute the required wall heat flux condition, which is an input to our semi-empirical analysis in this problem with an unsteady thermal boundary condition situation, in which the wall temperature continuously varies with time. It should be noted that, our chosen empirical method estimate the wall heat flux based on the Nusselt number value. Therefore, CFD largely helps to correct the actual heat flux at the airside. Another contribution of this work is to study frost formation in confined flow cases, in which the flow is developing both hydrodynamically and thermally. Evidently this is in contrast to the frost growth over a simple flat plate like geometry.

An Experimental Study of Natural Convection in Vertical, Open-Ended, Concentric, and Eccentric Annular Channels

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
G. H. Choueiri ◽  
S. Tavoularis
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Wall Temperature ◽  
Transfer Rate ◽  
Wall Heat Flux ◽  
Annular Channels ◽  
Cylindrical Annulus

The effects of eccentricity on the natural convection heat transfer from a vertical open-ended cylindrical annulus with diameter ratio of 1.63 and aspect ratio of 18:1 have been investigated experimentally. Within the range of present conditions, and with the possible exclusion of the highest eccentricities, it was found that the flow was thermally fully developed in a considerable section of the apparatus, as indicated by the linear variation of wall temperature with height. This made it possible to estimate the mass flow rate from the wall temperature gradient in the mid-section of the annulus, and use it to calculate the bulk Reynolds number, which was found to be weakly sensitive to eccentricity for a constant wall heat flux and to increase with increased wall heat flux. With the exception of the very low eccentricity range in which it was insensitive to eccentricity, the overall heat transfer rate diminished monotonically with increasing eccentricity. Plots of the local azimuthal variation of the Nusselt number showed that, at low eccentricities, the heat transfer rate increased near the wider gap but decreased near the narrower gap. The average Nusselt number was found to decrease measurably with increasing eccentricity and to increase slightly with increasing heat flux within the examined range. In contrast, the Grashof number was found to be much more sensitive to changes in heat flux and only had a weak dependence on eccentricity.

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