TURBULENT HEAT TRANSFER IN A TUBE WITH PRESCRIBED HEAT FLUX (APPROXIMATE METHOD TO PREDICT NUSSELT NUMBER BASED ON RELATIONSHIPS BETWEEN TWO FUNDAMENTAL SOLUTIONS OF UNIFORM WALL TEMPERATURE AND UNIFORM HEAT FLUX)

1970 ◽  
Author(s):  
Shu Hasegawa ◽  
Yasunobu Fujita
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Wall Temperature ◽  
Fundamental Solutions ◽  
Turbulent Heat Transfer ◽  
Uniform Heat Flux ◽  
Turbulent Heat ◽  
Uniform Wall Temperature ◽  
Uniform Wall

scholarly journals Exact and statistical computations of radiated flow of nano and Casson fluids under heat and mass flux conditions

2019 ◽  
Vol 6 (4) ◽  
pp. 593-605 ◽  
Author(s):  
Joby Mackolil ◽  
Basavarajappa Mahanthesh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Uniform Heat Flux ◽  
Statistical Tools ◽  
Dufour Effect ◽  
Uniform Wall Temperature ◽  
Uniform Wall

Abstract The statistical and exact analysis of the unsteady radiative flow of Nano and Casson fluids past a vertical plate with Dufour effect is carried out. The heat transport phenomenon is studied under uniform heat flux (UHF) and uniform wall temperature (UWT) conditions. The exact solution to the problem is found using the Laplace transform method (LTM). The effects of various parameters on velocity, temperature and concentration profiles are examined via graphs. The heat transfer rate and skin friction are analyzed through statistical tools like probable error and regression. The Dufour effect enhances the velocity and temperature profiles. It is also observed that the velocity profile is slightly greater in the case of UWT than the UHF case for both nanofluid and Casson fluid. From the regression analysis, it is established that the Dufour number and nanoparticle volume fraction have a negative impact whereas the radiative heat parameter has a positive impact on the rate of heat transfer. Highlights The statistical analysis of the unsteady radiated flow on a vertical plate with Dufour effect is performed. The uniform heat flux (UHF) and uniform wall temperature (UWT) conditions are accounted. The Nusselt number and friction factor are analysed through statistical tools. The velocity profile is greater for UWT case than the UHF case.

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.

Turbulent Heat Transfer Over a Free Rotating Disk: Analytical and Numerical Predictions Using Solutions of Direct and Inverse Problems

2001 ◽  
Author(s):  
I. V. Shevchuk
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Wall Temperature ◽  
Direct Problem ◽  
Rotating Disk ◽  
Analytical Form ◽  
Turbulent Heat Transfer ◽  
Radial Coordinate ◽  
Turbulent Heat ◽  
Numerical Predictions

Abstract All known analytical solutions of the integral equation of the turbulent thermal boundary layer for a rotating disk have been obtained for the case of direct problem. This means finding the Nusselt number at a given distribution of the wall temperature. This distribution is described by power law and is monotone (derivative of wall temperature with respect to the radial coordinate does not change its sign). Outlined in this paper is an analytical form of non-monotone distribution of the wall temperature, which provided a new analytical solution for the turbulent Nusselt number including earlier known equations as a specific particular case. The solution is based on the integral method, which proved to be more precise than known Dorfman’s approach. Chosen for validation of the proposed method were turbulent heat transfer experiments of Northrop and Owen (1988). Predictions presented include analytical studies using inverse and direct problem solutions as well as numerical simulations using polynomial approximations of the experimental wall temperature distributions.

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.

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.

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