Developing Flow and Flow Reversal in a Vertical Channel With Asymmetric Wall Temperatures

1986 ◽  
Vol 108 (2) ◽  
pp. 299-304 ◽  
Author(s):  
Win Aung ◽  
G. Worku
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Flow Reversal ◽  
Entry Length ◽  
Developing Flow ◽  
Cool Wall ◽  
Plate Channel ◽  
Transfer Flow

Numerical results are presented for the effects of buoyancy on the hydrodynamic and thermal parameters in the laminar, vertically upward flow of a gas in a parallel-plate channel. Solutions of the governing parabolic equations are obtained by the use of an implicit finite difference technique coupled with a marching procedure. It is found that buoyancy dramatically increases the hydrodynamic entry length but diminishes the thermal development distance. At a fixed wall temperature difference ratio, buoyancy enhances the heat transfer on the hot wall but has little impact on the cool wall heat transfer. Flow reversal is observed in some cases. Based on an analytical solution for fully developed flow, criteria for the occurrence of flow reversal are presented. The present numerical solutions yield results that asymptotically approach those from the analytical solution.

Analytical-Solution Based Corner Correction for Transient Thermal Measurement

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
H. Jiang ◽  
W. Chen ◽  
Q. Zhang ◽  
L. He
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Data Processing ◽  
Numerical Solutions ◽  
Thermal Measurement ◽  
Time Step ◽  
Experimental Data Processing ◽  
Numerical Solution Methods ◽  
Transient Thermal ◽  
Analytical Approaches

The one-dimensional (1D) conduction analytical approaches for a semi-infinite domain, widely adopted in the data processing of transient thermal experiments, can lead to large errors, especially near a corner of solid domain. The problems could be addressed by adopting 2D/3D numerical solutions (finite element analysis (FEA) or computational fluid dynamics (CFD)) of the solid field. In addition to needing the access to a conduction solver and extra computing effort, the numerical field solution based processing methods often require extra experimental efforts to obtain full thermal boundary conditions around corners. On a more fundamental note, it would be highly preferable that the experimental data processing is completely free of any numerical solutions and associated discretization errors, not least because it is often the case that the main purposes of many experimental measurements are exactly to validate the numerical solution methods themselves. In the present work, an analytical-solution based method is developed to enable the correction of the 2D conduction errors in a corner region without using any conduction solvers. The new approach is based on the recognition that a temperature time trace in a 2D corner situation is the result of the accumulated heat conductions in both the normal and lateral directions. An equivalent semi-infinite 1D conduction temperature trace for a correct heat transfer coefficient (HTC) can then be generated by reconstructing and removing the lateral conduction component at each time step. It is demonstrated that this simple correction technique enables the use of the standard 1D conduction analysis to get the correct HTC completely analytically without any aid of CFD or FEA solutions. In addition to a transient infrared (IR) thermal measurement case, two numerical test cases of practical interest with turbine blade tip heat transfer and film cooling are used for validation and demonstration. It has been consistently shown that the errors of the conventional 1D conduction analysis in the near corner regions can be greatly reduced by the new corner correction method.

scholarly journals Unsteady/Steady Hydromagnetic Convective Flow between Two Vertical Walls in the Presence of Variable Thermal Conductivity

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. M. Hamza ◽  
I. G. Usman ◽  
A. Sule
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Approximate Solutions ◽  
Variable Thermal Conductivity ◽  
Convection Flow

Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.

scholarly journals Experimental and Numerical Study of Free Convection in a Vertical Channel with Opposing Buoyancy Forces

2021 ◽  
Author(s):  
Derek Roeleveld
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Vertical Channel ◽  
Ansys Fluent ◽  
Fully Developed Flow ◽  
Wall Functions ◽  
Buoyancy Forces ◽  
Rayleigh Numbers ◽  
Steady Laminar

Free convective heat transfer inside a vertical channel was studied both experimentally and numerically. An experimental model of an isothermally, asymmetrically heated vertical channel was constructed to study various cases of opposing buoyancy forces. Many studies in the literature have investigated buoyancy forces in a single direction. The study presented here investigated opposing buoyancy forces, where one wall is warmer than the ambient and the other wall is cooler than the ambient. Five different temperature ratios were studied using four different channel spacings between the two channel walls. A Mach-Zehnder interferometer provided temperature field visualization. In addition, local and average heat transfer measurements were made with the interferometer. Flow visualization was conducted to determine the flow pattern inside the channel. The measured local and average Nusselt number data were compared to numerical solutions obtained using ANSYS FLUENT. A steady laminar model and a steady k-ε turbulence model with two different wall functions were used. Numerical solutions were obtained for a Prandtl number of 0.71 and Rayleigh numbers ranging from the laminar fully developed flow regime to the turbulent isolated boundary layer regime.

scholarly journals Slip Velocity Distribution on MHD Oscillatory Heat and Mass Transfer Flow of a Viscous Fluid in a Parallel Plate Channel

2017 ◽  
Vol 36 ◽  
pp. 91-112
Author(s):  
Venkateswarlu Malapati ◽  
Venkata Lakshmi Dasari
Keyword(s):  
Pulsatile Flow ◽  
Parallel Plate ◽  
Numerical Solutions ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Skin Friction Coefficient ◽  
Flow Problems ◽  
Flow Through ◽  
Plate Channel ◽  
Transfer Flow

The present investigation deals with the effect of slip on the hydromagnetic pulsatile flow through a parallel plate channel filled with saturated porous medium. Based on the pulsatile flow nature, the transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using two term perturbation technique. Exact solutions are obtained for the velocity, temperature and concentration fields. In particular skin friction coefficient, Nusselt number and Sherwood number are found to evolve into their steady state case in the large time limit. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems. Parametric study of the solutions are conducted and discussed.GANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 91-112

Determination of Surface Heat Flux in Quenching

1999 ◽  
Author(s):  
M. K. Alam ◽  
H. Pasic ◽  
K. Anagurthi ◽  
R. Zhong
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Analytical Solution ◽  
Surface Heat Flux ◽  
Measurement Errors ◽  
Numerical Solutions ◽  
Heat Conduction Problem ◽  
Initial Guess ◽  
Surface Heat

Abstract Quench probes have been used to collect temperature data in controlled quenching experiments; the data is then used to deduce the heat transfer coefficients in the quenching medium. The process of determination of the heat transfer coefficient at the surface is the inverse heat conduction problem, which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching carried out to determine the surface heat flux history during a quenching process by an inverse algorithm based on an analytical solution. The algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve obtained from the analytical solution is compared with experimental results. The inverse calculation appears to produce fast, stable, but approximate results. These results can be used as the initial guess to improve the efficiency of iterative numerical solutions which are sensitive to the initial guess.

Analysis of the Total Heat Transfer in an Evaporating Thin Film

2008 ◽  
Author(s):  
Hao Wang ◽  
Suresh V. Garimella ◽  
Jayathi Y. Murthy
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Solid Wall ◽  
Total Heat ◽  
Simplified Model ◽  
Total Heat Transfer ◽  
Molecular Forces ◽  
Meniscus Region

When a liquid wets a solid wall, the extended meniscus may be divided into three regions: a non-evaporating region where liquid is adsorbed on the wall; a thin-film region where effects of long-range molecular forces (disjoining pressure) are felt; and an intrinsic meniscus region where capillary forces dominate. In this work, a simplified model based on the augmented Young-Laplace equation is developed and an analytical solution is obtained to more easily evaluate the total heat transfer in the thin-film region. The results are consistent with previously published numerical solutions. The present work is valid for a much wider range of fluid thermal conductivity than a previous analytical solution by Schonberg et al, which is only applicable for fluids with very low conductivity.

A Study of Transient Heat Transfer through a Moving Fin with Temperature Dependent Thermal Properties

2020 ◽  
Vol 401 ◽  
pp. 1-13
Author(s):  
Luyanda Partner Ndlovu ◽  
Raseelo Joel Moitsheki
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Heat Dissipation ◽  
Numerical Solutions ◽  
Solution Technique ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Transform Method ◽  
Differential Transform ◽  
Numerical Solver

In this article, heat transfer through a moving fin with convective and radiative heat dissipation is studied. The analytical solutions are generated using the two-dimensional Differential Transform Method (2D DTM) which is an analytical solution technique that can be applied to various types of differential equations. The accuracy of the analytical solution is validated by benchmarking it against the numerical solution obtained by applying the inbuilt numerical solver in MATLAB ($pdepe$). A good agreement is observed between the analytical and numerical solutions. The effects of thermo-physical parameters, such as the Peclet number, surface emissivity coefficient, power index of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter and non-dimensional ambient temperature on non-dimensional temperature is studied and explained. Since numerous parameters are studied, the results could be useful in industrial and engineering applications.

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