Free Convection From a Vertical Plate With Discontinuous Wall Temperature

1971 ◽  
Vol 93 (4) ◽  
pp. 349-356 ◽  
Author(s):  
Matthew Kelleher
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Free Convection ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Asymptotic Series ◽  
Series Expansions ◽  
Temperature Profiles ◽  
Comparison Of The Results

Free convection from a vertical plate with a step discontinuity in wall temperature is analyzed by using asymptotic series. Expansions for the velocity and temperature profiles are obtained in the region immediately above the discontinuity. By series truncation, the wall heat flux is obtained in terms of a simple polynomial. Calculations are made for Pr = 0.72 and 10.0 and for various wall-temperature ratios. Comparison of the results with experimental data and previous numerical solutions is good.

Laminar Free-Convection Wake Above a Heated Vertical Plate

1964 ◽  
Vol 31 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Kwang-Tzu Yang
Keyword(s):  
Free Convection ◽  
Boundary Layers ◽  
Vertical Plate ◽  
Asymptotic Series ◽  
Integral Solution ◽  
Series Expansions ◽  
Temperature Profiles ◽  
Wake Region ◽  
Laminar Wake ◽  
Prandtl Numbers

The development of momentum and energy fields in the laminar-wake region above a heated finite vertical plate is studied analytically. Detailed velocity and temperature profiles in the immediate neighborhood of the trailing edge of the plate are calculated for two Prandtl numbers by means of asymptotic series expansions. These results are then continued to the rest of the wake region by an integral solution. It is found that the spreading of the boundary layers is rather gradual.

Free Convection Boundary Layer Over a Nonisothermal Vertical Flat Plate

2012 ◽  
Author(s):  
Roslinda Nazar ◽  
Norsarahaida Amin
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Free Convection ◽  
Wall Temperature ◽  
Convection Boundary Layer ◽  
Temperature Profiles ◽  
Convection Boundary ◽  
Prandtl Numbers ◽  
Free Convection Boundary Layer ◽  
Sinusoidal Wall

Penyelesaian berangka bagi masalah lapisan sempadan olakan bebas terhadap plat menegak dengan taburan suhu atau fluks haba yang ditetapkan akan dibincangkan. Perbincangan tertumpu kepada dua jenis syarat sempadan iaitu, variasi sinusoid suhu dinding dan variasi eksponen fluks haba. Dalam kajian ini, pengiraan berangka dilakukan menggunakan suatu skema beza terhingga tersirat yang efisien, yang dinamakan kaedah kotak Keller. Ilustrasi pengiraan dijalankan dan keputusan baru yang diperolehi dibandingkan dengan keputusan-keputusan lepas yang diperolehi menggunakan kaedah-kaedah penyelesaian yang lain, dan didapati bahawa hasil perbandingan adalah baik. Perbandingan melibatkan kecerunan suhu tak berdimensi bagi variasi sinusoid suhu dinding dan suhu tak berdimensi bagi variasi eksponen fluks haba. Keputusan baru bagi variasi tegasan ricih permukaan dengan pelbagai nombor Prandtl juga dibincangkan. Di samping itu, bagi kes variasi sinusoid suhu dinding, profil halaju dan suhu diberikan bagi beberapa nombor Prandtl iaitu 0.7, 1, 10 dan 100, manakala bagi kes variasi eksponen fluks haba, profil halaju dan suhu juga diketengahkan untuk beberapa nilai koordinat mengikut-strim yang terjelmakan ξ iaitu 0, 1, 10 and 100. Kata kunci: Olakan bebas; lapisan sempadan; plat menegak tak isoterma; kaedah berangka Numerical solutions are presented for the free convection boundary layer problems on a vertical flat plate with prescribed temperature or heat flux distributions, namely the sinusoidal wall temperature and the exponential heat flux variations. The numerical computation is carried out using a very efficient implicit finite difference scheme known as the Keller-box method. Illustrative computational examples are carried out and the present results are compared with previously available theoretical results obtained using other methods of solution, and they are found to be in good agreement. Comparisons of nondimensional temperature gradient for sinusoidal wall temperature variation and of nondimensional wall temperature with exponential variation in wall heat flux are made between the present and previous results. New results for the variation of the surface shear stress with various Prandtl numbers are also presented. In addition, for the case of sinusoidal wall temperature variation, representative velocity and temperature profiles are presented for Prandtl numbers 0.7, 1, 10 and 100, while for the case of exponential heat flux distribution, the velocity and temperature profiles for various transformed streamwise coordinate ξ = 0, 1, 10 and 100 are illustrated. Key words: Free convection; boundary layer; nanoisothermal vertical plate; numerical method

Experimental Study of Heat Transfer to Supercritical Pressure Water Flowing in a 2×2 Rod Bundle

2014 ◽  
Author(s):  
Han Wang ◽  
Qincheng Bi ◽  
Linchuan Wang ◽  
Haicai Lv ◽  
Laurence K. H. Leung
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
Pressure Drop ◽  
Wall Temperature ◽  
Mass Flux ◽  
Heat Fluxes ◽  
Outer Diameter ◽  
Square Channel ◽  
Rod Bundle

An experiment has recently been performed at Xi’an Jiaotong University to study the wall temperature and pressure drop at supercritical pressures with upward flow of water inside a 2×2 rod bundle. A fuel-assembly simulator with four heated rods was installed inside a square channel with rounded corner. The outer diameter of each heated rod is 8 mm with an effective heated length of 600 mm. Experimental parameters covered the pressure of 23–28 MPa, mass flux of 350–1000 kg/m2s and heat flux on the rod surface of 200–1000 kW/m2. According to the experimental data, it was found that the circumferential wall temperature distribution of a heated rod is not uniform. The temperature difference between the maximum and the minimum varies with heat flux and/or mass flux. Heat transfer characteristics of supercritical water in bundle were discussed with respect to various heat fluxes. The effect of heat flux on heat transfer in rod bundles is similar with that in tubes or annuli. In addition, flow resistance reflected in the form of pressure loss has also been studied. Experimental results showed that the total pressure drop increases with bulk enthalpy and mass flux. Four heat transfer correlations developed for supercritical pressures water were compared with the present test data. Predictions of Jackson correlation agrees closely with the experimental data.

scholarly journals Effects of Hall current on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate with Newtonian heating

2016 ◽  
Vol 21 (1) ◽  
pp. 187-203 ◽  
Author(s):  
G.S. Seth ◽  
S. Sarkar ◽  
R. Sharma
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Convection ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Hall Current ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Partial Differential ◽  
Present Solution

Abstract An investigation of unsteady hydromagnetic free convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively moving vertical plate with Newtonian surface heating embedded in a porous medium taking into account the effects of Hall current is carried out. The governing partial differential equations are first subjected to the Laplace transformation and then inverted numerically using INVLAP routine of Matlab. The governing partial differential equations are also solved numerically by the Crank-Nicolson implicit finite difference scheme and a comparison has been provided between the two solutions. The numerical solutions for velocity and temperature are plotted graphically whereas the numerical results of skin friction and the Nusselt number are presented in tabular form for various parameters of interest. The present solution in special case is compared with a previously obtained solution and is found to be in excellent agreement.

scholarly journals Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Nor Athirah Mohd Zin ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Thermal Radiation ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Dimensionless Time ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameterλ, Prandtl numberPr, Grashof numberGr, Hartmann numberHa, radiation parameterRd, and dimensionless timeτ. It is observed that the amplitude of velocity and temperature profile for isothermal are always higher than ramped wall temperature.

Thermal Convection in an Infinite Porous Medium Induced by a Heated Sphere

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
R. Ganapathy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Free Convection ◽  
Wall Temperature ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Series Expansions ◽  
Medium Permeability ◽  
Velocity And Temperature Fields

This paper investigates the transient behavior of the free convection motion and heat transfer induced by a heated sphere with prescribed wall temperature embedded instantaneously in an infinite porous medium. Solutions for the velocity and temperature fields have been obtained in the form of series expansions in Rayleigh number which is based on the medium permeability and the temperature of the sphere. All discussions are based on the assumption that the flow is governed by Darcy's law and the thermal Rayleigh number is small.

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