Laminar Free Convection From a Nonisothermal Cylinder

1965 ◽  
Vol 87 (2) ◽  
pp. 237-241 ◽  
Author(s):  
J. C. Y. Koh ◽  
J. F. Price
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Surface Temperature ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Linear Combinations ◽  
All Solutions ◽  
Wall Surface Temperature

Laminar free convection from a nonisothermal horizontal cylinder is analyzed. The wall surface temperature is assumed to be varied in the manner of a1(x/R)2 + a2(x/R)4. Special transformations are devised and employed so that the resulting differential equations and boundary conditions are free of the parameters a1 and a2. These differential equations are solved once and for all; solutions to the original equations for any particular values of a1 and a2 may then be read off easily as linear combinations of the numerical solutions given here. It is found that the dependence of heat transfer from a horizontal cylinder on Prandtl number is practically the same as that from a vertical plate. Furthermore, the heat transfer is greatly influenced by the surface temperature variations.

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.

The Free Convection of Heat from a Vertical Plate to Several Non-Newtonian “Pseudoplastic” Fluids

1972 ◽  
Vol 94 (1) ◽  
pp. 64-72 ◽  
Author(s):  
J. D. Dale ◽  
A. F. Emery
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Power Law ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Minor Importance ◽  
Large Tank ◽  
Pseudoplastic Fluids

The local heat transfer, temperature, and velocity profiles were measured and numerically predicted for the free convection of heat from a vertical constant flux plate to several concentrations of carboxymethylcellulose (CMC) and carboxypolymethylene (Carbopol) powders in water. The fluids were found to have the thermal properties of water and in the shear stress range of interest to follow the power law of Ostwald–de Waele with flow indices varying from 0.395 to 1.0 and with fluid consistencies of 30 to 2300 times that of water. The tests were conducted using either of two plates (12 and 24 in. high) immersed in such a large tank (3000 lb of fluid) that the viscometric properties of the fluid remained unchanged, even for the long test periods used. All fluids, including those with yield stresses and those which suffered free surface effects, were found to transfer heat which could be correlated by the generalized Newtonian correlation Nux=C(Grx*Prx*n)13n+2 which suggests that the precise velocity characteristics of the fluid are of minor importance in determining the heat transfer performance of the system. The numerical solutions, based upon the boundary layer assumptions and the power-law model, were in excellent agreement with the experimental measurements.

scholarly journals Numerical Solutions of Hybrid Nanofluids Flow Via Free Convection Over a Solid Sphere

2021 ◽  
Vol 83 (1) ◽  
pp. 34-45
Author(s):  
Mohammed Zaki Swalmeh
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Convection ◽  
Numerical Solutions ◽  
Solid Sphere ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Partial Differential ◽  
Hybrid Nanofluids

The purpose of the existing study is to examine how heat transfer enables consolidated by variations in the basic advantages of fluids in the existence of free convection with the assistance of suspended hybrid nanofluids. Iron-graphene oxide suspended in water as a hybrid nanofluid flow on a solid sphere is also considered in this work. The partial differential equations are gotten, for this problem, by transforming the mathematical governing equations using similarity equations (stream function). These partial differential equations are solved numerically by Keller-Box method and programmed by MATLAB program. the acquired numerical results are in excellent agreement with the preceding literature results. Graphical results of the influence of the hybrid nanofluid parameters on some physical quantities regarded to examine the behavior of hybrid nanofluid flow were attained, and they proved that hybrid nanofluid flow represents a more essential role in the operation of heat transfer than a regular nanofluid flow.

Free Convection From a Vertical Plate With Nonuniform Surface Temperature and Embedded in a Porous Medium

1987 ◽  
Vol 109 (1) ◽  
pp. 26-30 ◽  
Author(s):  
R. S. R. Gorla ◽  
A. H. Zinalabedini
Keyword(s):  
Porous Medium ◽  
Free Convection ◽  
Surface Temperature ◽  
Energy Equation ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Published Data ◽  
Universal Functions ◽  
Free Convection Flow

A procedure is described for the calculation of heat transfer due to free convection flow along a vertical plate embedded in a porous medium with an arbitrarily varying surface temperature. By applying the appropriate coordinate transformations and the Merk series, the governing energy equation is expressed as a set of orindary differential equations. Numerical solutions are presented for these equations which represent universal functions and the surface gradients of these universal functions are tabulated. Several computational examples are provided and the results are compared with published data in the case of two examples.

Laminar Condensation Heat Transfer on a Horizontal Cylinder

1959 ◽  
Vol 81 (4) ◽  
pp. 291-295 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Film Condensation ◽  
Number Range ◽  
Laminar Film Condensation ◽  
Layer Analysis ◽  
Inertia Forces

A boundary-layer analysis is made for laminar film condensation on a horizontal cylinder. The formulation includes both the inertia forces and energy convection terms, which are neglected in Nusselt’s simple theory. A similarity transformation, valid over most of the cylinder, is found which reduces the partial differential equations of the problem (the conservation laws) to ordinary differential equations. Numerical solutions of the resulting ordinary differential equations are available for the Prandtl number range from 0.003 to 100. Heat-transfer results are presented and discussed.

Effects of Microstructure on the Conjugated Mixed Forced and Free Convection-Conduction Analysis of Heat Transfer in a Vertical Plate Fin

1986 ◽  
Vol 108 (3) ◽  
pp. 580-584 ◽  
Author(s):  
Fue-Sang Lien ◽  
Cha’o-Kuang Chen
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transfer Coefficient ◽  
Micropolar Fluid ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Local Heat Transfer Coefficient

A conjugated convection-conduction analysis has been made for a vertical plate fin which exchanges heat with its micropolar fluid environment by mixed forced and free convection. The analysis is based on a one-dimensional model for the plate fin whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, angular momentum, and energy in the micropolar fluid boundary layer adjacent to the fin. The local heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. Numerical results of the overall heat transfer rate, the local heat transfer coefficient, the local heat flux, and the fin temperature distribution for Pr = 5 are presented for various values of Δ (dimensionless material parameter), Nc (conjugated convection-conduction parameter), and Ω (buoyancy parameter).

scholarly journals Combined Effects of Thermal Radiation and Nanoparticles on Free Convection Flow and Heat Transfer of Casson Fluid over a Vertical Plate

2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
M. G. Sobamowo
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Casson Fluid ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Flow And Heat Transfer

The influences of thermal radiation and nanoparticles on free convection flow and heat transfer of Casson nanofluids over a vertical plate are investigated. The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equations through similarity transformations. The resulting systems of fully coupled nonlinear ordinary differential equations are solved using the differential transformation method with Padé-approximant technique. The accuracies of the developed analytical methods are verified by comparing their results with the results of past works as presented in the literature. Thereafter, the analytical solutions are used to investigate the effects of thermal radiation, Prandtl number, nanoparticle volume fraction, shape, and type on the flow and heat transfer behaviour of various nanofluids over the flat plate. It is observed that both the velocity and temperature of the nanofluid as well as the viscous and thermal boundary layers increase with increase in the thermal radiation parameter. The velocity of the nanofluid decreases and the temperature of the nanofluid increase, respectively, as the Prandtl number and volume fraction of the nanoparticles in the base fluid increase. The decrease in velocity and increase in temperature are highest in lamina-shaped nanoparticle and followed by platelet-, cylinder-, brick-, and sphere-shaped nanoparticles, respectively. Using a common base fluid to all the nanoparticle types, it is established that the decrease in velocity and increase in temperature are highest in TiO2 and followed by CuO, Al2O3, and SWCNT nanoparticles, in that order. It is hoped that the present study will enhance the understanding of free convection boundary layer problems of Casson fluid under the influences of thermal radiation and nanoparticles as applied in various engineering processes.

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