scholarly journals Exact Solutions for Nonclassical Stefan Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Adriana C. Briozzo ◽  
Domingo A. Tarzia
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Exact Solutions ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Flux Boundary Condition ◽  
Similarity Type ◽  
Stefan Problems ◽  
First Case ◽  
Temperature Boundary

We consider one-phase nonclassical unidimensional Stefan problems for a source functionFwhich depends on the heat flux, or the temperature on the fixed facex=0. In the first case, we assume a temperature boundary condition, and in the second case we assume a heat flux boundary condition or a convective boundary condition at the fixed face. Exact solutions of a similarity type are obtained in all cases.

Double dispersion effects on non-Darcy free convective boundary layer flow of a nanofluid over vertical frustum of a cone with convective boundary condition

2017 ◽  
Vol 6 (4) ◽  
Author(s):  
Ch. RamReddy ◽  
Ch. Venkata Rao
Keyword(s):  
Boundary Condition ◽  
Volume Fraction ◽  
Concentration Field ◽  
Convective Boundary Condition ◽  
Complex Problem ◽  
Convection Flow ◽  
Surface Drag ◽  
Convective Boundary ◽  
Flux Boundary Condition ◽  
Double Dispersion

AbstractIn this paper, a numerical analysis is performed to investigate the effects of double dispersion and convective boundary condition on natural convection flow over vertical frustum of a cone in a nanofluid saturated non-Darcy porous medium. In addition, Brownian motion and thermophoresis effects have taken into consideration, and the uniform wall nanoparticle condition is replaced with the zero nanoparticle mass flux boundary condition to execute physically applicable results. For this complex problem, the similarity solution does not exist and hence suitable non-similarity transformations are used to transform the governing equations along with the boundary conditions into non-dimensional form. The Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM) is used to solve the reduced non-similar, coupled partial differential equations. To test the accuracy of proposed method, the error analysis and convergence tests are conducted. The effect of flow influenced parameters on non-dimensional velocity, temperature, nanoparticle volume fraction, regular concentration field as well as on the surface drag, heat transfer, nanoparticle and regular mass transfer rates are analyzed.

scholarly journals Effect of a Convective Boundary Condition on Boundary Layer Slip Flow and Heat Transfer Over a Stretching Sheet in View of the Exact Solution

2016 ◽  
Vol 46 (4) ◽  
pp. 85-95 ◽  
Author(s):  
Mona D. Aljoufi ◽  
Abdelhalim Ebaid
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Exact Solutions ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Convective Boundary Condition ◽  
Current Paper ◽  
Convective Boundary

Abstract The exact solutions of a nonlinear differential equations system, describing the boundary layer flow over a stretching sheet with a convective boundary condition and a slip effect have been obtained in this paper. This problem has been numerically solved by using the shooting method in literature. The aim of the current paper is to check the accuracy of these published numerical results. This goal has been achieved via first obtaining the exact solutions of the governing nonlinear differential equations and then, by comparing them with the approximate numerical results reported in literature. The effects of the physical parameters on the flow field and the temperature distribution have been re-investigated through the new exact solutions. The main advantage of the current paper is the simple computational approach that has been introduced to analyze exactly the present physical problem. This simple analytical approach can be further applied to investigate similar problems. Although no remarkable differences have been detected between the current figures and those obtained in literature, the authors believe that if some numerical calculations were available for the fluid velocity and the temperature in literature then the convergence criteria and the accuracy of the shooting method used in Ref. [15] can be validated in view of the current exact expressions.

scholarly journals SOME CONSIDERATIONS REGARDING THE EXACT SOLUTION IN THE ONE PHASE-STEFAN PROBLEM

2006 ◽  
Vol 5 (1) ◽  
pp. 03 ◽  
Author(s):  
A. Boucíguez ◽  
R. Lozano ◽  
M. A. Lara
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Exact Solution ◽  
Stefan Problem ◽  
Flux Boundary Condition ◽  
Temperature Boundary ◽  
Infinite Slab ◽  
Heat Flux Boundary Condition ◽  
The One ◽  
Temperature Boundary Condition

The one phase Stefan problem in a semi - infinite slab with heat flux boundary condition  proportional  to  t½   and  with  constant  temperature  boundary condition are presented here. In these two cases the exact solution exists, the relation  between  the  two  boundary  conditions  is  presented  here,  and  the equivalence between the two problems is demostrated.

scholarly journals Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Andrea N. Ceretani ◽  
Domingo A. Tarzia
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Mushy Zone ◽  
Phase Change ◽  
Convective Boundary Condition ◽  
Zone Model ◽  
Thermal Coefficient ◽  
Convective Boundary

A semi-infinite material under a solidification process with the Solomon-Wilson-Alexiades mushy zone model with a heat flux condition at the fixed boundary is considered. The associated free boundary problem is overspecified through a convective boundary condition with the aim of the simultaneous determination of the temperature, the two free boundaries of the mushy zone and one thermal coefficient among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat, and the two coefficients that characterize the mushy zone, when the unknown thermal coefficient is supposed to be constant. Bulk temperature and coefficients which characterize the heat flux and the heat transfer at the boundary are assumed to be determined experimentally. Explicit formulae for the unknowns are given for the resulting six phase-change problems, besides necessary and sufficient conditions on data in order to obtain them. In addition, relationship between the phase-change process solved in this paper and an analogous process overspecified by a temperature boundary condition is presented, and this second problem is solved by considering a large heat transfer coefficient at the boundary in the problem with the convective boundary condition. Formulae for the unknown thermal coefficients corresponding to both problems are summarized in two tables.

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