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.

Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

2019 ◽  
Vol 29 (1) ◽  
pp. 334-364 ◽  
Author(s):  
Haroun Ragueb ◽  
Kacem Mansouri
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Fluid Flow ◽  
Transfer Coefficient ◽  
Convective Boundary Condition ◽  
Bulk Temperature ◽  
Convective Boundary ◽  
Content Type ◽  
The Heat Transfer Coefficient

PurposeThe purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully.Design/methodology/approachFirst, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient.FindingsThe results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers.Originality/valueA complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

Phase Change Process Inside a Small-radii Cylinder Subjected to Cyclic Convective Boundary Conditions: a Numerical Study

2021 ◽  
Author(s):  
Yousef Kanani ◽  
Avijit Karmakar ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Surface Temperature ◽  
Phase Change ◽  
Phase Change Materials ◽  
Numerical Study ◽  
Convective Boundary Condition ◽  
Freezing Process ◽  
Fourier Number ◽  
Two Phase ◽  
Convective Boundary

Abstract We numerically investigate the melting and solidi?cation behavior of phase change materials encapsulated in a small-radii cylinder subjected to a cyclic convective boundary condition (square wave). Initially, we explore the effect of the Stefan and Biot numbers on the non-dimensionalized time required (i.e. reference Fourier number Tref ) for a PCM initially held at Tcold to melt and reach the cross?ow temperature Thot. The increase in either Stefan or Biot number decreases Tref and can be predicted accurately using a correlation developed in this work. The variations of the PCM melt fraction, surface temperature, and heat transfer rate as a function of Fourier number are reported and analyzed for the above process. We further study the effect of the cyclic Fourier number on the periodic melting and freezing process. The melting or freezing front initiates at the outer periphery of the PCM and propagates towards the center. At higher frequencies, multiple two-phase interfaces are generated (propagating inward), and higher overall heat transfer is achieved as the surface temperature oscillates in the vicinity of the melting temperature, which increases the effective temperature difference driving the convective heat transfer.

Sign in / Sign up

Export Citation Format

Share Document