scholarly journals The influence of crucible and crystal rotation on the hydrodynamics of a melt with a Prandtl number 16 and on heat transfer in the Czochralski method

2020 ◽  
Vol 1677 ◽  
pp. 012182
Author(s):  
V S Berdnikov ◽  
V V Vinokurov
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Czochralski Method ◽  
Crystal Rotation

scholarly journals Numerical and physical study of transitions to unsteady modes of melt flow with the Prandtl number 16 in the Czochralski method

2021 ◽  
Vol 2119 (1) ◽  
pp. 012165
Author(s):  
V S Berdnikov ◽  
V A Vinokurov ◽  
V V Vinokurov
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Unsteady Flow ◽  
Flow Structure ◽  
Characteristic Temperature ◽  
Temperature Drop ◽  
Czochralski Method ◽  
Melt Flow ◽  
Flow And Heat Transfer ◽  
Physical Study

Abstract The evolution of the flow structure and heat transfer with an increase in the characteristic temperature drop in the ranges of Grashof and Marangoni numbers 3558 ≤ Gr ≤ 7116 and 2970 ≤ Ma ≤ 5939 are investigated numerically. The boundary of the transition to unsteady flow and heat transfer regimes has been determined.

Improvement Of Free Convection From Three horizontal Finned Cylinders Fixed Between Two Walls

2018 ◽  
Vol 6 (2) ◽  
pp. 98-114 ◽  
Author(s):  
Hassan K. Abdullah ◽  
Haneen H. Rahman
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Prandtl Number ◽  
Convection Heat Transfer ◽  
Constant Heat Flux ◽  
Heat Fluxes ◽  
Head Orientation ◽  
Outer Diameter ◽  
Gravitational Acceleration ◽  
Convection Heat

Improvement of  free convection heat transfer from three finned cylinders arranged at a triangle shape fixed between two walls has been investigated in this study. Three mild steel finned cylinders fixed between two walls from Pyrex glass have been used as a test rig. It has been changed the spacing between the cylinders (X/D=1,2,3 & S/D=2,4,6) and the head orientation of a triangle to the top under constant heat flux values (38, 254, 660, 1268) W/m2 and compare with case of three finned cylinders arranged in vertical array in line fixed between two wall. The experiments are carried for Rayleigh number (Ra) from (15x103 to 14 x104 ) and Prandtl  number from (0.706-0.714 ). The results indicated an increase in Nu with increasing Ra for all cylinders. Furthermore,hx and Nu increased proportionally with the increasing of cylinder spacings for all heat fluxes. Also the experimental results show the case of triangle arrangement is improvement the heat transfer more than case of vertical arrangement. Heat transfer dimensionless correlating equation is also proposed.              Nomeclature: Ax: surface area(m2), T∞: surrounding temperature(k), D: the outer diameter of fin (m), Kf: the thermal conductivity for air at film temperature(W/m.k), hx: Local convection heat transfer(W/m2.k),  Gravitational acceleration(m/s2), I: Electric current (Amp), Nu: Nusselt number, Pr: Prandtl number

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

Numerical Study of Convective Heat Transfer From Expanding Annular Pipe Flows

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Diameter Ratio ◽  
Wall Heat Transfer ◽  
Reattachment Point ◽  
Transfer Rates ◽  
Pipe Flows ◽  
Annular Pipe

Convective heat transfer from suddenly expanding annular pipe flows are numerically investigated within the steady laminar flow regime. A parametric study is performed to reveal the influence of the annular diameter ratio, k, the Prandtl number, Pr, and the Reynolds number, Re, over the following range of parameters: k = {0, 0.5, 0.7}, Pr = {0.7, 1, 7, 100}, and Re = {25, 50, 100}. Heat transfer enhancement downstream of the expansion plane is only observed for Pr > 1. Peak wall-heat-transfer-rates always appear downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e. k = 0. However, for suddenly expanding annular pipe flows, i.e., k = 0.5 and 0.7, peak wall-heat-transfer-rates always appear upstream of the flow reattachment point. The observed heat transfer augmentation is more dramatic for suddenly expanding annular flows, in comparison with the one observed for suddenly expanding pipe flows. For a given annular diameter ratio and Reynolds number, increasing the Prandtl number, always results in higher wall-heat-transfer-rates downstream the expansion plane.

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