Evaluation of Nusselt Number for a Flow in a Parallel Plates Using MHD Second Order Slip Model

2021 ◽  
Author(s):  
Hatice Simsek
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Slip Flow ◽  
Mhd Flow ◽  
Second Order ◽  
Parallel Plates ◽  
First Order ◽  
Condition Model ◽  
Boundary Condition Model

Abstract In this study, two separate boundary condition models, as proposed by Beskok and Karniadakis [1] and Deissler [2], widely preferred for the second order boundary condition, were used. These two proposed boundary condition models were solved in the presence of a magnetic field moving normal to the plate surface in magneto-hydrodynamic (MHD) flow between micro-parallel plates with constant wall heat flux. The energy equation for the second-order temperature jump boundary condition, taking into account the momentum and viscous dissipation, as well as the corresponding Nusselt value were solved analytically in slip flow regime.The flow of an incompressible viscous flow between fixed micro-parallel plates with electrical conductivity is assumed to be constant, laminar, hydrodynamically and thermally developed. The closed form solutions for the temperature field and the fully developed Nusselt number are derived as a function of the Magnetic parameter (MHD), Knudsen number and Brinkman number and shown graphically and in a tabular form. The second order boundary condition model proposed by Deissler [2] predicts the Nusselt number to be at lower values when compared to the first order boundary condition model, and the second order boundary condition model proposed by Beskok and Karniadakis [1] predicts the Nusselt number to be at higher values than that of the first order boundary condition model. Moreover, increasing the magnetic field parameter M, led to higher Nusselt values in the slip flow model proposed by both Deissler [2] and Beskok and Karniadakis [1] compared to that when M = 0.

Isothermal Microtube Heat Transfer With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Susan Thomas ◽  
Tim Ameel
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Order Model ◽  
First Order ◽  
Second Order Model

Two analytical models are presented in which the continuum momentum and energy equations, coupled with second-order slip flow and temperature jump boundary conditions, are solved. An isothermal boundary condition is applied to a microchannel with a circular cross section. The flow is assumed to be hydrodynamically fully developed and thermal field is either fully developed or thermally developing from the tube entrance. A traditional first-order slip boundary condition is found to over predict the slip velocity compared to the second-order model. Heat transfer increases at the upper limit of the slip regime for the second-order model. The maximum second-order correction to the first-order Nusselt number is on the order of 18% for air. The second-order effect is also more significant in the entrance region of the tube. The Nusselt number decreases relative to the no-slip value when slip and temperature jump effects are of the same order or when temperature jump effects dominate. When temperature jump effects are small, the Nusselt number increases relative to the no-slip value. Comparisons to a previously reported model for an isoflux boundary condition indicate that the Nusselt number for the isoflux boundary condition exceeds that for the isothermal case at all axial locations.

Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Tim Ameel
Keyword(s):  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Order Approximation ◽  
Slip Flow ◽  
Order Effect ◽  
Second Order ◽  
First Order ◽  
Slip Regime ◽  
Energy Equations

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, first-order boundary conditions are found to over predict the effects of slip and temperature jump, while the effect of the second-order terms is most significant at the upper limit of the slip regime. The second-order terms are found to provide a correction to the first-order approximation. For airflows, the maximum second-order correction to the Nusselt number is on the order of 50%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.

scholarly journals Reversibility of the Magnetocaloric Effect in the Bean-Rodbell Model

2021 ◽  
Vol 7 (5) ◽  
pp. 60
Author(s):  
Luis M. Moreno-Ramírez ◽  
Victorino Franco
Keyword(s):  
Magnetic Field ◽  
Thermal Hysteresis ◽  
Entropy Change ◽  
Second Order ◽  
Zero Field ◽  
First Order ◽  
Magnetic Field Change ◽  
Magnetocaloric Materials ◽  
Moderate Magnetic Field ◽  
The Magnetic Field

The applicability of magnetocaloric materials is limited by irreversibility. In this work, we evaluate the reversible magnetocaloric response associated with magnetoelastic transitions in the framework of the Bean-Rodbell model. This model allows the description of both second- and first-order magnetoelastic transitions by the modification of the η parameter (η<1 for second-order and η>1 for first-order ones). The response is quantified via the Temperature-averaged Entropy Change (TEC), which has been shown to be an easy and effective figure of merit for magnetocaloric materials. A strong magnetic field dependence of TEC is found for first-order transitions, having a significant increase when the magnetic field is large enough to overcome the thermal hysteresis of the material observed at zero field. This field value, as well as the magnetic field evolution of the transition temperature, strongly depend on the atomic magnetic moment of the material. For a moderate magnetic field change of 2 T, first-order transitions with η≈1.3−1.8 have better TEC than those corresponding to stronger first-order transitions and even second-order ones.

scholarly journals Natural convection of Bingham fluids in rectangular cross-sectional cylindrical annuli with differentially heated vertical walls

2019 ◽  
Vol 29 (1) ◽  
pp. 43-77 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Natural Convection ◽  
Yield Stress ◽  
Thermal Transport ◽  
Second Order ◽  
Bingham Fluids ◽  
Cross Sectional ◽  
Content Type ◽  
The Mean

PurposeThis paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (ri/L1/8 to 16, whereLis the difference between outer and inner radii); aspect ratio (AR=H/Lfrom 1/8 to 8 whereHis the enclosure height); and nominal Rayleigh number (Rafrom 103to 106) for a single representative value of Prandtl number (Pris 500).Design/methodology/approachThe Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.FindingsIt is found that the mean Nusselt number based on the inner peripheryNu¯iincreases (decreases) with an increase inRa(Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasingri/Lfor both Newtonian (i.e.Bn= 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt numberNu¯inormalised by the corresponding Nusselt number due to pure conductive transport (i.e.Nu¯i/(Nu¯i)cond) shows a non-monotonic trend with increasingARin the CWT configuration for a given set of values ofRa,Pr,Lifor both Newtonian (i.e.Bn= 0) and Bingham fluids, whereasNu¯i/(Nu¯i)condincreases monotonically with increasingARin the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasingAR, and these competing effects are responsible for the non-monotonicNu¯i/(Nu¯i)condvariation withARin the CWT configuration.Originality/valueDetailed scaling analysis is utilised to explain the observed influences ofRa,BN,ri/LandAR, which along with the simulation data has been used to propose correlations forNu¯i.

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