scholarly journals Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes

2012 ◽  
Vol 02 (04) ◽  
pp. 111-119 ◽  
Author(s):  
J. Sheela-Francisca ◽  
C. P. Tso ◽  
Dirk Rilling
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Poiseuille Flow ◽  
Heat Fluxes

scholarly journals Numerical solutions of compressible convection with an infinite Prandtl number: comparison of the anelastic and anelastic liquid models with the exact equations

2019 ◽  
Vol 873 ◽  
pp. 646-687 ◽  
Author(s):  
Jezabel Curbelo ◽  
Lucia Duarte ◽  
Thierry Alboussière ◽  
Fabien Dubuffet ◽  
Stéphane Labrosse ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Ideal Gas ◽  
Heat Fluxes ◽  
Necessary Condition ◽  
Earth Planet ◽  
Viscous Forces ◽  
Wide Range

We developed a numerical method for the set of equations governing fully compressible convection in the limit of infinite Prandtl numbers. Reduced models have also been analysed, such as the anelastic approximation and the anelastic liquid approximation. The tests of our numerical schemes against self-consistent criteria have shown that our numerical simulations are consistent from the point of view of energy dissipation, heat transfer and entropy budget. The equation of state of an ideal gas has been considered in this work. Specific effects arising because of the compressibility of the fluid are studied, like the scaling of viscous dissipation and the scaling of the heat flux contribution due to the mechanical power exerted by viscous forces. We analysed the solutions obtained with each model (fully compressible model, anelastic and anelastic liquid approximations) in a wide range of dimensionless parameters and determined the errors induced by each approximation with respect to the fully compressible solutions. Based on a rationale on the development of the thermal boundary layers, we can explain reasonably well the differences between the fully compressible and anelastic models, in terms of both the heat transfer and viscous dissipation dependence on compressibility. This could be mostly an effect of density variations on thermal diffusivity. Based on the different forms of entropy balance between exact and anelastic models, we find that a necessary condition for convergence of the anelastic results to the exact solutions is that the product $\unicode[STIX]{x1D716}q$ must be small compared to unity, where $\unicode[STIX]{x1D716}$ is the ratio of the superadiabatic temperature difference to the adiabatic difference, and $q$ is the ratio of the superadiabatic heat flux to the heat flux conducted along the adiabat. The same condition seems also to be associated with a convergence of the computed heat fluxes. Concerning the anelastic liquid approximation, we confirm previous estimates by Anufriev et al. (Phys. Earth Planet. Inter., vol. 152, 2005, pp. 163–190) and find that its results become generally close to those of the fully compressible model when $\unicode[STIX]{x1D6FC}T{\mathcal{D}}$ is small compared to unity, where $\unicode[STIX]{x1D6FC}$ is the isobaric thermal expansion coefficient, $T$ is the temperature (here $\unicode[STIX]{x1D6FC}T=1$ for an ideal gas) and ${\mathcal{D}}$ is the dissipation number.

Forced Convection in Channels With Viscous Dissipation for the Simplified Phan-Thien–Tanner Fluid

1999 ◽  
Author(s):  
Fernando T. Pinho ◽  
Paulo J. Oliveira
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Coupling Effect ◽  
Threshold Value ◽  
Heat Fluxes ◽  
Effect Of Temperature ◽  
Brinkman Number ◽  
Heating And Cooling ◽  
Fluid Elasticity

Abstract The temperature distribution and the heat transfer coefficient for forced convection in laminar channel flow with viscous dissipation are derived for the simplified Phan-Thien–Tanner fluid with a linear stress coefficient. Fully-developed thermal and hydrodynamic conditions are assumed with a constant wall heat flux imposed on both walls. As a simplifying assumption the effect of temperature variations on the material parameters is neglected. The results show that, in all circumstances, ie for wall heating and cooling and regardless of the magnitude of viscous dissipation, an increase of fluid elasticity and/or an increase of ε results in enhanced heat transfer. As a beneficial consequence the range of temperatures inside the duct is reduced. There is also a coupling effect of viscous dissipation and fluid elasticity: heat transfer enhancement by fluid elasticity is stronger in the presence of a more intense viscous dissipation. For positive wall heat fluxes, ie wall cooling, whenever the Brinkman number exceeds a threshold value, the viscous dissipation overcomes the wall cooling effect and the fluid heats up longitudinally. Fluid elasticity delays this critical Brinkman number to higher values.

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

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