Closure to “Discussions of ‘Thermal Conductivity and Prandtl Number of Carbon Dioxide and Carbon-Dioxide Air Mixtures at One Atmosphere’” (1961, ASME J. Heat Transfer, 83, pp. 131–132)

1961 ◽  
Vol 83 (2) ◽  
pp. 132-132
Author(s):  
Jerome L. Novotny ◽  
Thomas F. Irvine
Keyword(s):  
Heat Transfer ◽  
Carbon Dioxide ◽  
Thermal Conductivity ◽  
Prandtl Number

Thermal Conductivity and Prandtl Number of Carbon Dioxide and Carbon-Dioxide Air Mixtures at One Atmosphere

1961 ◽  
Vol 83 (2) ◽  
pp. 125-131 ◽  
Author(s):  
Jerome L. Novotny ◽  
Thomas F. Irvine
Keyword(s):  
Carbon Dioxide ◽  
Thermal Conductivity ◽  
Prandtl Number ◽  
Maximum Error ◽  
Intermolecular Force ◽  
Temperature Range ◽  
Average Temperature ◽  
Pure Carbon ◽  
Prandtl Numbers ◽  
Pure Carbon Dioxide

By measuring laminar recovery factors in a high velocity gas stream, experimental determinations were made of the Prandtl number of carbon dioxide over a temperature range from 285 to 450 K and of carbon-dioxide air mixtures at an average temperature of 285 K with a predicted maximum error of 1.5 per cent. Thermal conductivity values were deduced from these Prandtl numbers and compared with literature values measured by other methods. Using intermolecular force constants determined from literature experimental data, viscosities, thermal conductivities, and Prandtl numbers were calculated for carbon-dioxide air mixtures over the temperature range 200 to 1500 deg for mixture ratios from pure air to pure carbon dioxide.

Natural Convective Heat Transfer Through a Liquid Between a Heated Horizontal Surface and a Vertical Fin Attached to a Cooled Surface

1999 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Lower Surface ◽  
Horizontal Surface ◽  
Finite Element Procedure ◽  
Liquid Depth ◽  
Rayleigh Numbers

Abstract Natural convective heat transfer from a heated horizontal surface directly exposed to a liquid into which vertical fins, attached to a cooled horizontal surface, project vertically downwards has been numerically studied. It has been assumed that the flow is steady, laminar and two-dimensional. The governing equations have been written in terms of dimensionless variables and have been solved using the finite element procedure. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless half-width i.e. the ratio of the half-distance between the fins to the liquid depth, the dimensionless gap between the bottom of the fin and the lower surface, and the ratio of the thermal conductivity of the fin material to that of the liquid. Because of the application being considered, the Prandtl number has been taken as 5. Solutions have been obtained for Rayleigh numbers of between 10 and 1,000,000 for dimensionless half-widths of between 1 and 0.2 for thermal conductivity ratios of 20, 10 and 4 for a range of dimensionless fin gaps and widths.

Effects of Radiation and Variable Thermal Conductivity on the MHD Flow of a Viscoelastic Fluid and Heat Transfer Over a Stretching Porous Sheet

2008 ◽  
Author(s):  
P. Anuradha ◽  
S. Krishnambal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Viscoelastic Fluid ◽  
Variable Thermal Conductivity ◽  
Integration Scheme ◽  
Viscoelastic Parameter ◽  
Porous Sheet ◽  
Effects Of Radiation

A numerical study on the effects of radiation and variable thermal conductivity on the flow and heat transfer in the boundary layer of a viscoelastic fluid (Walters’ liquid B’ model) over a stretching porous sheet in the presence of a magnetic field is studied. The momentum differential equation is solved exactly. Two cases of sheet surface conditions are considered — (i) PST case involving prescribed surface temperature and (ii) PHF case involving prescribed heat flux at the surface. The energy equation is solved with the application of the shooting technique using the fourth order Runge-Kutta integration scheme. Numerical results are obtained for various values of non-dimensional parameters — which include among others, the Prandtl number (P), the Eckert number (E) and the Radiation number (N). The significant conclusions are: (1) the momentum boundary layer can be minimized by considering the sheet to be influenced by a continuous suction of the fluid through the porous boundary and by choosing large values for the viscoelastic parameter and the magnetic parameter (2) an ideal combination for faster cooling of the thermal boundary layer would be to consider the suction velocity of the fluid along with a large value for the Prandtl number combined with small values for Radiation and Eckert numbers.

scholarly journals Heat transfer for two types of viscoelastic fluid over an exponentially stretching sheet with variable thermal conductivity and radiation in porous medium

2014 ◽  
Vol 18 (4) ◽  
pp. 1079-1093 ◽  
Author(s):  
V. Singh ◽  
Shweta Agarwal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Wall Temperature ◽  
Stretching Sheet ◽  
Variable Thermal Conductivity ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

An Analysis has been carried out to study the boundary layer flow and heat transfer characteristics of second order fluid and second grade fluid with variable thermal conductivity and radiation over an exponentially stretching sheet in porous medium. The basic boundary layer equations governing the flow and heat transfer in prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformations. Numerical solutions of the resulting boundary value problem are solved by using the fourth order Runge-Kutta method with shooting technique for various values of the physical parameters. The effect of variable thermal conductivity, porosity, Prandtl number, radiation parameter and viscoelastic parameters on velocity and temperature profiles (in PST and PHF cases) are analyzed and discussed through graphs. Numerical values of wall temperature gradient in PST case and wall temperature in PHF case are obtained and tabulated for various values of the governing parameters. In this study Prandtl number also treated as variable inside the boundary layer because it depends on thermal conductivity. The results are also verified by using finite difference method.

scholarly journals Nonlinear Heat Transfer From Particles in Supercritical Carbon Dioxide Near the Critical Point

2019 ◽  
Vol 12 (3) ◽  
Author(s):  
Michael James Martin ◽  
Elizabeth G. Rasmussen ◽  
Shashank Yellapantula
Keyword(s):  
Heat Transfer ◽  
Carbon Dioxide ◽  
Thermal Conductivity ◽  
Supercritical Carbon Dioxide ◽  
Critical Point ◽  
Materials Synthesis ◽  
Energy Technologies ◽  
Property Changes ◽  
The Impact ◽  
Supercritical Carbon

Abstract Particle to fluid heat transfer in supercritical carbon dioxide (sCO2) is encountered in energy technologies and in materials synthesis. Near the critical point, the extreme pressure and temperature sensitivity of sCO2’s thermal conductivity will change the expected heat transfer in these systems. The current work combines the Kirchoff transformation for thermal conductivity with the conduction shape factor for a sphere, allowing prediction of heat transfer in these systems and quantification of the impact of these property changes. Results show that the heat transfer is non-linear for supercritical heat transfer, with the non-linearity particularly significant near the critical point. The results also show that approaches such as an average thermal conductivity based on film temperature are unlikely to accurately predict heat transfer in this region. The methods described in this paper can be applied to fluid–particle heat transfer at low Reynolds number in other fluids with large variations in thermal conductivity.

Instantaneous Heat Flux Simulation of a Motored Reciprocating Engine: Unsteady Thermal Boundary Layer With Variable Turbulent Thermal Conductivity

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Abdalla Agrira ◽  
David R. Buttsworth ◽  
Mior A. Said
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Thermal Boundary Layer ◽  
Combustion Engine ◽  
Turbulent Viscosity ◽  
Spark Ignition Engine ◽  
Turbulent Prandtl Number

Due to the inherently unsteady environment of reciprocating engines, unsteady thermal boundary layer modeling may improve the reliability of simulations of internal combustion engine heat transfer. Simulation of the unsteady thermal boundary layer was achieved in the present work based on an effective variable thermal conductivity from different turbulent Prandtl number and turbulent viscosity models. Experiments were also performed on a motored, single-cylinder spark-ignition engine. The unsteady energy equation approach furnishes a significant improvement in the simulation of the heat flux data relative to results from a representative instantaneous heat transfer correlation. The heat flux simulated using the unsteady model with one particular turbulent Prandtl number model agreed with measured heat flux in the wide open and fully closed throttle cases, with an error in peak values of about 6% and 35%, respectively.

Effect of Turbulent Prandtl Number on Convective Heat Transfer to Turbulent Upflow of Supercritical Carbon Dioxide

2009 ◽  
Author(s):  
Majid Bazargan ◽  
Mahdi Mohseni
Keyword(s):  
Heat Transfer ◽  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Prandtl Number ◽  
Convection Heat Transfer ◽  
Turbulent Prandtl Number ◽  
Upward Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Supercritical Carbon

A two-dimensional model is developed to simultaneously solve the momentum and energy equations and thus predict convection heat transfer to an upward flow of supercritical carbon dioxide in a round tube. The effect of the turbulent Prandtl number, Prt, on heat transfer coefficients has been extensively studied. A number of constant values of Prt, as well as a number of suggested equations accounting for variations of Prt with flow conditions, have been examined. The investigation has been carried out for both regimes of enhanced and deteriorated heat transfer. The results of this study show that the increase of Prt, even in the viscous sublayer, cause the heat transfer coefficients to decrease. The models of Prt leading to best agreement with experiments in either regimes of heat transfer were recognized. From the effect Prt has on heat transfer coefficients, it has been deduced that the buoyancy effects in upward flow of a supercritical fluid causes the Prt to decrease and hence the heat transfer coefficients to increase.

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