Unsteady Stagnation Point Heat Transfer with Blowing or Suction

1981 ◽  
Vol 103 (3) ◽  
pp. 448-452 ◽  
Author(s):  
Takao Sano
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Prandtl Number ◽  
Asymptotic Solution ◽  
Stagnation Point ◽  
Wall Temperature ◽  
Step Change ◽  
Surface Heat ◽  
Unsteady Heat Transfer ◽  
Prandtl Numbers

The effects of blowing and suction on unsteady heat transfer at a stagnation point due to a step change in wall temperature are examined. Two asymptotic solutions for the temperature field at large and small Prandtl numbers are presented. It is shown that the asymptotic solution for large Prandtl number gives sufficiently accurate results for the surface heat transfer even for the moderate values of Prandtl number if Euler transformation is applied to the series.

Condensation of a Quiescent Vapor by a Stagnation-Point Liquid Flow

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
R. Balasubramaniam ◽  
E. Ramé
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Asymptotic Solution ◽  
Stagnation Point ◽  
Excellent Agreement ◽  
Liquid Flow ◽  
Vapor Flow ◽  
Liquid Temperature ◽  
Subcooled Liquid ◽  
Noncondensable Gas

We analyze the condensation of a quiescent vapor, that is in equilibrium with its liquid, induced by a stagnation point flow in the liquid. The liquid flow brings subcooled liquid from far away to the interface. The ensuing heat transfer causes the vapor to condense. A similarity formulation for the liquid and vapor flow fields and the liquid temperature field is pursued, and a perturbation solution is performed when the ratio of the product of viscosity and density of the vapor to that of the liquid is small. A two-term higher order asymptotic solution is shown to be in excellent agreement with numerical results. The reduction in the rate of condensation due to the presence of a noncondensable gas in the vapor that is insoluble in the liquid is also analyzed.

Slip effects on steady and transient stagnation-point heat transfer in axisymmetric geometries

2014 ◽  
Vol 228 (15) ◽  
pp. 2765-2777
Author(s):  
Khalid M Ramadan
Keyword(s):  
Heat Transfer ◽  
Growth Rate ◽  
Heat Transfer Coefficient ◽  
Prandtl Number ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Stagnation Point ◽  
Wall Temperature ◽  
Convective Heat Transfer Coefficient ◽  
Slip Effects

Steady and transient heat convection in axisymmetric stagnation point flow with momentum and thermal slip effects are studied numerically for different flow parameters. The thermal response to time-dependent wall temperature variations in surface cooling and heating processes is analyzed in terms of temporal variations in the heat transfer coefficient, thermal jump, and fluid temperature at the surface. The transition time from an initial to a final steady state is also investigated over a range of slip factor and decay/growth rate of the wall temperature. A criterion in the form of a relation between Prandtl number and the specific heat ratio that characterizes the variation of the convective heat transfer coefficient with the slip factor is established. The results presented show that the convective heat transfer coefficient is less influenced by transient conditions as rarefaction increases. Higher Prandtl number flows are more influenced by transients. The transition time is found to increase with slip and decrease with the decay/growth rate of the wall temperature and is most influenced at relatively low values of both slip and decay/growth rate of the wall temperature.

Local Nonsimilarity Solution of Free Convection Flow and Heat Transfer from an Inclined Isothermal Plate

1979 ◽  
Vol 101 (4) ◽  
pp. 642-647 ◽  
Author(s):  
M. M. Hasan ◽  
R. Eichhorn
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Free Convection ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Convection Flow ◽  
Appreciable Effect ◽  
Free Convection Flow ◽  
Flow And Heat Transfer ◽  
Prandtl Numbers

The effect of the angle of inclination on free convection flow and heat transfer from an isothermal surface is analyzed by the local nonsimilarity method of solution. An inclination parameter ξ as obtained from the analysis is tan γ/4 (Grx/4)1/4, where γ is the angle of inclination measured from the vertical and Grx is the local Grashof number, based on the component of the gravity vector along the surface. Numerical solutions of the equations are obtained for Prandtl numbers of 0.1, 0.7, 6 and 275. Results show an appreciable effect of ξ on the velocity field, and practically none on the temperature field, except for very large angles of inclination from the vertical or for very small values of the Prandtl number. In the limiting case of very large Prandtl number, ξ has no effect either on the velocity or the temperature field.

Analytical Study of the Convection Heat Transfer From an Isothermal Wedge Surface to Fluids

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Bachiri ◽  
A. Bouabdallah
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Ad Hoc ◽  
Convection Heat Transfer ◽  
Analytical Approximation ◽  
Numerical Results ◽  
Convection Heat ◽  
Governing Equations ◽  
Wedge Surface ◽  
Prandtl Numbers

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

Boiling Heat Transfer Characteristics of Rotary Hollow Cylinders with In-Line and Staggered Multiple Arrays of Water Jets

2021 ◽  
Author(s):  
Mohammad Jahedi ◽  
Bahram Moshfegh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Stagnation Point ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Maximum Heat ◽  
Water Jets ◽  
Maximum Heat Flux ◽  
Inner Surface ◽  
Hollow Cylinders

Abstract Transient heat transfer studies of quenching rotary hollow cylinders with in-line and staggered multiple arrays of jets have been carried out experimentally. The study involves three hollow cylinders (Do/d = 12 to 24) with rotation speed 10 to 50 rpm, quenched by subcooled water jets (ΔTsub=50-80 K) with jet flow rate 2.7 to 10.9 L/min. The increase in area-averaged and maximum heat flux over quenching surface (Af) has been observed in the studied multiple arrays with constant Qtotal compared to previous studies. Investigation of radial temperature distribution at stagnation point of jet reveals that the footprint of configuration of 4-row array is highlighted in radial distances near the outer surface and vanishes further down toward the inner surface. The influence of the main quenching parameters on local average surface heat flux at stagnation point is addressed in all the boiling regimes where the result indicates jet flow rate provides strongest effect in all the boiling regimes. Effectiveness of magnitude of maximum heat flux in the boiling curve for the studied parameters is reported. The result of spatial and temporal heat flux by radial conduction in the solid presents projection depth of cyclic variation of surface heat flux in the radial axis as it disappears near inner surface of hollow cylinder. In addition, correlations are proposed for area-averaged Nusselt number as well as average and maximum local heat flux at stagnation point of jet for the in-line and staggered multiple arrays.

A Study Regarding the Unsteady Heat Transfer and Phase Change

2014 ◽  
Vol 659 ◽  
pp. 353-358
Author(s):  
Gelu Coman ◽  
Cristian Iosifescu ◽  
Valeriu Damian
Keyword(s):  
Heat Transfer ◽  
Numerical Modeling ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Finite Elements ◽  
Experimental Research ◽  
Theoretical Study ◽  
Ice Formation ◽  
Unsteady Heat Transfer ◽  
Cooling Pipes

The paper presents the experimental and theoretical study for temperature distribution around the cooling pipes of an ice rink pad. The heat transfer in the skating rink track is nonstationary and phase changing. In case of skating rinks equipped with pipe registers, the temperature field during the ice formation process can’t be modeled by analytical methods. The experimental research was targeted on finding the temperatures in several points of the pad and also details on ice shape and quality around the pipes. The temperatures measured on the skating ring surface using thermocouples is impossible due to the larger diameter of the thermocouple bulb compared with the air-water surfaces thickness. For this reason we used to measure the temperature by thermography method, thus reducing the errors The experimental results were compared against the numerical modeling using finite elements.

scholarly journals MODELING HEAT EXCHANGE DEPENDING ON THE PRANDTL NUMBER FOR VARIOUS GEOMETRIC AND REGIME PARAMETERS

2020 ◽  
Vol 46 (4) ◽  
pp. 91-101
Author(s):  
I. E. Lobanov
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Prandtl Number ◽  
Energy Equation ◽  
Transport Model ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Shear Stress Transport Model ◽  
Small Reynolds Numbers ◽  
Prandtl Numbers

Objectives. The aim is to study the dependency of the distribution of integral heat transfer during turbulent convective heat transfer in a pipe with a sequence of periodic protrusions of semicircular geometry on the Prandtl number using the calculation method based on a numerical solution of the system of Reynolds equations closed using the Menter’s shear stress transport model and the energy equation on different-sized intersecting structured grids.Method. A calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations by factored finite-volume method closed with the help of the Menter shear stress transport model, as well as the energy equation on different-scaled intersecting structured grids (fast composite mesh method (FCOM)).Results. The calculations performed in the work showed that with an increase in the Prandtl number at small Reynolds numbers, there is an initial noticeable increase in the relative heat transfer. With additional increase in the Prandtl number, the relative heat transfer changes less: for small steps, it increases; for median steps it is almost stabilised, while for large steps it declines insignificantly. At large Reynolds numbers, the relative heat transfer decreases with an increase in the Prandtl number followed by its further stabilisation.Conclusion. The study analyses the calculated dependencies of the relative heat transfer on the Pr Prandtl number for various values of the relative h/D height of the turbulator, the relative t/D pitch between the turbulators and for various values of the Re Reynolds number. Qualitative and quantitative changes in calculated parameters are described all other things being equal. The analytical substantiation of the obtained calculation laws is that the height of the turbuliser is less for small Reynolds numbers, while for large Reynolds numbers, it is less than the height of the wall layer. Consequently, only the core of the flow is turbulised, which results in an increase in hydroresistance and a decrease in heat transfer. In the work on the basis of limited calculation material, a tangible decrease in the level of heat transfer intensification for small Prandtl numbers is theoretically confirmed. The obtained results of intensified heat transfer in the region of low Prandtl numbers substantiate the promising development of research in this direction. The theoretical data obtained in the work have determined the laws of relative heat transfer across a wide range of Prandtl numbers, including in those areas where experimental material does not currently exist. 

Effect of Uneven Wall Temperature on Local Heat Transfer in a Rotating Square Channel With Smooth Walls and Radial Outward Flow

1992 ◽  
Vol 114 (4) ◽  
pp. 850-858 ◽  
Author(s):  
J.-C. Han ◽  
Y. M. Zhang
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Surface Heat ◽  
Transfer Coefficients ◽  
Surface Heat Transfer ◽  
Square Channel ◽  
Heat Transfer Coefficients ◽  
Rotation Numbers

The influence of uneven wall temperature on the local heat transfer coefficient in a rotating square channel with smooth walls and radial outward flow was investigated for Reynolds numbers from 2500 to 25,000 and rotation numbers from 0 to 0.352. The square channel, composed of six isolated copper sections, has a length-to-hydraulic diameter ratio of 12. The mean rotating radius to the channel hydraulic diameter ratio is kept at a constant value of 30. Three cases of thermal boundary conditions were studied: (A) four walls uniform temperature, (B) four walls uniform heat flux, and (C) leading and trailing walls hot and two side walls cold. The results show that the heat transfer coefficients on the leading surface are much lower than that of the trailing surface due to rotation. For case A of four walls uniform temperature, the leading surface heat transfer coefficient decreases and then increases with increasing rotation numbers, and the trailing surface heat transfer coefficient increases monotonically with rotation numbers. The decreased (or increased) heat transfer coefficients on the leading (or trailing) surface are due to the cross-stream and centrifugal buoyancy-induced flows from rotations. However, the trailing surface heat transfer coefficients, as well as those for the side walls, for case B are higher than for case A and the leading surface heat transfer coefficients for cases B and C are significantly higher than for case A. The results suggest that the local uneven wall temperature creates the local buoyancy forces, which change the effect of the rotation. Therefore, the local heat transfer coefficients on the leading, trailing, and side surfaces are altered by the uneven wall temperature.

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