A Theoretical Analysis of Laminar Forced Flow and Heat Transfer About a Rotating Cone

1965 ◽  
Vol 87 (2) ◽  
pp. 184-190 ◽  
Author(s):  
C. L. Tien ◽  
I. J. Tsuji
Keyword(s):  
Heat Transfer ◽  
Cone Angle ◽  
Forced Flow ◽  
Zeroth Order ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Flow And Heat Transfer ◽  
Rotating Cone ◽  
Fast Rotating

The present paper presents analytically a method of attack on the problem of laminar forced flow and heat transfer about a rotating cone. The nonsimilar nature of the general problem requires that separate consideration be given to a slow rotating cone and a fast rotating cone, depending on the relative magnitude of the rotating speed with respect to the free-stream velocity. The Mangler transformation first reduces the problem of a slow rotating cone to one of wedge flow with a transverse velocity component. The problem is then solved by a perturbation scheme which uses the solution of wedge flow as the zeroth-order solution. The case of a fast rotating cone is solved by a series-expansion scheme which gives successive corrections to the zeroth-order solution, i.e. the solution of a rotating disk in a quiescent fluid. The zeroth-order and first-order equations for both cases are given in the present work, together with the numerical results for the special case of a cone of about 107-deg cone angle. The first-order results in both cases are shown for the drag and torque coefficients, and the local Nusselt number. Higher-order results can be obtained according to the present analysis. The effect of cone angle on the flow and heat-transfer characteristics is indicated by the comparison between the results of the 107-deg cone and those of the disk, i.e., the 180-deg cone.

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

1974 ◽  
Vol 25 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W H Hui ◽  
J Hamilton
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Power Series ◽  
Unsteady Flow ◽  
The Body ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

Numerical Simulation of Nonlinear Flow and Heat Transfer in a Sudden Expansion and Contraction Channel

2016 ◽  
Author(s):  
M. Yang ◽  
L. Q. Yang ◽  
W. Lu ◽  
L. Li ◽  
Q. X. Liu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Rectangular Channel ◽  
Flow Region ◽  
Nonlinear Flow ◽  
Forced Flow ◽  
Sudden Expansion ◽  
Symmetric State ◽  
Flow And Heat Transfer

Numerical simulation of forced flow in sudden-expansion followed by sudden-contraction rectangular channel was presented for the whole flow region. The nonlinear flow and heat transfer characteristics were investigated by various Reynolds number and geometrical dimension and the critical Reynolds numbers under different conditions have been calculated. The results show flow and heat transfer from symmetric state to asymmetric state with the increase of Re. When Re<Rec (critical Reynolds number for flow transformation), the symmetric state is stable. On the other hand, when Re ≥Rec, the flow loses stability and from symmetric to asymmetric via a symmetry-breaking bifurcation. And the heat transfer performance have relevant characteristics as fluid flow.

Numerical Investigation of Heat Transfer in Rough Microchannels Using a Kinetic Continuum Solver

2015 ◽  
Author(s):  
Olga Rovenskaya ◽  
Giulio Croce
Keyword(s):  
Heat Transfer ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Channel Height ◽  
First Order ◽  
Slip Boundary ◽  
Relative Roughness ◽  
Flow And Heat Transfer ◽  
Hybrid Solutions ◽  
Hybrid Solver

A numerical analysis of flow and heat transfer fields in a rough microchannel is carried out using a hybrid solver dynamically coupling kinetic and Navier–Stokes solutions computed in local rarefied and continuum areas of the flow, respectively. The roughness geometry is modeled as a series of triangular obstructions and a relative roughness up to 5% of the channel height is considered. Keeping Mach number low (incompressible flow) while varying Knudsen number allow us to investigate different rarefaction levels of the flow. The competition between roughness, rarefaction and heat transfer effects is discussed in terms of averaged Nusselt and Poiseuille numbers and mass flow rate. Discrepancy between the full Navier–Stokes and hybrid solutions is investigated, assessing the range of applicability of the first order slip boundary condition for rough geometries with and without heat transfer presence.

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