A review of studies on forced, natural and mixed heat transfer to fluid and nanofluid flow in an annular passage.

The enhancement of the thermal performance of heat exchanging equipment transport energy at low financial cost by various techniques is presented in this review. Various annular passage configurations have been used in the reviewed studies, namely circular, ellipse, rectangular, square, triangular, and rhombic annular channels with different fluid and boundary conditions. The effect of eccentricity in both horizontal and vertical directions on heat transfer rate in most numerical and experimental investigations for horizontal and vertical annular passages is studied. The effects of heater length, as well as the Darcy, Prandtl, Reynolds, Grashof and Rayleigh numbers on heat transfer in concentric and eccentric annular passages are also investigated. In case of rotating the inner, outer or both cylinders of the annular cylinder arrangement, the generated secondary flow influences the heat transfer to fluid flow in an annular passage. The effect of nanofluid on the increased enhancement of heat transfer in an annular channel is presented. Related studies on curved, covered annular channels showed augmented heat transfer rate in comparison with straight annular channels. In this review, a good agreement is evident between experimental and numerical data, which could help researchers design thermal systems supported by annular passages with the goal of retarding energy consumption by equipment and machineries in applications that could ultimately contribute to appeasing the global energy crisis.

[1]  Michael L. Trombetta Laminar forced convection in eccentric annuli , 1971 .

[2]  B. K. Reddy,et al.  Heat generation effects in natural convection inside a porous annulus , 2010 .

[3]  Turbulent flow in channels in terms of turbulent shear and normal stresses , 1995 .

[4]  Fujio Tachibana,et al.  Convective Heat Transfer of the Rotational and Axial Flow between Two Concentric Cylinders , 1963 .

[5]  W. T. Snyder,et al.  An analysis of fully developed laminar flow in an eccentric annulus , 1965 .

[6]  G. Narasimham,et al.  Natural convection in a vertical annulus driven by a central heat generating rod , 2008 .

[7]  J. Cannon,et al.  Constant heat flux solutions for natural convection between concentric and eccentric horizontal cylinders , 1986 .

[8]  Juan M. Lopez,et al.  Numerical study of natural convection in a vertical porous annulus with discrete heating , 2011 .

[9]  Roydon Andrew Fraser,et al.  Second law analysis of heat transfer and fluid flow inside a cylindrical annular space , 2002 .

[10]  A. Sarhan,et al.  Free Convection Effects on the Developing Laminar Flow in Vertical Concentric Annuli , 1980 .

[11]  E. Mokheimer,et al.  Correlations for maximum possible induced flow rates and heat transfer parameters in open-ended vertical eccentric annuli , 2007 .

[12]  M. Gareche,et al.  Numerical study of a thermodependent non-Newtonian fluid flow between vertical concentric cylinders , 2007 .

[13]  C Shu,et al.  Numerical simulation of natural convection in a concentric annulus between a square outer cylinder and a circular inner cylinder using the Taylor-series-expansion and least-squares-based lattice Boltzmann method. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  S. Nada Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers , 2008 .

[15]  J. Szmyd,et al.  Laminar forced convection heat transfer in eccentric annuli , 1990 .

[16]  W. Kays,et al.  HEAT TRANSFER WITH LAMINAR FLOW IN CONCENTRIC ANNULI WITH CONSTANT AND VARIABLE WALL TEMPERATURE AND HEAT FLUX , 1963 .

[17]  Gildas Lalizel,et al.  Convective heat transfer in the entry region of an annular channel with slotted rotating inner cylinder , 2013 .

[18]  A. Hussein,et al.  Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations , 2011 .

[19]  J. Caltagirone Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders , 1976, Journal of Fluid Mechanics.

[20]  Young Don Choi,et al.  Analysis of periodically fully developed turbulent flow and heat transfer by k-ε equation model in artificially roughened annulus , 1988 .

[21]  Mohd Nashrul Mohd Zubir,et al.  Numerical simulation of heat transfer to separation air flow in an annular pipe , 2012 .

[22]  C. L. Tien,et al.  Natural convection in porous media bounded by concentric spheres and horizontal cylinders , 1979 .

[23]  M. Venkatachalappa,et al.  Numerical Study of Natural Convection in a Vertical Cylindrical Annulus Using a Non-Darcy Equation , 2002 .

[24]  Geoffrey Ingram Taylor,et al.  Distribution of velocity and temperature between concentric rotating cylinders , 1935 .

[25]  C. Yeh Numerical investigation of the three-dimensional natural convection inside horizontal concentric annulus with specified wall temperature or heat flux , 2002 .

[26]  P. M. Worsøe-Schmidt Heat transfer in the thermal entrance region of circular tubes and annular passages with fully developed laminar flow , 1967 .

[27]  C. Desaubry,et al.  Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder , 1998 .

[28]  M. Daguenet,et al.  Natural Steady Convection in a Space Annulus Between Two Elliptic Confocal Ducts: Influence of the Slope Angle , 2006 .

[29]  Ching-Jenq Ho,et al.  Transition to oscillatory natural convection of cold water in a vertical annulus , 1998 .

[30]  Abdalla M. Al-Amiri,et al.  Numerical simulation of double-diffusive mixed convection within a rotating horizontal annulus , 2006 .

[31]  I. Shahrour,et al.  Experimental Study for Double Pipe Heat Exchanger with Rotating Inner Pipe , 2012 .

[32]  Fujio Tachibana,et al.  Heat Transfer in an Annulus with an Inner Rotating Cylinder , 1959 .

[33]  C. Shu,et al.  Numerical simulation of natural convection between two elliptical cylinders using DQ method , 2004 .

[34]  James F. Klausner,et al.  A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow , 1997 .

[35]  T. Adachi,et al.  Three-dimensional linear stability of natural convection in horizontal concentric annuli , 2007 .

[36]  H. Barrow Fluid Flow and Heat Transfer in an Annulus with a Heated Core Tube , 1955 .

[37]  H Asan Natural convection in an annulus between two isothermal concentric square ducts , 2000 .

[38]  H. Kim,et al.  Convective heat transfer to CO2 at a supercritical pressure flowing vertically upward in tubes and an annular channel , 2009 .

[39]  M. T. Mehrabani,et al.  A numerical study of fluid flow and heat transfer in eccentric curved annuli , 2010 .

[40]  M. Sankar,et al.  Natural convection in an annulus between two rotating vertical cylinders , 2001 .

[41]  K. Karki,et al.  Laminar mixed convection in a horizontal eccentric annulus , 1992 .

[42]  M. Farhadi,et al.  Lattice Boltzmann simulation of mixed convection heat transfer in eccentric annulus , 2011 .

[43]  Fernando T. Pinho,et al.  Effects of inner cylinder rotation on laminar flow of a Newtonian fluid through an eccentric annulus , 2000 .

[44]  Jin Ho Song,et al.  EXPERIMENTAL INVESTIGATIONS ON HEAT TRANSFER TO CO2FLOWING UPWARD IN A NARROW ANNULUS AT SUPERCRITICAL PRESSURES , 2008 .

[45]  M. Farhadi,et al.  Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method , 2013 .

[46]  C. S. Yang,et al.  Flow and Heat Transfer of Natural Convection in Horizontal Annulus With a Heating Element on Inner Cylinder , 2009 .

[47]  C. Prakash,et al.  Effect of buoyancy on laminar fully developed flow in a vertical annular passage with radial internal fins , 1985 .

[48]  Yoon Y. Bae,et al.  Mixed convection heat transfer to carbon dioxide flowing upward and downward in a vertical tube and an annular channel , 2011 .

[49]  E. Mokheimer,et al.  Developing Free Convection in Open-Ended Vertical Eccentric Annuli With Isothermal Boundaries , 1999 .

[50]  Maximum density effects on natural convection in a vertical annulus filled with a non-Darcy porous medium , 1998 .

[51]  E. Alawadhi Natural convection flow in a horizontal annulus with an oscillating inner cylinder using Lagrangian–Eulerian kinematics , 2008 .

[52]  F. Moukalled,et al.  Laminar Natural Convection in a Horizontal Rhombic Annulus , 1993 .

[53]  John-Chang Chen,et al.  Entrance region and variable heat flux effects in turbulent heat transfer to liquid metals flowing in concentric annuli , 1970 .

[54]  Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio , 2009 .

[55]  W. T. Snyder An analysis of slug flow heat transfer in an eccentric annulus , 1963 .

[56]  H. Beer,et al.  Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli , 1985 .

[57]  M. El-Shaarawi,et al.  Developing laminar free convection in a heated vertical open-ended concentric annulus , 1981 .

[58]  Kenneth J. Witt,et al.  numerical investigation of free convection between two vertical coaxial cylinders , 1970 .

[59]  D. Ingham,et al.  Developing combined convection of non-Newtonian fluids in an eccentric annulus , 1997 .

[60]  E. Sparrow,et al.  Results of laminar flow analysis and turbulent flow experiments for eccentric annular ducts , 1965 .

[61]  Pao-Tung Hsu,et al.  The inverse estimation of the thermal behavior and the viscosity of fluid between two horizontal concentric cylinders with rotating inner cylinder , 2008 .

[62]  M. Charrier-Mojtabi Numerical simulation of two- and threedimensional free convection flows in a horizontal porous annulus using a pressure and temperature formulation , 1997 .

[63]  Chang Shu,et al.  AN EFFICIENT APPROACH TO SIMULATE NATURAL CONVECTION IN ARBITRARILY ECCENTRIC ANNULI BY VORTICITY-STREAM FUNCTION FORMULATION , 2000 .

[64]  N. Sheriff,et al.  Heat-transfer and friction properties of surfaces with discrete roughnesses , 1966 .

[65]  R. M. Manglik,et al.  Effect of eccentricity and thermal boundary conditions on laminar fully developed flow in annular ducts , 1995 .

[66]  J. Quaresma,et al.  INTEGRAL TRANSFORM METHOD FOR LAMINAR HEAT TRANSFER CONVECTION OF HERSCHEL-BULKLEY FLUIDS WITHIN CONCENTRIC ANNULAR DUCTS , 2001 .

[67]  Joo-Sik Yoo Mixed convection of air between two horizontal concentric cylinders with a cooled rotating outer cylinder , 1998 .

[68]  D. Reda Natural convection experiments in a liquid-saturated porous medium bounded by vertical coaxial cylinders , 1983 .

[69]  Richard J Goldstein,et al.  A Parametric Study of Prandtl Number and Diameter Ratio Effects on Natural Convection Heat Transfer in Horizontal Cylindrical Annuli , 1980 .

[70]  R. E. Powe,et al.  Free Convective Flow Patterns in Cylindrical Annuli , 1969 .

[71]  Keun-Shik Chang,et al.  Patterns of Natural Convection Around a Square Cylinder Placed Concentrically in a Horizontal Circular Cylinder , 1983 .

[72]  Mohd Khairol Anuar Mohd Ariffin,et al.  Heat Transfer and Turbulent Fluid Flow over Vertical Double Forward-Facing Step , 2014 .

[73]  Zhaoli Guo,et al.  Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus , 2006 .

[74]  F. Badr Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations , 2009 .

[75]  M. Nili-Ahmadabadi,et al.  HEAT TRANSFER AND FLOW REGION CHARACTERISTICS STUDY IN A NON-ANNULAR CHANNEL BETWEEN ROTOR AND STATOR , 2012 .

[76]  Mina Shahi,et al.  A numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder , 2011 .

[77]  Hiroyasu Ohtake,et al.  Critical Heat Flux of Counter-Current Two-Phase Flow in Vertical-Narrow-Annular Flow Passages , 2002 .

[78]  K. Hirose,et al.  Natural convection heat transfer in eccentric horizontal annuli between a heated outer tube and a cooled inner tube with different orientation: The case of an elliptical outer tube , 2001 .

[79]  C. Wang Forced Convection in a Polygonal Duct With a Circular Core , 2011 .

[80]  F. Moukalled,et al.  Natural convection in the annulus between concentric horizontal circular and square cylinders , 1996 .

[81]  K. N. Astill Studies of the Developing Flow Between Concentric Cylinders With the Inner Cylinder Rotating , 1964 .

[82]  I. Pop,et al.  Buoyant Flow with Viscous Heating in a Vertical Circular Duct Filled with a Porous Medium , 2008 .

[83]  O. Takahashi,et al.  Mercury-argon two-phase heat transfer in a vertical annulus under transverse magnetic field , 1982 .

[84]  A. E. Bergles,et al.  THE INFLUENCE OF ULTRASONIC VIBRATIONS ON HEAT TRANSFER TO WATER FLOWING IN ANNULI , 1965 .

[85]  N. E. Todreas,et al.  Mixed convection friction factors and Nusselt numbers in vertical annular and subchannel geometries , 1988 .

[86]  E. Wood,et al.  HEAT TRANSFER WITH TURBULENT FLOW IN CONCENTRIC AND ECCENTRIC ANNULI WITH CONSTANT AND VARIABLE HEAT FLUX , 1962 .

[87]  M.A.I. El-Shaarawi,et al.  Natural convection in uniformly heated vertical annuli , 1987 .

[88]  F. Shahraki MODELING OF BUOYANCY-DRIVEN FLOW AND HEAT TRANSFER FOR AIR IN A HORIZONTAL ANNULUS: EFFECTS OF VERTICAL ECCENTRICITY AND TEMPERATURE-DEPENDENT PROPERTIES , 2002 .

[89]  E. Merzari,et al.  Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels , 2009 .

[90]  F. Kulacki,et al.  Natural convection in a vertical porous annulus , 1984 .

[91]  Manfred Wimmer,et al.  An experimental investigation of Taylor vortex flow between conical cylinders , 1995 .

[92]  K. Vafai,et al.  An investigation of transient three-dimensional buoyancy-driven flow and heat transfer in a closed horizontal annulus , 1991 .

[93]  Darryl L. James,et al.  CFD Calculation of Internal Natural Convection in the Annulus between Horizontal Concentric Cylinders , 2002 .

[94]  Bo Yu,et al.  The computed characteristics of turbulent flow and convection in concentric circular annuli. Part II. Uniform heating on the inner surface , 2005 .

[95]  R. H. Sabersky,et al.  Heat transfer in an annular gap , 1976 .

[96]  Ahmet Murat Ozbayoglu,et al.  An Experimental and Numerical Study of Two-phase Flow in Horizontal Eccentric Annuli , 2013 .

[97]  F. M. Mahfouz,et al.  Numerical simulation of free convection within an eccentric annulus filled with micropolar fluid using spectral method , 2013, Appl. Math. Comput..

[98]  O. E. Dwyer,et al.  HEAT TRANSFER TO LIQUID METALS FLOWING TURBULENTLY IN ECCENTRIC ANNULI. I , 1966 .

[99]  Orhan Aydin,et al.  Laminar forced convection slip-flow in a micro-annulus between two concentric cylinders , 2008 .

[100]  S. Chang,et al.  Jet-array impingement heat transfer in a concentric annular channel with rotating inner cylinder , 2009 .

[101]  J. Prusa,et al.  Natural Convection Heat Transfer Between Eccentric Horizontal Cylinders , 1982 .

[102]  H. Yoon,et al.  A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations , 2008 .

[103]  Sassi Ben Nasrallah,et al.  Free convection in a vertical cylindrical enclosure , 2000 .

[104]  E. Saatdjian,et al.  Natural convection in porous cylindrical annuli , 1995 .

[105]  M. Sankar,et al.  Numerical simulation of free convection heat transfer in a vertical annular cavity with discrete heating , 2010 .

[106]  Application of differential quadrature method to simulate natural convection in a concentric annulus , 1999 .

[107]  G. D. Davis,et al.  Heat transfer in a vertical rotating annulus - A numerical study , 1982 .

[108]  Laminar flow in regular polygonal shaped ducts with circular centered cores , 1968 .

[109]  M. Havstad,et al.  Convective heat transfer in vertical cylindrical annuli filled with a porous medium , 1982 .

[110]  C. Shu,et al.  Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method , 2001 .

[111]  Feng-Chen Li,et al.  MHD effect on flow structures and heat transfer characteristics of liquid metal–gas annular flow in a vertical pipe , 2005 .

[112]  L. Robillard,et al.  Natural convection between horizontal concentric cylinders filled with a porous layer with internal heat generation , 1984 .

[113]  Reza Hosseini,et al.  An experimental study of heat transfer in an open-ended vertical eccentric annulus with insulated and constant heat flux boundaries , 2005 .

[114]  H. Sung,et al.  DIRECT NUMERICAL SIMULATION OF TURBULENT CONCENTRIC ANNULAR PIPE FLOW , 2002, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

[115]  A. W. Date,et al.  Numerical prediction of natural convection heat transfer in horizontal annulus , 1986 .

[116]  Pinhas Z. Bar-Yoseph,et al.  Convection-induced enhancement of mass transfer through an interface separating two immiscible liquids in a two-layer horizontal annulus , 2003 .

[117]  M. Teamah Numerical simulation of double diffusive laminar mixed convection in a horizontal annulus with hot, solutal and rotating inner cylinder , 2007 .

[118]  J. Quaresma,et al.  Thermal entry region analysis through the finite integral transform technique in laminar flow of Bingham fluids within concentric annular ducts , 2002 .

[119]  A. Smati,et al.  Finite element study of mixed convection for non-Newtonian fluid between two coaxial rotating cylinders , 2006 .

[120]  Alan Quarmby Some measurements of turbulent heat transfer in the thermal entrance region of concentric annuli , 1967 .

[121]  G. Lauriat,et al.  Numerical study of heat transfer in a non-Newtonian Carreau-fluid between rotating concentric vertical cylinders , 2000 .

[122]  Xi-Yun Lu,et al.  Large eddy simulation of turbulent flows in a rotating concentric annular channel , 2005 .

[123]  B. Sharma,et al.  Unsteady flow through porous medium induced by periodically rotating half-filled horizontal concentric cylindrical annulus with heat transfer , 2011 .

[124]  R. Shah Laminar Flow Forced convection in ducts , 1978 .

[125]  Mohd Khairol Anuar Mohd Ariffin,et al.  Numerical Study of Turbulent Heat Transfer in Annular Pipe with Sudden Contraction , 2013 .

[126]  M. Altamush Siddiqui,et al.  Heat transfer studies during natural convection boiling in an internally heated annulus , 2003 .

[127]  A numerical study of three-dimensional natural convection in a horizontal porous annulus with Galerkin method , 1988 .

[128]  G. Guj,et al.  Natural convection in a horizontal concentric cylindrical annulus: oscillatory flow and transition to chaos , 1998, Journal of Fluid Mechanics.

[129]  W. Kays,et al.  Heat transfer between concentric rotating cylinders , 1959 .

[130]  G. D. Davis,et al.  Natural Convection between Concentric Vertical Cylinders , 1969 .

[131]  Richard J Goldstein,et al.  An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli , 1978 .

[132]  J. Esperança,et al.  Natural convection heat transfer in horizontal eccentric elliptic annuli containing saturated porous media , 2000 .

[133]  C. T. Carley,et al.  A Numerical Solution for Natural Convection in Cylindrical Annuli , 1971 .

[134]  F. Stella,et al.  NATURAL CONVECTION IN HORIZONTAL ECCENTRIC ANNULI: NUMERICAL STUDY , 1995 .

[135]  Chang Shu,et al.  APPLICATION OF GDQ METHOD FOR THE STUDY OF NATURAL CONVECTION IN HORIZONTAL ECCENTRIC ANNULI , 2002 .

[136]  M. Lacroix,et al.  Étude du transfert de chaleur dans un espace annulaire rhombique horizontal avec et sans ailettes , 1999 .

[137]  A. Mosyak,et al.  Effect of surfactant concentration on saturated flow boiling in vertical narrow annular channels , 2007 .

[138]  M. Kim,et al.  Three-dimensional linear stability of mixed-convective flow between rotating horizontal concentric cylinders , 1995 .

[139]  Joo-Sik Yoo,et al.  Transition and multiplicity of flows in natural convection in a narrow horizontal cylindrical annulus: Pr = 0.4 , 1999 .

[140]  E. Podryabinkin,et al.  Moment and forces exerted on the inner cylinder in eccentric annular flow , 2011 .

[141]  M. Ariffin,et al.  Numerical Study of Heat Transfer and Laminar Flow over a Backward Facing Step with and without Obstacle , 2014 .

[142]  R. M. Manglik,et al.  FULLY DEVELOPED LAMINAR HEAT TRANSFER IN CIRCULAR-SEGMENT DUCTS WITH UNIFORM WALL TEMPERATURE , 1994 .

[143]  Fumimaru Ogino,et al.  Effect of radial electric field on heat and momentum transfers in dielectric organic liquid for laminar flow through concentric annuli , 1980 .

[144]  M. Dalle Donne,et al.  Heat transfer and friction coefficients for turbulent flow of air in smooth annuli at high temperatures , 1973 .

[145]  Ahmad Badarudin,et al.  CFD Simulation of Heat Transfer and Turbulent Fluid Flow over a Double Forward-Facing Step , 2013 .

[146]  Chin‐Hsiang Cheng,et al.  NUMERICAL PREDICTION OF THE BUOYANCY-DRIVEN FLOW IN THE ANNULUS BETWEEN HORIZONTAL ECCENTRIC ELLIPTICAL CYLINDERS , 1996 .

[147]  An Analysis of Heat Transfer for Fully Developed Turbulent Flow in Concentric Annuli , 1968 .

[148]  Rao Yan-Fei,et al.  Flow patterns of natural convection in horizontal cylindrical annuli , 1985 .

[149]  M. A. Waheed An Approach to the Simulation of Natural-Convective Heat Transfer between Two Concentric Horizontal Cylindrical Annuli , 2007 .

[150]  Haim H. Bau,et al.  Two-dimensional bifurcation phenomena in thermal convection in horizontal, concentric annuli containing saturated porous media , 1988, Journal of Fluid Mechanics.

[151]  J. Chung,et al.  NUMERICAL INVESTIGATION ON THE BIFURCATIVE NATURAL CONVECTION IN A HORIZONTAL CONCENTRIC ANNULUS , 1999 .

[152]  Ching-Jenq Ho,et al.  A numerical study of natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions , 1989 .

[153]  A. I. Osipov,et al.  Natural convection in an annulus between coaxial horizontal cylinders with internal heat generation , 2005 .

[154]  M. A. Waheed Heatfunction Formulation of Thermal Convection in Rectangular Enclosures Filled with Porous Media , 2009 .

[155]  Yan Wei-Mon,et al.  Mixed convection heat and mass transfer in vertical annuli with asymmetric heating , 1991 .

[156]  A. K. Mohanty,et al.  Buoyancy induced flow and heat transfer through a vertical annulus , 1996 .

[157]  Joo-Sik Yoo,et al.  Transitions and chaos in natural convection of a fluid with Pr = 0.1 in a horizontal annulus , 2000 .

[158]  R. Sakr,et al.  Experimental and Numerical Investigation of Natural Convection Heat Transfer in Horizontal Elliptic Annuli , 2008 .

[159]  K. C. Cheng,et al.  Laminar forced convection in eccentric annuli , 1968 .

[160]  Jin Ho Song,et al.  Heat transfer to supercritical pressure carbon dioxide flowing upward through tubes and a narrow annulus passage , 2008 .

[161]  K. Raju,et al.  Combined Free and Forced Convection Laminar Heat Transfer in a Vertical Annulus , 1975 .

[162]  Forchheimer and Brinkman extended Darcy flow model on natural convection in a vertical cylindrical porous annulus , 1995 .

[163]  Chang Shu,et al.  SIMULATION OF NATURAL CONVECTION IN ECCENTRIC ANNULI BETWEEN A SQUARE OUTER CYLINDER AND A CIRCULAR INNER CYLINDER USING LOCAL MQ-DQ METHOD , 2005 .

[164]  Natural Convection in Vertical Annuli: A Numerical Study for Constant Heat Flux on the Inner Wall , 1989 .

[165]  Tülay A. Özbelge,et al.  Heat transfer enhancement in water—feldspar upflows through vertical annuli , 1996 .

[166]  Prasanta Kumar Das,et al.  CFD simulation of core annular flow through sudden contraction and expansion , 2012 .

[167]  Abdalla M. Al-Amiri,et al.  Combined Forced- and Natural-Convection Heat Transfer in Horizontally CounterRotating Eccentric and Concentric Cylinders , 2007 .

[168]  I. Frigaard,et al.  Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder , 2009 .

[169]  Wang Suo-fang An experimental and numerical study of natural convection heat transfer in horizontal annuli between eccentric cylinders , 1995 .

[170]  Chi-Wang Shu,et al.  Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder , 2002 .

[171]  Experimental study of heating fluid between two concentric cylinders with cavities , 2008 .

[172]  E. H. Bishop,et al.  NATURAL CONVECTION BETWEEN HORIZONTAL CONCENTRIC CYLINDERS FOR LOW RAYLEIGH NUMBERS , 1968 .

[173]  Joon Sang Lee,et al.  Large eddy simulation of heated vertical annular pipe flow in fully developed turbulent mixed convection , 2004 .

[174]  S. Tavoularis,et al.  An Experimental Study of Natural Convection in Vertical, Open-Ended, Concentric, and Eccentric Annular Channels , 2011 .

[175]  Tülay A. Özbelge,et al.  Assessment of flow and heat transfer characteristics for proposed solid density distributions in dilute laminar slurry upflows through a concentric annulus , 2003 .

[176]  C. Nouar,et al.  Laminar mixed convection in an eccentric annular horizontal duct for a thermodependent non-Newtonian fluid , 2011, 2211.01754.

[177]  E. Mokheimer,et al.  Developing laminar forced convection in eccentric annuli , 1998 .

[178]  T. S. Lee,et al.  Laminar fluid convection between concentric and eccentric heated horizontal rotating cylinders for low‐Prandtl‐number fluids , 1992 .

[179]  M. Nobari,et al.  A Numerical Investigation of Flow and Mixed Convection Inside a Vertical Eccentric Annulus , 2008 .

[180]  Young Kyu Hwang,et al.  Experimental study on the vortex flow in a concentric annulus with a rotating inner cylinder , 2003 .

[181]  Marta Cianfrini,et al.  Natural convection heat transfer of nanofluids in annular spaces between horizontal concentric cylinders , 2011 .

[182]  Joo-Sik Yoo,et al.  Prandtl number effect on bifurcation and dual solutions in natural convection in a horizontal annulus , 1999 .

[183]  M. N. Özişik,et al.  Correlation for laminar natural convection between confocal horizontal elliptical cylinders , 1990 .

[184]  K. Cen,et al.  Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure , 2009 .

[185]  F. Kulacki,et al.  Free convection in a vertical, porous annulus with constant heat flux on the inner wall—experimental results , 1986 .

[186]  Hyung Jin Sung,et al.  Large-eddy simulation of turbulent mixed convection in a vertical annulus with a rotating inner cylinder , 2006 .

[187]  C. V. Raghavarao,et al.  Natural convection heat transfer of cold water in an eccentric horizontal cylindrical annulus — a numerical study , 1996 .

[188]  T. Adachi,et al.  Transitions of natural convection in a horizontal annulus , 2001 .

[189]  Joo-Sik Yoo Dual steady solutions in natural convection between horizontal concentric cylinders , 1996 .

[190]  Richard J Goldstein,et al.  An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders , 1976, Journal of Fluid Mechanics.

[191]  E. Mokheimer,et al.  Developing mixed convection in vertical eccentric annuli , 2004 .

[192]  K. Cen,et al.  Transient natural convective heat transfer of a low-Prandtl-number fluid inside a horizontal circular cylinder with an inner coaxial triangular cylinder , 2010 .

[193]  Prasanta Kumar Das,et al.  Review of oil water core annular flow , 2009 .

[194]  A. Shaija,et al.  Laminar conjugate natural convection in horizontal annuli , 2008 .

[195]  Mamoru Ishii,et al.  Droplet entrainment correlation in annular two-phase flow , 1989 .

[196]  Qiu Suizheng,et al.  Two-phase flow and boiling heat transfer in two vertical narrow annuli , 2005 .

[197]  J. F. Osterle,et al.  A numerical solution of laminar developing flow in eccentric annular ducts , 1982 .

[198]  B. Jha,et al.  Unsteady/Steady Natural Convection Flow of Reactive Viscous Fluid in a Vertical Annulus , 2013 .

[199]  J. Karni,et al.  Heat Transfer In Gas-Cooled Annular Channels , 1987 .

[200]  Hyung Jin Sung,et al.  Direct numerical simulation of turbulent concentric annular pipe flow: Part 2: Heat transfer , 2003 .

[201]  Jamshid M. Nouri,et al.  Flow of Newtonian and non-Newtonian fluids in an eccentric annulus with rotation of the inner cylinder , 1994 .

[202]  Vitor A. F. Costa,et al.  Steady mixed convection in a differentially heated square enclosure with an active rotating circular cylinder , 2010 .

[203]  R. M. Cotta,et al.  Laminar flow and convective heat transfer of non-Newtonian fluids in doubly connected ducts , 2010 .

[204]  Ranganathan Kumar Study of natural convection in horizontal annuli , 1988 .

[205]  Joo-Sik Yoo,et al.  Natural convection in a narrow horizontal cylindrical annulus: Pr ≤ 0.3 , 1998 .

[206]  D. Robinson,et al.  Mass transfer for turbulent flow in an annulus with non-axisymmetric boundary conditions , 1978 .

[207]  K. Cen,et al.  A numerical study of laminar natural convective heat transfer around a horizontal cylinder inside a concentric air-filled triangular enclosure , 2010 .

[208]  Salim Newaz Kazi,et al.  An experimental study of heat transfer to turbulent separation fluid flow in an annular passage , 2011 .

[209]  Heat transfer in vertical annular laminar flow of two immiscible liquids , 1977 .

[210]  Jun-young Choi,et al.  Three-dimensional linear stability of natural convective flow between concentric horizontal cylinders , 1993 .

[211]  J. F. Osterle,et al.  A numerical solution of developing temperature for laminar developing flow in eccentric annular ducts , 1982 .

[212]  R. G. Boothroyd,et al.  Flowing gas-solids suspensions , 1971 .

[213]  H. Bau Thermal convection in a horizontal, eccentric annulus containing a saturated porous medium—an extended perturbation expansion , 1984 .

[214]  S. Mahmud,et al.  Mixed convection and entropy generation in a vertical annular space , 2002 .

[215]  I. Pop,et al.  DESIGN OF A VERTICAL ANNULUS WITH MHD FLOW USING ENTROPY GENERATION ANALYSIS , 2013 .

[216]  Study of conjugate natural convection between vertical coaxial rectangular cylinders , 2012 .

[217]  Chie-Yuan Chen Heat Transfer in Annuli , 1943 .

[218]  Ioan Pop,et al.  Natural convection flow and heat transfer in an eccentric annulus filled by Copper nanofluid , 2013 .

[219]  Q. Bi,et al.  Experimental investigation of heat transfer for supercritical pressure water flowing in vertical annular channels , 2011 .

[220]  A. Hatton,et al.  Predictions and measurements of non-axisymmetric turbulent diffusion in an annular channel , 1978 .

[221]  T. Lee Numerical computation of fluid convection with air enclosed between the annuli of eccentric heated horizontal rotating cylinders , 1992 .

[222]  Chang Wen-Jeng,et al.  Natural convection in a vertical cylinder filled with anisotropic porous media , 1993 .

[223]  Kaoru Iwamoto,et al.  Heat and fluid flow in cylindrical and conical annular flow-passages with through flow and inner-wall rotation , 2011 .

[224]  Jayanthi Pillutla LAMINAR NON-NEWTONIAN FLOWS IN ECCENTRIC ANNULI WITH INNER CYLINDER ROTATION , 2001 .

[225]  Bakhtier Farouk,et al.  An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder , 1989 .

[226]  V. Prasad Numerical study of natural convection in a vertical, porous annulus with constant heat flux on the inner wall , 1986 .

[227]  Ching-Jenq Ho,et al.  Thermal convection heat transfer of air/water layers enclosed in horizontal annuli with mixed boundary conditions , 1989 .

[228]  Hans Beer,et al.  NUMERICAL ANALYSIS OF LAMINAR NATURAL CONVECTION BETWEEN CONCENTRIC AND ECCENTRIC CYLINDERS , 1981 .

[229]  Keun-Shik Chang,et al.  Numerical Simulation of Natural Convection in Concentric and Eccentric Horizontal Cylindrical Annuli , 1982 .

[230]  M. Kim,et al.  MULTICELLULAR NATURAL CONVECTION OF A LOW PRANDTL NUMBER FLUID BETWEEN HORIZONTAL CONCENTRIC CYLINDERS , 1994 .

[231]  J. W. Hiby The Flow of Complex Mixtures in Pipes. Von G. W. Govier und K. Aziz. Van Nostrand Reinhold Comp., New York‐London 1972. 1. Aufl., XLVII, 792 S., zahlr. Abb., Ln. £ 17.65 , 1973 .

[232]  R. Anand,et al.  Turbulent heat transfer in the thermal entrance region of concentric annuli with uniform wall heat flux , 1970 .

[233]  D. Groulx,et al.  Forced and mixed convection in the annulus between two horizontal confocal elliptical cylinders , 2013 .

[234]  Chuguang Zheng,et al.  Natural convection and entropy generation in a vertically concentric annular space , 2010 .

[235]  M. Azaïez,et al.  Numerical and experimental study of multicellular free convection flows in an annular porous layer , 1991 .

[236]  G. Petrone,et al.  Stability of free convection in air-filled horizontal annuli: influence of the radius ratio , 2004 .

[237]  D. Naylor,et al.  Experimental and numerical study of natural convection between two eccentric tubes , 1989 .

[238]  R. Hosseini,et al.  Experimental study of turbulent forced convection in vertical eccentric annulus , 2009 .

[239]  W. Kays,et al.  Heat transfer in annular passages—hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux , 1963 .

[240]  G. D. Davis,et al.  Mixed convection in vertical, cylindrical annuli , 1987 .

[241]  S. Tavoularis,et al.  An Experimental Study of Mixed Convection in Vertical, Open-Ended, Concentric and Eccentric Annular Channels , 2013 .

[242]  Joseph Kaye,et al.  Measurements of Diabatic Flow in an Annulus With an Inner Rotating Cylinder , 1962 .

[243]  Shahab Khushnood,et al.  Experimental study of conjugate heat transfer within a bottom heated vertical concentric cylindrical enclosure , 2012 .

[244]  A. Badarudin,et al.  A Review of Experimental Study of Turbulent Heat Transfer in Separated Flow , 2011 .

[245]  K. Cen,et al.  Transient natural convective heat transfer from a heated triangular cylinder to its air-filled coaxial cylindrical enclosure , 2010 .

[246]  Toshiyuki Hayase,et al.  Numerical Calculation of Convective Heat Transfer Between Rotating Coaxial Cylinders With Periodically Embedded Cavities , 1992 .

[247]  C. Hickox,et al.  A numerical study of natural convection in a vertical, annular, porous layer , 1985 .

[248]  Mohd Khairol Anuar Mohd Ariffin,et al.  Heat Transfer to Laminar Flow over a Double Backward-Facing Step , 2013 .

[249]  Ehsan Fattahi,et al.  Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus , 2010 .

[250]  B. Farouk,et al.  Three-dimensional mixed convection flows in a horizontal annulus with a heated rotating inner circular cylinder , 1992 .

[251]  Emad Sadeghinezhad,et al.  Numerical simulation of laminar to turbulent nanofluid flow and heat transfer over a backward-facing step , 2014, Appl. Math. Comput..

[252]  Janusz S. Szmyd,et al.  EXPERIMENTAL AND NUMERICAL ANALYSIS OF THERMO-MAGNETIC CONVECTION IN A VERTICAL ANNULAR ENCLOSURE , 2010 .

[253]  S. Kiwan,et al.  Effect of Using Porous Inserts on Natural Convection Heat Transfer Between Two Concentric Vertical Cylinders , 2007 .

[254]  S. Patankar,et al.  LAMINAR, FULLY DEVELOPED MIXED CONVECTION IN A VERTICAL ECCENTRIC ANNULUS , 1992 .

[255]  A. Hussein,et al.  Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations , 2010 .

[256]  G. Lauriat,et al.  Non-darcian effects on natural convection in a vertical porous enclosure , 1989 .

[257]  Tülay A. Özbelge Heat transfer enhancement in turbulent upward flows of liquid-solid suspensions through vertical annuli , 2001 .

[258]  R. M. Manglik,et al.  Thermal processing of viscous non-Newtonian fluids in annular ducts: effects of power-law rheology, duct eccentricity, and thermal boundary conditions , 2002 .

[259]  Mark P. Dyko,et al.  A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus , 1999 .

[260]  K. Cen,et al.  Prandtl number dependence of laminar natural convection heat transfer in a horizontal cylindrical enclosure with an inner coaxial triangular cylinder , 2010 .

[261]  H. Barrow,et al.  Paper 28: Turbulent Heat Transfer to Air in the Vicinity of the Entry of an Internally Heated Annulus , 1967 .

[262]  Tülay A. Özbelge,et al.  Direct contact heat transfer between two immiscible liquids flowing in a horizontal concentric annulus , 1995 .

[263]  Fukuda Kenji,et al.  Three-dimensional natural convection in an inclined cylindrical annulus , 1984 .

[264]  C. J. Scott,et al.  Turbulent Heat Transfer Studies in Annulus With Inner Cylinder Rotation , 1975 .

[265]  H. Oztop,et al.  Parametric Study of Entropy Generation in a Fluid with Internal Heat Generation between Two Rotating Cylinders Subjected to Convective Cooling at the Surface , 2012 .

[266]  R. Roy,et al.  Velocity and temperature fields in turbulent liquid flow through a vertical concentric annular channel , 1992 .

[267]  H. Aoki,et al.  Convective Heat Transfer in an Annulus with an Inner Rotating Cylinder , 1966 .

[268]  E. Mokheimer,et al.  Maximum possible induced flow rates in open‐ended vertical eccentric annuli with uniform heat flux , 2005 .

[269]  K. Becker,et al.  The Influence of a Radial Temperature Gradient on the Instability of Fluid Flow in an Annulus With an Inner Rotating Cylinder , 1962 .

[270]  Bakhtier Farouk,et al.  Mixed Convection around a Heated Rotating Horizontal Square Cylinder in a Circular Enclosure , 1995 .

[271]  Shiva N. Singh,et al.  Natural convection between confocal horizontal elliptical cylinders , 1985 .

[272]  On the reduction of natural convection heat transfer in horizontal eccentric annuli containing saturated porous media , 1997 .

[273]  Joo-Sik Yoo,et al.  Dual free-convective flows in a horizontal annulus with a constant heat flux wall , 2003 .

[274]  P. Puchkov,et al.  Heat transfer and hydraulic resistance in annular channels with smooth and rough heat transfer surfaces , 1967 .

[275]  Combined forced-free laminar convection in the entry region of a vertical annulus with a rotating inner cylinder , 1982 .

[276]  E. Bilgen,et al.  ANALYTICAL AND NUMERICAL STUDY OF NATURAL CONVECTION HEAT TRANSFER IN A VERTICAL POROUS ANNULUS , 1995 .

[277]  Mohd Khairol Anuar Mohd Ariffin,et al.  Numerical study of turbulent heat transfer in separated flow: review , 2013 .