Study on Laminar Natural Convection Heat Transfer from a Hemisphere with Uniform Heat Flux Surface
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摘要
By employing the modified model based on Bejan et al., laminar natural convection heat transfer from a hemisphere with uniform heat flux surface has been numerically investigated. Extensive results of two different surface boundary conditions are obtained for a wide range of Grashof numbers(10 ≤ Gr ≤ 10~7) and Prandlt number of 0.72. The characteristics of heat transfer and fluid flow are analyzed in terms of isotherm contours and streamline patterns, radial and tangential velocities, dimensionless temperature profiles, local friction and pressure drag coefficients, as well as local and average Nusselt numbers. Meanwhile, the effects of Grashof number and adiabatic surface on flow motion and heat transfer have been studied. No recirculation zone or flow separation generates over the top of the hemisphere compared to the isothermal sphere. Owing to the curvature effect, the maximum values of local friction and pressure drag coefficients appear at the corner point B. Comparisons with the previous results are also reported in detail. All the results are in good agreement with the numerical data. Moreover, both local and average Nusselt numbers show a positive dependence on Grashof number. The values of the non-adiabatic case are smaller than that of the adiabatic case due to the preheating effect. Finally, two precise and general correlations of average Nusselt number varying with Grashof numbers have been presented, which can provide an effective prediction for the heat transfer rate in engineering applications, and offer academic values for the future research.
By employing the modified model based on Bejan et al., laminar natural convection heat transfer from a hemisphere with uniform heat flux surface has been numerically investigated. Extensive results of two different surface boundary conditions are obtained for a wide range of Grashof numbers(10 ≤ Gr ≤ 10~7) and Prandlt number of 0.72. The characteristics of heat transfer and fluid flow are analyzed in terms of isotherm contours and streamline patterns, radial and tangential velocities, dimensionless temperature profiles, local friction and pressure drag coefficients, as well as local and average Nusselt numbers. Meanwhile, the effects of Grashof number and adiabatic surface on flow motion and heat transfer have been studied. No recirculation zone or flow separation generates over the top of the hemisphere compared to the isothermal sphere. Owing to the curvature effect, the maximum values of local friction and pressure drag coefficients appear at the corner point B. Comparisons with the previous results are also reported in detail. All the results are in good agreement with the numerical data. Moreover, both local and average Nusselt numbers show a positive dependence on Grashof number. The values of the non-adiabatic case are smaller than that of the adiabatic case due to the preheating effect. Finally, two precise and general correlations of average Nusselt number varying with Grashof numbers have been presented, which can provide an effective prediction for the heat transfer rate in engineering applications, and offer academic values for the future research.
By employing the modified model based on Bejan et al., laminar natural convection heat transfer from a hemisphere with uniform heat flux surface has been numerically investigated. Extensive results of two different surface boundary conditions are obtained for a wide range of Grashof numbers(10 ≤ Gr ≤ 10~7) and Prandlt number of 0.72. The characteristics of heat transfer and fluid flow are analyzed in terms of isotherm contours and streamline patterns, radial and tangential velocities, dimensionless temperature profiles, local friction and pressure drag coefficients, as well as local and average Nusselt numbers. Meanwhile, the effects of Grashof number and adiabatic surface on flow motion and heat transfer have been studied. No recirculation zone or flow separation generates over the top of the hemisphere compared to the isothermal sphere. Owing to the curvature effect, the maximum values of local friction and pressure drag coefficients appear at the corner point B. Comparisons with the previous results are also reported in detail. All the results are in good agreement with the numerical data. Moreover, both local and average Nusselt numbers show a positive dependence on Grashof number. The values of the non-adiabatic case are smaller than that of the adiabatic case due to the preheating effect. Finally, two precise and general correlations of average Nusselt number varying with Grashof numbers have been presented, which can provide an effective prediction for the heat transfer rate in engineering applications, and offer academic values for the future research.
引文
[1]Gebhart B.,Jaluria Y.,Mahajan R.L.,Sammakia B.Buoyancy-induced flows and transport,Hemisphere Publishing Corporation,New York,1988.
[2]Dudek D.R.,Fletcher T.H.,Longwell J.P.,et al.,Natural convection induced drag forces on spheres at low Grashof numbers:comparison of theory with experiment International Journal of Heat and Mass Transfer,1988,31(4):863-873.
[3]Martynenko O.G.,Khramtsov P.P.,Free-convective heat transfer:with many photographs of flows and heat exchange,Springer Science&Business Media,2005.
[4]Bovy A.J.,Woelk G.,Experiments on free convection at plane surfaces,Datacrtica,1971,4:105-112.
[5]King W.J.,The basic laws and data of heat transmission Mechnical Engineering,1932,54:347-353.
[6]Astrauskas P.,Natural convection mass transfer to particles,M.A.Sc.thesis,Department of Chemical Engineering,McGill University,Montreal,1980.
[7]Merk H.J.,Prins J.A.,Thermal convection in laminary boundary layers,Applied Scientific Research,Section A,1954,4:207-221.
[8]Acrivos A.,A theoretical analysis of laminar natural convection heat transfer to non-Newtonian fluids,AIChEJournal,1960,6:584-590.
[9]Chiang T.,Ossin A.,Tien C.L.,Laminar free convection from a sphere.Journal of Heat Transfer,1964,86(4):537-541.
[10]Potter J.M.,Riley N.,Free convection from a heated sphere at large Grashof number.Journal of Fluid Mechanics,1980,100(4):769-783.
[11]Fendell F.E.,Laminar natural convection about an isothermally heated sphere at small Grashof number.Journal of Fluid Mechanics,1968,34(1):163-176.
[12]Hossain A.,Gebhart B.,Natural convection about a sphere at low Grashof number.International Heat Transfer Conference 4,vol.17,Begel House Inc.,1970.
[13]Singh S.N.,Hasan M.M.,Free convection about a sphere at small Grashof number.International Journal of Heat and Mass Transfer,1983,26:781-783.
[14]Geoola F.,Cornish A.R.H.,Numerical solution of steadystate free convective heat transfer from a solid sphere.International Journal of Heat and Mass Transfer,1981,24(8):1369-1379.
[15]Geoola F.,Cornish A.R.H.,Numerical simulation of free convective heat transfer from a sphere.International Journal of Heat and Mass Transfer,1982,25(11):1677-1687.
[16]Shlien D.J.,Boxman R.L.,Laminar starting plume temperature field measurement.International Journal of Heat and Mass Transfer,1981,24(5):919-931.
[17]Farouk B.,Natural convection heat transfer from anisothermal sphere,Thermal Science,1983,16:347-364.
[18]Fujii T.,Fujii M.,Honda T.,A numerical analysis of laminar free convection around an isothermal sphere.Numerical Heat Transfer,1981,4(1):69-84.
[19]Riley N.,The heat transfer from a sphere in free convective flow.Computers&Fluids,1986,14(3):225-237.
[20]Jia H.,Gogos G.,Transient laminar natural convection heat transfer from isothermal spheres.Numerical Heat Transfer,Part A Applications,1996,29(1):83-101.
[21]Jia H.,Gogos G.,Laminar natural convection heat transfer from isothermal spheres.International Journal of Heat and Mass Transfer,1996,39(8):1603-1615.
[22]Langmuir I.,Convection and conduction of heat in gases.Physical Review(Series I),1912,34(6):401-422.
[23]Raithby G.D.,Hollands K.G.T.,A general method of obtaining approximate solutions to laminar and turbulent free convection problems,Advances in Heat Transfer,Elsevier,1975,11:265-315.
[24]Raithby G.D.,Hollands K.G.T.,Analysis of heat transfer by natural convection or film condensation for three dimensional flows.6th International Heat Transfer Conference,Volume 2.1978,2:187-192.
[25]Saito K.,Raghavan V.,Gogos G.,Numerical study of transient laminar natural convection heat transfer over a sphere subjected to a constant heat flux.Heat and Mass Transfer,2007,43(9):923-933.
[26]Jaluria Y.,Gebhart B.,On the buoyancy-induced flow arising from a heated hemisphere.International Journal of Heat and Mass Transfer,1975,18(3):415-431.
[27]Snoek C.W.,Heat transfer from inflatable structures,1977.
[28]Lewandowski W.M.,Kubski P.,Khubeiz J.M.,et al.,Theoretical and experimental study of natural convection heat transfer from isothermal hemisphere.International Journal of Heat and Mass Transfer,1996,40(1):101-109.
[29]Liu J.,Zhao C.J.,Liu H.,Lu W.Q.,Numerical study of laminar natural convection heat transfer from a hemisphere with adiabatic plane and isothermal hemispherical surface,International Journal of Thermal Sciences,2018,131:132-143.
[30]Sasmal C.,Chhabra R.P.,Laminar free convection in power-law fluids from a heated hemisphere.Journal of Thermophysics and Heat Transfer,2014,28(4):750-763.
[31]Sasmal C.,Shyam R.,Chhabra R.P.,Laminar flow of power-law fluids past a hemisphere:Momentum and forced convection heat transfer characteristics.International Journal of Heat and Mass Transfer,2013,63:51-64.
[32]Nalluri S.V.,Patel S.A.,Chhabra R.P.,Mixed convection from a hemisphere in Bingham plastic fluids.International Journal of Heat and Mass Transfer,2015,84:304-318.
[33]Prhashanna A.,Chhabra R.P.,Free convection in power-law fluids from a heated sphere.Chemical Engineering Science,2010,65(23):6190-6205.
[34]Shyam R.,Sasmal C.,Chhabra R.P.,Natural convection heat transfer from two vertically aligned circular cylinders in power-law fluids.International Journal of Heat and Mass Transfer,2013,64:1127-1152.
[35]Bejan A.,Fowler A.J.,Stanescu G.,The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection.International Journal of Heat and Mass Transfer,1995,38(11):2047-2055.
[36]Liu J.,Liu H.,Zhen Q.,Lu W.Q.,Numerical investigation of the laminar natural convection heat transfer from two horizontally attached horizontal cylinders.International Journal of Heat and Mass Transfer,2017,104:517-532.
[37]Liu J.,Liu H.,Zhen Q.,Lu W.Q.,Laminar natural convection heat transfer from a pair of attached horizontal cylinders set in a vertical array.Applied Thermal Engineering,2017,115:1004-1019.
[38]Bejan A.,Convection heat transfer,4th ed.,John Wiley&Sons,2013.
[39]Eslami M.,Jafarpur K.,Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape:a new dynamic model.Heat and Mass Transfer,2012,48(2):301-315.
[2]Dudek D.R.,Fletcher T.H.,Longwell J.P.,et al.,Natural convection induced drag forces on spheres at low Grashof numbers:comparison of theory with experiment International Journal of Heat and Mass Transfer,1988,31(4):863-873.
[3]Martynenko O.G.,Khramtsov P.P.,Free-convective heat transfer:with many photographs of flows and heat exchange,Springer Science&Business Media,2005.
[4]Bovy A.J.,Woelk G.,Experiments on free convection at plane surfaces,Datacrtica,1971,4:105-112.
[5]King W.J.,The basic laws and data of heat transmission Mechnical Engineering,1932,54:347-353.
[6]Astrauskas P.,Natural convection mass transfer to particles,M.A.Sc.thesis,Department of Chemical Engineering,McGill University,Montreal,1980.
[7]Merk H.J.,Prins J.A.,Thermal convection in laminary boundary layers,Applied Scientific Research,Section A,1954,4:207-221.
[8]Acrivos A.,A theoretical analysis of laminar natural convection heat transfer to non-Newtonian fluids,AIChEJournal,1960,6:584-590.
[9]Chiang T.,Ossin A.,Tien C.L.,Laminar free convection from a sphere.Journal of Heat Transfer,1964,86(4):537-541.
[10]Potter J.M.,Riley N.,Free convection from a heated sphere at large Grashof number.Journal of Fluid Mechanics,1980,100(4):769-783.
[11]Fendell F.E.,Laminar natural convection about an isothermally heated sphere at small Grashof number.Journal of Fluid Mechanics,1968,34(1):163-176.
[12]Hossain A.,Gebhart B.,Natural convection about a sphere at low Grashof number.International Heat Transfer Conference 4,vol.17,Begel House Inc.,1970.
[13]Singh S.N.,Hasan M.M.,Free convection about a sphere at small Grashof number.International Journal of Heat and Mass Transfer,1983,26:781-783.
[14]Geoola F.,Cornish A.R.H.,Numerical solution of steadystate free convective heat transfer from a solid sphere.International Journal of Heat and Mass Transfer,1981,24(8):1369-1379.
[15]Geoola F.,Cornish A.R.H.,Numerical simulation of free convective heat transfer from a sphere.International Journal of Heat and Mass Transfer,1982,25(11):1677-1687.
[16]Shlien D.J.,Boxman R.L.,Laminar starting plume temperature field measurement.International Journal of Heat and Mass Transfer,1981,24(5):919-931.
[17]Farouk B.,Natural convection heat transfer from anisothermal sphere,Thermal Science,1983,16:347-364.
[18]Fujii T.,Fujii M.,Honda T.,A numerical analysis of laminar free convection around an isothermal sphere.Numerical Heat Transfer,1981,4(1):69-84.
[19]Riley N.,The heat transfer from a sphere in free convective flow.Computers&Fluids,1986,14(3):225-237.
[20]Jia H.,Gogos G.,Transient laminar natural convection heat transfer from isothermal spheres.Numerical Heat Transfer,Part A Applications,1996,29(1):83-101.
[21]Jia H.,Gogos G.,Laminar natural convection heat transfer from isothermal spheres.International Journal of Heat and Mass Transfer,1996,39(8):1603-1615.
[22]Langmuir I.,Convection and conduction of heat in gases.Physical Review(Series I),1912,34(6):401-422.
[23]Raithby G.D.,Hollands K.G.T.,A general method of obtaining approximate solutions to laminar and turbulent free convection problems,Advances in Heat Transfer,Elsevier,1975,11:265-315.
[24]Raithby G.D.,Hollands K.G.T.,Analysis of heat transfer by natural convection or film condensation for three dimensional flows.6th International Heat Transfer Conference,Volume 2.1978,2:187-192.
[25]Saito K.,Raghavan V.,Gogos G.,Numerical study of transient laminar natural convection heat transfer over a sphere subjected to a constant heat flux.Heat and Mass Transfer,2007,43(9):923-933.
[26]Jaluria Y.,Gebhart B.,On the buoyancy-induced flow arising from a heated hemisphere.International Journal of Heat and Mass Transfer,1975,18(3):415-431.
[27]Snoek C.W.,Heat transfer from inflatable structures,1977.
[28]Lewandowski W.M.,Kubski P.,Khubeiz J.M.,et al.,Theoretical and experimental study of natural convection heat transfer from isothermal hemisphere.International Journal of Heat and Mass Transfer,1996,40(1):101-109.
[29]Liu J.,Zhao C.J.,Liu H.,Lu W.Q.,Numerical study of laminar natural convection heat transfer from a hemisphere with adiabatic plane and isothermal hemispherical surface,International Journal of Thermal Sciences,2018,131:132-143.
[30]Sasmal C.,Chhabra R.P.,Laminar free convection in power-law fluids from a heated hemisphere.Journal of Thermophysics and Heat Transfer,2014,28(4):750-763.
[31]Sasmal C.,Shyam R.,Chhabra R.P.,Laminar flow of power-law fluids past a hemisphere:Momentum and forced convection heat transfer characteristics.International Journal of Heat and Mass Transfer,2013,63:51-64.
[32]Nalluri S.V.,Patel S.A.,Chhabra R.P.,Mixed convection from a hemisphere in Bingham plastic fluids.International Journal of Heat and Mass Transfer,2015,84:304-318.
[33]Prhashanna A.,Chhabra R.P.,Free convection in power-law fluids from a heated sphere.Chemical Engineering Science,2010,65(23):6190-6205.
[34]Shyam R.,Sasmal C.,Chhabra R.P.,Natural convection heat transfer from two vertically aligned circular cylinders in power-law fluids.International Journal of Heat and Mass Transfer,2013,64:1127-1152.
[35]Bejan A.,Fowler A.J.,Stanescu G.,The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection.International Journal of Heat and Mass Transfer,1995,38(11):2047-2055.
[36]Liu J.,Liu H.,Zhen Q.,Lu W.Q.,Numerical investigation of the laminar natural convection heat transfer from two horizontally attached horizontal cylinders.International Journal of Heat and Mass Transfer,2017,104:517-532.
[37]Liu J.,Liu H.,Zhen Q.,Lu W.Q.,Laminar natural convection heat transfer from a pair of attached horizontal cylinders set in a vertical array.Applied Thermal Engineering,2017,115:1004-1019.
[38]Bejan A.,Convection heat transfer,4th ed.,John Wiley&Sons,2013.
[39]Eslami M.,Jafarpur K.,Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape:a new dynamic model.Heat and Mass Transfer,2012,48(2):301-315.