Laminar free convection from a non-isothermal cone

Hering, R. G.; Grosh, R. J.

doi:10.1016/0017-9310(62)90059-5

Cited by 124 publications

(72 citation statements)

References 4 publications

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“…For the natural convection from cones, Hering and Grosh [20] examined the laminar free convection from a non-isothermal cone. The laminar natural convection over a frustum convection about a truncated cone was studied by Na and Chiou [21].…”

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confidence: 99%

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

Gaffar

Prasad²,

Reddy

et al. 2016

J Braz. Soc. Mech. Sci. Eng.

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The nonlinear, non-isothermal steady-state boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian (viscoelastic) fluid from a vertical permeable cone with magnetic field are studied. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using the second-order accurate implicit finite difference Keller-box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely a Weissenberg number (We), rheological power law index (m), surface temperature exponent (n), Prandtl number (Pr), magnetic parameter (M) suction/injection parameter (f w ) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime, is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is observed that velocity, surface heat transfer rate and local skin friction are reduced with increasing Weissenberg number, but temperature is increased. Increasing m enhances velocity and surface heat transfer rate but reduces temperature and local skin friction. An increase in non-isothermal power law index (n) is observed to decrease the velocity and temperature. Increasing magnetic parameter (M) is found to decrease the velocity and increase the temperature. Overall, the primary influence on free convection is sustained through the magnetic body force parameter, M, and also the surface mass flux (injection/suction) parameter, f w . The rheological effects, while still prominent, are not as dramatic. Boundary layers (both hydrodynamic and thermal) are, therefore, most strongly modified by the applied magnetic field and wall mass flux effect. The study is pertinent to smart coatings, e.g., durable paints, aerosol deposition processing and water-based solvent thermal treatment in chemical engineering.

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confidence: 99%

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

Gaffar

Prasad²,

Reddy

et al. 2016

J Braz. Soc. Mech. Sci. Eng.

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“…the numerical solutions obtained from the Equations (11)-(13) using boundary conditions (14) are independent of cone semi vertical angle φ) are compared with the available results of Hering and Grosh [3], Hering [4], and Pop et al [9], are found to be in excellent agreement. along surface of the cone from the apex (x = 0) and y measures the distance normally outward.…”

Section: Mathematical Analysismentioning

confidence: 63%

“…In addition, local skin-friction τ X and local Nusselt number N u X values for different Prandtl number and exponent n are compared with the results of Hering [4] in Table 1 and 2 respectively, where f ′′ (0), −θ ′ (0) are the local skin friction and the local Nusselt number obtained by Hering and Grosh [3] and Hering [4]. Here * indicates the values obtained for pure free convection at ξ = 1 by Pop et al [9] in Table 1, 2 and ** indicates the values obtained at X = 1.0 for free convection by Hering and Grosh [3] in Table 2. f ′′ (1, 0), −θ ′ (1, 0) are the local skin friction and the local Nusselt number obtained by Pop et al [9] for free convection flow past a vertical cone at ǫ = 1.…”

Section: Resultsmentioning

confidence: 99%

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NSM Solution on Transient Natural Convective Viscous Fluid Flow Past a Vertical Cone

Immanuel¹,

Pullepu²,

Rani³

2016

Int. J. of Pure and Appl. Math.

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The unsteady free convective flow of the non-isothermal vertical cone with wall surface temperature varying as power function of distance from the apex (x = 0) with the effects of viscous dissipation is considered here. The dimensionless parabolic integro-partial differential equations that are non-linear, unsteady and coupled are solved using a new method NSM technique. The velocity, temperature profiles and the local as well as average skinfriction and Nusselt number have been studied and analyzed graphically for the effect of viscous dissipation for various parameters of angle φ, Prandtl number P r and n (exponent in power law variation in surface temperature). The present results are compared with available results in literature and are found to be in good agreement.

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“…These studies have included heat transfer (important for thermal treatment), mass transfer (critical to doping modification of polymers), viscous heating, M agnetohydrodynamic (for electro-conductive polymers) and many other phenomena. Hering and Grosh (1962) presented an early classical study on natural convection boundary layers' non-isothermal cone, showing that similarity solutions exist when the wall temperature distribution is a power function of distance along a cone ray. T hey further documented solutions for an isothermal surface as well as for the surface maintained at the temperature varying linearly with the distance measured from the apex of the cone for Prandtl number of 0.7.…”

Section: Introductionmentioning

confidence: 99%

Thermal and Momentum Slip Effects on Hydromagnetic Convection Flow of a Williamson Fluid Past a Vertical Truncated Cone

Amanulla¹,

Nagendra²,

Reddy³

2017

Frontiers in Heat and Mass Transfer

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In this article, the combined theoretical and computational study of the magneto hydrodynamic heat transfer in an electro-conductive polymer on the external surface of a vertical truncated cone under radial magnetic field is presented. Thermal and velocity (hydrodynamic) slip are considered at the vertical truncated cone surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum and energy equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Williamson viscoelastic fluid parameter, magnetic body force parameter, Thermal and velocity (hydrodynamic) slip parameters, stream wise variable and Prandtl number on thermos-fluid characteristics are studied graphically. The model is relevant to the simulation of magnetic polymer materials processing.

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Laminar free convection from a non-isothermal cone

Cited by 124 publications

References 4 publications

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

NSM Solution on Transient Natural Convective Viscous Fluid Flow Past a Vertical Cone

Thermal and Momentum Slip Effects on Hydromagnetic Convection Flow of a Williamson Fluid Past a Vertical Truncated Cone

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