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Natural convection flow from an isothermal horizontal circular cylinder with temperature dependent viscosity

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Abstract

Free convection flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to an inverse linear function of temperature is studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity equations which are solved numerically by a very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity and viscosity profiles of the fluid as well as heat transfer characteristics, namely the local heat transfer rate and the local skin-friction coefficients for a wide range of viscosity parameter ε (= 0.0, 0.5, 1.0, 2.0, 3.0,4.0) and the Prandtl number Pr (= 1.0, 7.0, 10.0, 15.0, 20.0, 30.0).

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Abbreviations

a :

Radius of the circular cylinder

C p :

Specific heat at constant pressure

C f :

Local skinfriction

f :

Dimensionless stream function

g :

Acceleration due to gravity

Gr:

Grashof number

k :

Thermal conductivity

Nu:

Local Nusselt number

Pr:

Prandtl number

q w :

Heat flux at the surface

T :

Temperature of the fluid in the boundary layer

T w :

Temperature at the surface

u,v :

The dimensionless x and y component of the velocity

\(\hat u,\hat \upsilon \) :

The dimensional \({\hat x}\) and \({\hat y}\) component of the velocity

x,y :

Axis in the direction along and normal to the surface

β:

Volumetric coefficient of thermal expansion

ψ:

Stream function

τw:

Shearing stress

ε:

Viscosityvariation parameter

γ:

Constant

ρ:

Ddensity of the fluid

ν∞:

Reference kinematic viscosity

μ (T):

Viscosity of the fluid

μ∞:

Dynamic viscosity of the ambient fluid

θ:

Dimensionless temperature function

w:

Wall conditions

∞:

Ambient temperature

x :

Differentiation with respect to x

′:

Differentiation with respect to y

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Authors and Affiliations

  1. Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka, 1000, Bangladesh

    Md. Mamun Molla

  2. Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

    Md. Anwar Hossain

  3. Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, USA

    Rama Subba Reddy Gorla

Authors
  1. Md. Mamun Molla
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  2. Md. Anwar Hossain
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  3. Rama Subba Reddy Gorla
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Corresponding author

Correspondence to Rama Subba Reddy Gorla.

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Molla, M.M., Hossain, M.A. & Gorla, R.S.R. Natural convection flow from an isothermal horizontal circular cylinder with temperature dependent viscosity. Heat Mass Transfer 41, 594–598 (2005). https://doi.org/10.1007/s00231-004-0576-7

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  • DOI: https://doi.org/10.1007/s00231-004-0576-7

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