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Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface

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Abstract

The mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent fluid is analyzed using similarity solution technique. Wall temperature and stretching velocity are assumed to have specific exponential function forms. The influence of buoyancy along with viscous dissipation on the convective transport in the boundary layer region is analyzed in both aiding and opposing flow situations. The flow is governed by the mixed convection parameter Gr/Re2. The velocity and temperature inside the boundary layer are observed to be influenced by the parameters like Prandtl number Pr, Gebhart number Gb. Significant changes are observed in non-dimensional skin friction and heat transfer coefficients due to viscous dissipation in the medium. The flow and temperature distributions inside the boundary layer are analyzed and the results for non-dimensional skin friction and heat transfer coefficients are discussed through computer generated plots.

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Abbreviations

C f :

skin friction coefficient (Refer Eq. 11)

c p :

specific heat at constant pressure, J/kg K

g :

acceleration due to gravity, m/s2

Gb:

Gebhart number, u 20 /c p T0

Gr/Re2:

mixed convection parameter, gβ T0e2x/L L3/(LUw)2

k :

thermal conductivity of the fluid, W/mK

Nu x :

local Nusselt number (Refer Eq. 14)

Pr:

Prandtl number, ν/α

Re x :

local Reynolds number (Refer Eq. 16)

T :

temperature, K

T 0 :

temperature parameter of the stretching surface, K

u, v:

velocity in x, y directions, m/s

u 0 :

velocity parameter of the stretching surface, m/s

β:

coefficient of thermal expansion, K−1

θ:

non-dimensional temperature (Refer Eq. 7)

μ:

viscosity, N s/m2

ν:

kinematic viscosity, m2/s

ρ:

density of the fluid, kg/m3

ψ:

non-dimensional stream function (Refer Eq. 6)

α:

thermal diffusivity, m2/s

η:

similarity variable (Refer Eq. 5)

w, ∞:

conditions on the wall and in the ambient medium

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721 302, West Bengal, India

    MK Partha, PVSN Murthy & GP Rajasekhar

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  1. MK Partha
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  2. PVSN Murthy
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  3. GP Rajasekhar
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Correspondence to PVSN Murthy.

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Partha, M., Murthy, P. & Rajasekhar, G. Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat Mass Transfer 41, 360–366 (2005). https://doi.org/10.1007/s00231-004-0552-2

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