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Mixed Convection of Water at 4 °C Along a Wedge with Variable Surface Temperature in a Porous Medium

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Abstract

In this study, the mixed convection of water at 4 °C along a wedge in a porous medium is investigated numerically using a finite difference method. To explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable walltemperature boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and the Nusselt number are obtained and compared with available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ ranged from 0 to 1 in both regimes, whereas different values of λ are considered for the purpose of comparison of heat transfer results.

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Abbreviations

C f :

Skin friction

f :

Dimensionless stream function

g :

Acceleration due to gravity, m · s−2

h :

Heat transfer coefficient, W · m−2 · K−1

K :

Permeability of the porous medium, m2

m :

Wedge flow parameter

Nu :

Nusselt number

Pe x :

Local Peclet number

Ra x :

Local Rayleigh number

T :

Temperature, °C

U ∞ :

Free stream velocity, m · s−1

u, v :

Velocity components in x- and y-direction

x, y :

Coordinates along and normal to wedge surface

f:

Forced convection-dominated regime

∞:

Free stream conditions

n :

Free convection-dominated regime

w:

Wall

α :

Thermal diffusivity of porous medium, m2 · s−1

β :

Thermal expansion coefficient for water at 4 °C, °C−2

η :

Similarity variable

γ :

Semi-wedge angle

λ :

Temperature variation parameter

μ :

Absolute viscosity, Pa · s

ν :

Kinematic viscosity, m2 · s−1

ρ :

Fluid density, kg · m−3

ψ :

Stream function

θ :

Dimensionless temperature

ξ :

Mixed convection parameter

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Authors and Affiliations

  1. Department of Engineering Sciences, PN Engineering College, National University of Science and Technology, Karachi, 75350, Pakistan

    Waqar A. Khan

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

    Rama Subba Reddy Gorla

Authors
  1. Waqar A. Khan
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  2. Rama Subba Reddy Gorla
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Correspondence to Rama Subba Reddy Gorla.

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Khan, W.A., Gorla, R.S.R. Mixed Convection of Water at 4 °C Along a Wedge with Variable Surface Temperature in a Porous Medium. Int J Thermophys 32, 2079–2091 (2011). https://doi.org/10.1007/s10765-011-1069-9

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  • DOI: https://doi.org/10.1007/s10765-011-1069-9

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