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Numerical Analysis of Heat Transfer and Entropy Generation for Natural Convection in a Quadrantal Cavity with Non-uniform Heating at the Bottom Wall

  • Shantanu DuttaEmail author
  • Arup Kumar Biswas
  • Sukumar Pati
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

We analyze the characteristics of thermal transport along with entropy generation in a quadrantal cavity, which is non-uniformly heated along the bottom boundary wall, the upright wall maintained at a constant temperature, while the arched wall being maintained adiabatic. The numerical experimentation is carried out for Rayleigh number (Ra) in the range of 103–106. The results are depicted through the distribution of streamline contour and isotherm contour within the enclosure, local heat transfer rate (Nu) along the bottom boundary wall and cold upright wall, and also average heat transfer rate. Further, the irreversibility characteristics are also presented in the form of distribution of local entropy generation due to heat transfer attributes and fluid friction attributes within the enclosure and the average Bejan number. The results reveal that Nu at the bottom wall follows a sinusoidal variation and primarily at lesser values of Ra chosen for the study, the means of heat transfer is conduction, while at higher Ra the mechanism is essentially convection. The study also enlightens the fact that at low Ra (=103), the irreversibility is essentially owing to heat transfer irreversibility (IHT) while at larger values of Ra (=105 as well 106) fluid friction irreversibility (IFF) is predominant over IHT. For an intermediate range of Ra, both IHT and IFF are comparable.

Keywords

Natural convection Quadrantal enclosure Non-uniform heating Nusselt number 

Nomenclature

cp

Specific thermal capacity (J kg−1 K−1)

g

Acceleration owing to gravity (m s−2)

h

Heat transfer coefficient (W m2 K−1)

k

Thermal conductivity (W m−1 K−1)

L

Enclosure length (m)

\(\overline{Nu}\)

Average Nusselt number

Nu

Nusselt number (dimensionless)

P

Dimensionless pressure

p

Pressure (N m2)

Pr

Prandtl number (dimensionless)

Ra

Rayleigh number (dimensionless)

T

Temperature (K)

U, V

Dimensionless velocity component in the X- and Y-directions

u, v

Velocity component in the x- and y-directions (m s−1)

X, Y

Dimensionless coordinates

x, y

Cartesian coordinate system

Greek symbols

α

Thermal diffusivity (m2 s−1)

β

Coefficient of thermal expansion (K−1)

θ

Dimensionless temperature

\(\nu\)

Kinematic viscosity (m2 s−1)

ρ

Density (kg m−3)

ψ

Stream vorticity (m2 s)

Ψ

Dimensionless stream

Vorticity

(=ψ/α)

Subscripts

Avg

Average

c

Cold wall

h

Hot, bottom wall

max

Maximum

min

Minimum

num

Number

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Shantanu Dutta
    • 1
    Email author
  • Arup Kumar Biswas
    • 1
  • Sukumar Pati
    • 2
  1. 1.Department of Mechanical EngineeringNational Institute of TechnologyDurgapurIndia
  2. 2.Department of Mechanical EngineeringNational Institute of Technology SilcharSilcharIndia

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