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Nomenclature
Roman letters
G , = gravitational acceleration
L , = length of the cubical cavity
L , = distance between the left wall and heat source
Nu , = local Nusselt number
[figure omitted; refer to PDF] [figure omitted; refer to PDF] Nu¯ = average Nusselt number
Pr , = Prandtl number
Ra , = Rayleigh number
T , = dimensional temperature
T , = dimensional time
Tc , , = dimensional cooled wall temperature
Th , , = dimensional heated wall temperature
U , = dimensionless velocity component in X , -direction
V , = dimensionless velocity component in Y , -direction
W , = dimensionless velocity component in Z , -direction
X, Y, Z , = dimensionless Cartesian coordinates
x, y, z , = dimensional Cartesian coordinates
Greek symbols
[alpha] = thermal diffusivity
[beta] = thermal expansion coefficient
[Delta]T , = temperature difference
[Theta] = dimensionless temperature
[nu] = kinematic viscosity
I,, = dimensionless time
[Psi]x , [Psi]y , [Psi]z , = dimensionless vector potential functions
[Omega]x , [Omega]y , [Omega]z , = dimensionless components of vorticity vector
Subscripts
c = cooled wall
h = heated wall
1.Introduction
Natural convection in enclosures plays an important role due to widespread engineering and natural applications, including geothermal systems, underground spread of pollutants, storage of nuclear waste materials, solidification of casting, thermal insulation, electronic cooling, food and medical industries and many others (Jaluria, 1998; Bejan, 2013; Shenoy et al. , 2016). In the field of electronics, one of the main problems is an effective cooling of heat sources using passive or active cooling systems (Kakac et al. , 1994). For solution to such problem, it is necessary to conduct numerical simulation of convective heat transfer in three-dimensional enclosures with heat sources (Frederic and Quiroz, 2001; Abraham and Sparrow, 2003; Martyushev and Sheremet, 2014; Oztop et al. , 2015; Sheremet et al. , 2015; Purusothaman et al. , 2016a , 2016b; Yang and Wu, 2016). Thus, Oztop et al. (2015) have reviewed papers about natural convection in enclosures under the effect of local heaters. It has been shown that majority of papers include analysis of convective heat transfer in the case of infinitely thin...