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References in periodicals archive ?
The Grashof number comprises the acceleration of gravity g, the stream length, the kinematic viscosity of the surrounding air [v.sub.air] the temperature difference between the pipe wall temperature and the surrounding air ([T.sub.cell] - [T.sub.amb]), and the isobaric volume expansion coefficient [beta], as in Equation 17 [28].
Where M = [[sigma][beta]0]/a is the magnetic field parameter, Pr = [vf]/[[mirco]]/[mu]f is the Prandtl number, [mathematical expression not reproducible] is the radiation parameter, [mathematical expression not reproducible] is the Grashof number and the corresponding boundary conditions are
Rayleigh number, Grashof number, and Prandtl number are defined as the following equations:
The results were presented for a wide range of Reynolds and Grashof numbers. The main application of the proposed scheme would be in solving all the incompressible flows in different and complex geometries with heat transfer accurately such as heat exchangers, vortex tubes and etc.
Exact solutions are obtained and the results are plotted for various embedded parameters, namely, permeability parameter K, magnetic parameter M, radiation parameter R, Prandtl number Pr, thermal Grashof number Gr, mass Grashof number Gm, spin gradient parameter [eta], and micropolar fluid parameter [beta] on velocity and microrotation distributions in order to highlight the flow behavior.
Dimensionless Terms Nu: Nusselt number Pr: Prandtl number Ra: Rayleigh number Gr: Grashof number.
The numerical results represented by the patterns of the streamlines, isotherms, heatlines and entropy generation are discussed for the set of related parameters in this work such as; Marangoni number (-[10.sup.4] to +[10.sup.4]), Prandtl number (0.015, 0.054, 0.16, 0.71, 6.2, 100), Biot number (0 to 100) and Grashof number (2*[10.sup.4] to 2*[10.sup.5]).
Key Words: MHD flow, Hartmann number, Grashof number, Prandtl number, stretching sheet
where Nu is a dimensionless group called Nusselt criterion; C, n, m, p are coefficients; [Pr.sub.0], [Pr.sub.s] are Prandtl numbers correspondingly for cooling medium and cooling surface; [Gr.sub.0] is Grashof number for cooling medium; [Re.sub.0] is Reynolds criterion for cooling medium; [alpha] is value of heat exchange coefficient which is average for the exposed surface W/[m.sup.2][degrees]C; l is characteristic dimension, m; [lambda] is medium's coefficient of heat conductivity W/m[degrees]C.
Comparison of the Grashof number for free convection in still air or C[O.sub.2] with the Reynolds number for forced convection in the same gas confirms that on both planets, free convection at this minimum relative wind speed is only about a tenth of the forced convection and so may be neglected (Incropera and DeWitt 1996).
Ambient temperature [infinity]]: [C.sub.p]: Specific heat at constant pressure K: Thermal conductivity [omega]: Frequency of temperature fluctuation Re: Reynolds number Pr: Prandtl number Gr: Grashof number Ec: Eckert number M: Hartmann number [tau]: Dimensionless skin friction Nu: Nusselt number [K.sub.p]: Permeability of the medium [rho]: Density.