Grashof number


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Grashof number

[′gräs‚hȯf ‚nəm·bər]
(fluid mechanics)
A dimensionless number used in the study of free convection of a fluid caused by a hot body, equal to the product of the fluid's coefficient of thermal expansion, the temperature difference between the hot body and the fluid, the cube of a typical dimension of the body and the square of the fluid's density, divided by the square of the fluid's dynamic viscosity. Also known as free convection number.
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pre-exponential factor/surface [C.sub.D] drag coefficient [C.sub.P] specific isobaric heat capacity d diameter D diffusion coefficient [E.sub.A] activation energy F force g acceleration of gravity Gr Grashof number h specific enthalpy [h.sub.c] heat transfer coefficient K K-number (regime classification) k chemical rate constant [k.sub.c] mass transfer coefficient l length m mass m mass flux M molar mass Nu Nusselt number p pressure Pr Prandtl number Q heat flux R universal gas constant Ra Rayleigh number Re Reynolds number Sc Schmidt number Sh Sherwood number t time t temperature [T*.sub.crit] critical temperature coefficient v velocity V volume We Weber number x current position [X.sub.rel] relative humidity A.
[Gr.sub.d]: Grashof number based on the width of the left side slot
To evaluate the accuracy and convergence of MACB scheme with conventional methods, a couple of simulations were conducted at different Reynolds and Grashof Numbers. Also, conventional CB was tested and its results were reported here.
The influence of thermal Grashof number Gr and mass Grashof number Gm on velocity and microrotation is depicted from Figures 8-11.
Nomenclature a': Accelerating parameter a: Dimensionless accelerating parameter [a.sup.*]: Absorption coefficient [C.sub.p]: Specific heat at constant pressure [B.sub.0]: Transverse magnetic field strength Gr: Grashof number g: Acceleration due to gravity [kappa]: Thermal conductivity of the fluid k': Permeability parameter k: Dimensionless permeability parameter M: Magnetic field parameter Nu: Nusselt number Pr: Prandtl number [q.sub.r]: Radiative heat flux in the y direction R: Radiation parameter t':.
The fluid flow covers the whole domain but it is weak because of lower Grashof number (2*[10.sup.4]) and it is clear in magnitude of maximum stream function ([[PSI].sub.max]=+0.07109).
Effects of the parameters namely Hartmann number M Grashof number Gr heat source parameter N and Prandtl number P have been observed on velocity and temperature distributions.
Grashof number considers natural convection's impact inside the medium.
Figure 4(d) demonstrates the effect of thermal and concentration buoyancy forces, that is, Grashof number (Gr) and modified Grashof number (Gm) on the microrotation profiles.
where [alpha] is the thermal conductivity, Gr and Le are the Grashof number and Lewis number, respectively.
In addition, the empirical correlations of the natural convection, radiation, and total heat loss Nusselt numbers versus the Grashof number, tilt angle, and ambient temperature were proposed.
At each value of the magnetic field, an increase in the Grashof number would directly increase the velocity via the increased Boussinesq source terms and hence also the magnitude of the slope of the velocity at the wall.