solutal

It can be visualised that the solutal boundary layer thickness for the second solutions are higher to that of the first solutions, which reveal that the second solutions are less stable compared to the first solutions.

Temperature and concentration gradients also develop [50-53], leading to surface tension gradients, resulting in thermal Marangoni flow [54-59] or/and solutal Marangoni flow [60].

MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions, Computer and Fluids 75: 1-10.

is the thermal volumetric coefficient, [T.sup.*] is the temperature, [[alpha].sub.C] is the solutal volumetric coefficient, [C.sup.*] is the solute concentration, c is the specific heat, [c.sub.p] is the specific heat of the nanoparticles, [kappa] is the nanofluid's thermal conductivity, [D.sub.TC] is the Dufour diffusivity, [D.sub.B] is the Brownian diffusion coefficient, [D.sub.T] is the thermophoretic diffusion coefficient, [D.sub.S] is the solutal diffusivity, and [D.sub.CT] is the Soret diffusivity.

Copper casting alloys are commonly divided into three groups based on their freezing range, which governs the degree of solutal undercooling, associated dendritic growth, and tendency to form microporosity.

Themal and solutal transport by fluid flowing through a porous matrix is a phenomenon of great interest from both the theory and application point of view.

Promotion of steam condensation heat transfer using solutal Marangoni condensation Trans.

where Ec is the Eckert number, Pr is the Prandtl number, Sc is the Schmidt number, Sr is the Soret number, Du is the Dufour number, M is the Magnetic field parameter, Gr is the thermal Grashof number, Gc is the Solutal Grashof number, k is the porous parameter, [b.sub.1] is the joule-heating parameter, [lambda] is the variable thermal conductivity, and [gamma] is the variable suction parameter while u and v are dimensionless velocity components in x- and y-directions, respectively, and t is the dimensionless time.

In addition, we employ the velocity and thermal and solutal slip conditions because the recent findings that rarefied gas flows with slip boundary conditions are often encountered in the microscale devices and low-pressure situations (Kumaran and Pop [23]).

where [[rho].sub.[infinity]] is the constant fluid density, [T.sub.[infinity]] and [C.sub.[infinity]] are the fluid temperature and solutal concentration, respectively, [[beta].sub.0] and [[beta].sub.2] are the coefficients of thermal and solutal expansion, and [[beta].sub.1] denotes the nonlinear coefficient of thermal expansion.