A Class of New Exact Solutions of Navier-Stokes Equations with Body Force For Viscous Incompressible Fluid - Ahmed, Mushtaq; Naeem, Rana Khalid; Ali, Syed Anwer (International Journal of Applied Mathematical Research, 2018)
This paper is to indicate a class of new exact solutions of the equations governing the two-dimensional steady motion of incompressible fluid of variable viscosity in the presence of body force. The class consists of the stream function ψ characterized by equation θ=f(r)+ a ψ + b in polar coordinates r, θ , where a continuously differentiable function is f(r) and a eq 0 , b are constants. The exact solutions are determined for given one component of the body force, for both the cases when f(r) is arbitrary and when it is not. When f(r) is arbitrary, we find a=1 and we can construct an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for the cases when R_eP_r=1 and when R_eP_r eq 1 where R_e represents Reynolds number and P_rPrandtl number. For the case when f(r) is not arbitrary we can find solutions for the cases R_eP_r eq a and R_eP_r=a where "a" remains arbitrary.Â