| Summary: | The study of viscoelastic fluids gives many opportunities to mathematicians, numerical analysts and simulationists to introduce suitable algorithms for computing the flow due to fulfil many application of it such as in paints, coating, inks, and jet fuels. In this thesis, the mixed convection boundary layer flow of a viscoelastic fluid past a sphere subjected to constant temperature has been studied. The constitutive equations of viscoelastic fluids usually generate a higher-order derivative term in the momentum equation than equations of Newtonian fluid. Thus, we are facing the problem where the boundary conditions insufficient to solve the problems of viscoelastic fluid completely. Therefore, we need an extra boundary condition by augmenting an extra boundary condition at infinity. The governing boundary layer equations are first transformed into a non-dimensional form, and then, into a set of non similar boundary layer equations, which are solved numerically using an efficient implicit finite-difference method known as Keller-box method. Numerical results are presented for different values of the viscoelastic and mixed convection parameters K and ? , respectively, and with the Prandtl number Pr = 0.7, 1 and 7. It is found that both skin friction f C and heat transfer w Q coefficients decrease as K is increased. Further, for cases of cooling sphere (? ?0) and heating sphere(? ?0), the boundary layer separates from the sphere. It is worth mentioning that the result obtained in viscoelastic fluid when we set the value of K = 0 (Newtonian fluid), are in excellent agreement with those obtained in viscous fluid.
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