In the present work we investigate the effects of Joule heating and viscous dissipation on MHD fluid flow. The viscous incompressible fluid flows over a stretching porous horizontal sheet subjected to power law heat flux in presence of heat source. The equations of momentum and heat transfer governing the problem are transformed into a system of dimensionless differential equations, which in turn solved numerically using shooting technique. The effects of the Joule heating parameter, permeability parameter, heat source parameter, Eckert number and Prandtl number are discussed and tabulated.
We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G n is already the whole of G n , for various equationally defined subsets. We link this with the inner measure of the set of solutions of an equation in a group, leading to new results and/or proofs in equational probabilistic group theory. Example 1.1. (1) G finite, µ the counting measure. (2) G 1 a group, µ 1 a left-invariant measure on G 1 , and G = G n 1 with the product measure µ = µ n 1. (3) More generally, G 1 a group, G ≤ G n 1 and µ a left-invariant measure on G. (4) G arbitrary and the measure algebra reduced to {∅, G}. While this setup trivialises the probability statements, the largeness results remain meaningful. If X is a measurable subset of G we can interpret µ(X) as the probability that a random element of G lies in X. If H is another group, f : G → H is a function and c ∈ H some constant, we put µ(f (x) = c) = µ({g ∈ G : f (g) = c}).
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