Analysis of mixed convective heat transfer from a sphere with an aligned magnetic field. (December 2020) - Sundar Raju, B. Hema
Highlights: Mixed convective heat transfer for magnetohydrodynamic flow past a sphere. Relationship is established between drag coefficient and interaction parameter. Three different regimes are identified based on variation of Nusselt number. Heat transfer varies strongly with Re, interaction parameter and Richardson number. Correlations are developed for drag coefficient and average Nusselt number. Abstract: Numerical computations are performed to examine the flow and heat transfer characteristics for mixed convective flow past a sphere in an assisting flow arrangement with an aligned magnetic field. The flow is considered as laminar, steady and incompressible and the working fluids as Newtonian. A spherical geometry higher order compact scheme (SGHOCS) is employed to solve the set of non-linear governing transport equations. The results are enumerated in terms of streamlines, isotherms, drag coefficient together with local and average Nusselt number on the surface of the sphere by varying the following parameters: Reynolds number 1 ≤ Re ≤ 200; Prandtl number 0.72 and 7; Richardson number 0 ≤ Ri ≤ 1.5; interaction magnetic parameter 0 ≤ N ≤ 10. For lower values of Ri, although the flow separation phenomena in the downstream region suppresses for weaker strength of the magnetic field ( N ≤ 0.5), it again increases on further increase in N . For higher values of Ri, with an increase of N, the flow separation phenomena completely suppresses. The drag coefficient ( CD ) increases with N for any values of Re, Ri and Pr and for N ≥ 1, C D = K N + B where K and B are constants that depends on Ri and Pr and K = 0.32 for Ri = 0 which is consistent with the results in the literature. On the basis of variation of Nu on the sphere surface, three different regions are identified and moreover a strong interplay between N and Ri in dictating the characteristic of heat transfer is found for all values of Re . In the mixed convection domain the average Nusselt number ( N u ¯ ) first decreases with N and then tends to a constant value for higher values of Reynolds number, in contrast with the forced convection case, when N u ¯ decreases with N and then tends to increase almost linearly with N . Based on the numerical results for the considered range of parameters, correlations are developed for CD and N u ¯, which are relatively in good agreement with reported results in the literature for special cases of both forced and mixed convective flows past a sphere in the absence of a magnetic field.