Meccanica(2013)48:2149-2158 2157 12 100 60 Y=Q.01,0.1,1,10,1000 B=0.01.0.1,1.10.1000 1 02 Q15 Y=0.01,0.1,1,10,1000 =0.01.0.11.10.1000 a.05 Y=0.01,01,1,101000 7=0.01,0.1,1,10,1000 0.6 2 Fig.Velocity.pressure and temperature profiles forM-1 Fig.7 Velocity,pressure and temperature profiles for M=10 on y,see Fig.2(b).Our asymptotic results showed perature condition on the boundary-layer convection that the skin friction was large,of (M )and the on a horizontal surface.These types of flows.some wall temperature became small,of O(M- )Our times referred to as'indirect co ction'.have feature asymptotic theory for M large showed that,for the nt to those seen in temperature field,a more appropriate parameter was tion on 6=Co()2.This asymptotic limit was from studies of these latter also considered,see expression(33). over to horiz We have limited our attention to a relatively sim- ple set up,namely we have attempted to assess the ef- nding the cal in fects of an outer flow and a convective surface tem- est.For example,convection of nanoparticles on hori SpringerMeccanica (2013) 48:2149–2158 2157 Fig. 7 Velocity, pressure and temperature profiles for M = 10 on γ , see Fig. 2(b). Our asymptotic results showed that the skin friction was large, of O(M3/2) and the wall temperature became small, of O(M−1/2). Our asymptotic theory for M large showed that, for the temperature field, a more appropriate parameter was δ = γ M1/2 = C1/5 0 ( ν U0 )1/2. This asymptotic limit was also considered, see expression (33). We have limited our attention to a relatively sim￾ple set up, namely we have attempted to assess the ef￾fects of an outer flow and a convective surface tem￾Fig. 8 Velocity, pressure and temperature profiles for M = 100 perature condition on the boundary-layer convection on a horizontal surface. These types of flows, some￾times referred to as ‘indirect convection’, have features which can be quite different to those seen in convec￾tion on a vertical surface. As a consequence, conclu￾sions drawn from studies of these latter flows cannot always be taken over to horizontal convective flows. Future studies are suggested extending the present re￾sults to problems with, perhaps, a more practical inter￾est. For example, convection of nanoparticles on hori-