Heat Mass Transfer (2015)51:1061-1066 D0I10.1007/s00231-014-1477-z CrossMark ORIGINAL Boundary layer flow past a stretching sheet with fluid-particle suspension and convective boundary condition Reddy Gorla Abstract The steady two-dimensional boundary Mass of the dust particles the bo the sheet b ching sm the fuid (K a hot fluid is Hot Auid te ure (K) Temperature at large distance(K) T Temperature of the dust Particles(K) numerically by a Runge-Kutta-Fehlberg fourth-fifth order Velocity components of the fluid along x and y method (RKF45 Method)with the help of MAPLE.The directions (ms-) effects of convective Biot number,fluid particle interaction Velocity components of the dust particle alongx parameter,and Prandtl number on the heat transter charac andy directions(ms-1) teristics are disc sed.It is found that the temperature of x.y Cartesian co-ordinates (m) and dus ihed and pre mpara excellen Density of the fuid (k Density of the dust particles (kgm) Li过t of symbols Relative density Bi Biot number Similarity variable(m) Stretching rate Dimensionless fluid temperature Specifie heat of the particles Dimensionless dust phase temperature s Specific heat of the fluid (Jkg-K) Viscosity of the fluid(Ns m-) ess stream function Relaxation time of the particle phase Thermal re axation time Density ratio The tivity (Wm-K) 1 Introduction G.K.Ramesh Boundary laver flow and heat transfer over a stretched sur face has received considerable attention in recent years. The problem has scientific and engineering applications such as aerodynamic extrusion of plastic sheets and fibers B.J.Gire ineering.Cleveland State University.Cleveland. drawing,annealing and tinning of copperwire,paper pro OH44U5 USA duction.crystal growing and glass blowing.Such applica- c-mail:r.gorla@csuohio.cdu tions involve cooling of a molten liquid by drawing it into a Springer1 3 Heat Mass Transfer (2015) 51:1061–1066 DOI 10.1007/s00231-014-1477-z ORIGINAL Boundary layer flow past a stretching sheet with fluid‑particle suspension and convective boundary condition G. K. Ramesh · B. J. Gireesha · Rama Subba Reddy Gorla Received: 23 December 2013 / Accepted: 15 December 2014 / Published online: 8 January 2015 © Springer-Verlag Berlin Heidelberg 2015 m Mass of the dust particles Pr Prandtl number T Temperature of the fluid (K) Tf Hot fluid temperature (K) T∞ Temperature at large distance (K) Tp Temperature of the dust Particles (K) u, v Velocity components of the fluid along x and y directions (ms−1 ) up, vp Velocity components of the dust particle along x and y directions (ms−1 ) x, y Cartesian co-ordinates (m) Greek symbols β Fluid particle interaction parameter ρ∞ Density of the fluid (kg m−3 ) ρp Density of the dust particles (kg m−3 ) ρr Relative density η Similarity variable (m) θ Dimensionless fluid temperature θp Dimensionless dust phase temperature μ Viscosity of the fluid (Ns m−2 ) τ Relaxation time of the particle phase L0 Thermal relaxation time ω Density ratio 1 Introduction Boundary layer flow and heat transfer over a stretched sur￾face has received considerable attention in recent years. The problem has scientific and engineering applications such as aerodynamic extrusion of plastic sheets and fibers, drawing, annealing and tinning of copperwire, paper pro￾duction, crystal growing and glass blowing. Such applica￾tions involve cooling of a molten liquid by drawing it into a Abstract The steady two-dimensional boundary layer flow of a viscous dusty fluid over a stretching sheet with the bottom surface of the sheet heated by convection from a hot fluid is considered. The governing partial differential equations are transformed into ordinary differential equa￾tions using a similarity transformation, before being solved numerically by a Runge–Kutta–Fehlberg fourth-fifth order method (RKF45 Method) with the help of MAPLE. The effects of convective Biot number, fluid particle interaction parameter, and Prandtl number on the heat transfer charac￾teristics are discussed. It is found that the temperature of both fluid and dust phase increases with increasing Biot number. A comparative study between the previous pub￾lished and present results in a limiting sense is found in an excellent agreement. List of symbols Bi Biot number c Stretching rate cs Specific heat of the particles cp Specific heat of the fluid (J kg−1 K) f Dimensionless stream function F Particle velocity component hf Heat transfer coefficient K Stokes’ resistances k Thermal conductivity (Wm−1 K) G. K. Ramesh · B. J. Gireesha Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Shimoga 577 451, Karnataka, India e-mail: gkrmaths@gmail.com B. J. Gireesha · R. S. R. Gorla (*) Mechanical Engineering, Cleveland State University, Cleveland, OH 44115, USA e-mail: r.gorla@csuohio.edu