Correlating convection heat transfer for Falkner-Skan flow Liang Zhang a,b,⇑ , Liwu Fan a,b , Zitao Yu a , Renwei Mei c,⇑ a Institute of Thermal Science and Power Systems, College of Energy Engineering, Zhejiang University, Hangzhou 310027, PR China b State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China c Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250, USA article info Article history: Received 19 August 2018 Received in revised form 2 November 2018 Accepted 8 November 2018 Keywords: Falkner-Skan flow Correlation Thermal boundary layer Asymptotic behavior abstract Forced convection heat transfer in a laminar Falkner-Skan boundary layer flow with constant wall tem- perature is considered over a wide range of pressure gradient parameter b and entire range of Prandtl number Pr. A new asymptotic behavior for the Nusselt number Nu x for large b and arbitrary Pr is discov- ered by examining the dependence of the ratio of the heat transfer for arbitrary Pr to its small Pr limit on Pr=b. Correlations for Nu x are developed for 0.19883774  b < 1 and all Pr for boundary layer flows without flow reversal. The thermal boundary layer for point-sink flow, which is the limiting case of Falkner-Skan problem as b ? 1, is analyzed. The peculiar behavior of Nu x = 0 as b ? 1 in the Falkner- Skan thermal problem is caused by the loss of self-similarity for the solution of boundary layer temper- ature in the point-sink flow. Ó 2018 Elsevier Ltd. All rights reserved. 1. Introduction The thermal boundary layer (BL) heat transfer problems of incompressible laminar flow over a wedge has been a common interest in the fields of aerodynamics and convection heat transfer. An extensive research work on the BL flow over the wedge and related problems has been performed and summarized in the past [1–10]. The potential flow over a wedge of angle pb has the invis- cid surface velocity U e ðxÞ¼ Ax m ; m ¼ b=ð2  bÞ ð1Þ where x is the distance measured from the stagnation point or tip of the wedge. The wedge angle parameter b is also known as pressure gradient parameter. The self-similar solution for the velocity of a laminar BL flow over the wedge was first given by Falkner and Skan [1]. The solu- tion to the Falkner-Skan equation has been obtained and discussed by various authors [11–24]. The Falkner-Skan flow over a wedge with moving boundary conditions was investigated in [25–27]. The Falkner-Skan problem for nanofluids over a wedge were recently discussed in [28–33]. The mixed convection Falkner- Skan flows of Maxwell fluid [34–36], Cason fluid [37] and power- law fluid [38] were reported by a number of researchers. The convection heat transfer by the BL flow of constant free stream temperature, T 1 , over the wedge of a constant wall temper- ature, T w , is a classical textbook problem. The solution for the cor- responding heat transfer coefficient, h, is often expressed in terms of local Nusselt number,Nu x ¼ hx=k; in which k is the fluid thermal conductivity. Typical results for Nu x were given in the form of [9,10] Nu x =Re 1=2 x ¼ 0:22 Pr 0:27 ; flow at separation; b ¼ b s ¼0:19883774 ðaÞ 0:332 Pr 1=3 ; flow over a flat plate; b ¼ 0; and 0:5 < Pr < 15 ðbÞ 0:57 Pr 0:4 ; stagnation point flow; b ¼ 1; Pr not too far from 1 ðcÞ 8 > < > : ð2Þ or for flow over a flat plate [8,10]. Nu x =Re 1=2 x ¼ ¼ 0:565 Pr 1=2 ; for Pr  1 ðaÞ ¼ 0:339 Pr 1=3 ; for Pr  1 ðbÞ ( ð3Þ In the above, Re x ¼ xU e =m is the local Reynolds number and Pr, the ratio of fluid kinematic viscosity, m, to its thermal diffusivity, a, is the Prandtl number. Churchill and Ozoe [11] proposed a sim- ilar correlation for flow over a flat plate for the entire range of Pr, 0:886Re 1=2 x Pr 1=2 x =Nu x ¼ 1 þ Pr=0:0207 ð Þ n=6 h i 1=n ð4Þ with an adjustable exponent n. For more general cases, Lin and Lin [22] presented a correlation for forced convection heat transfer from wedges to fluids of any Prandtl number in the form of https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.046 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved. ⇑ Corresponding authors at: Institute of Thermal Science and Power Systems, College of Energy Engineering, Zhejiang University, Hangzhou 310027, PR China (L. Zhang). E-mail addresses: jackway@zju.edu.cn (L. Zhang), rwmei@ufl.edu (R. Mei). International Journal of Heat and Mass Transfer 131 (2019) 101–108 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt