Dual Solutions on Thermosolutal Marangoni Forced Convection Boundary Layer with Suction and Injection

Table 1

Values of 𝑓^(0), −𝜃^(0), and −ℎ^(0) for 𝜀=0 (absent Marangoni effect) and 𝑓₀=0 (impermeable surface) for different values of 𝛽 when Pr=0.7.

		Pop et al. [21]						Present
𝛽	𝑓0	𝑓^(0)	−𝜃^(0)	−ℎ^(0)				𝑓^(0)	−𝜃^(0)	−ℎ^(0)
0.1	−1							20.42222 (7.52155)	2.73049 (1.39352)	1.33457 (0.55567)	2.50450 (1.25965)	2.83556 (1.45391)	2.89636 (1.48832)
	0							5.63217 (1.13296)	1.66616 (0.63301)	0.81816 (0.34081)	1.52112 (0.57999)	1.73479 (0.65856)	1.77485 (0.67361)
	1							2.18587 (0.32671)	1.51789 (0.81825)	0.69038 (0.36368)	1.36228 (0.72258)	1.59367 (0.86650)	1.63858 (0.89559)
0.2	−1							6.88979 (3.22734)	1.70167 (0.89556)	0.91512 (0.42147)	1.57757 (0.81507)	1.75892 (0.93265)	1.79192 (0.95395)
	0							3.14160 (0.96668)	1.40729 (0.58243)	0.72749 (0.30936)	1.29013 (0.53105)	1.46279 (0.60744)	1.49521 (0.62224)
	1							1.87556 (0.23194)	1.54931 (0.65695)	0.72307 (0.29068)	1.39337 (0.57422)	1.62523 (0.69967)	1.67021 (0.72573)
0.3	−1							4.09080 (2.49526)	1.38372 (0.82414)	0.78472 (0.39756)	1.29037 (0.75041)	1.42662 (0.85849)	1.45130 (0.87834)
	0							2.44523 (0.97452)	1.34800 (0.54113)	0.71088 (0.26932)	1.23812 (0.48650)	1.40007 (0.56816)	1.43051 (0.58430)
	1							1.73727 (0.24512)	1.59029 (0.43442)	0.75025 (0.20410)	1.43243 (0.37519)	1.66711 (0.46669)	1.71261 (0.48694)
0.4	−1							3.09833 (2.2474)	1.26054 (0.14478)	0.73410 (0.36768)	1.17886 (0.56070)	1.29804 (7.84348)	1.31959 (1.83203)
	0							2.14605 (1.08908)	1.34240 (0.35840)	0.71485 (0.22042)	1.23425 (0.35627)	1.39369 (0.34761)	1.42366 (0.33547)
	1							1.65874 (0.34764)	1.62937 (−1.28801)	0.77466 (0.07600)	1.46934 (−0.48622)	1.70719 (−2.35420)	1.75326 (−3.77805)
0.5	−1							2.63924	1.21201	0.71510	1.13497	1.24737	1.26770
	0	1.98426	1.35416	0.72496	1.24583	1.40553	1.43556	1.98427	1.35417	0.72506	1.24583	1.40553	1.43556
	1							1.60781	1.66444	0.79602	1.50233	1.74322	1.78986
1.0	−1							1.98027	1.21194	0.72270	1.13609	1.24683	1.26692
	0	1.69687	1.44233	0.77894	1.32869	1.49624	1.52774	1.69687	1.44233	0.77786	1.32866	1.49623	1.52774
	1							1.49425	1.78801	0.86768	1.61811	1.87042	1.91915
2.0	−1							1.74213	1.29145	0.77020	1.21009	1.32898	1.35062
	0	1.56595	1.55062	0.84232	1.42944	1.60807	1.64166	1.56595	1.55061	0.84097	1.42942	1.60807	1.64166
	1							1.42871	1.90694	0.93762	1.72918	1.99303	2.04390
5.0	−1							1.61621	1.38658	0.82498	1.29840	1.42734	1.45087
	0	1.48856	1.65944	0.90415	1.53047	1.72058	1.75632	1.48857	1.65943	0.90322	1.53045	1.72057	1.75631
	1							1.38478	2.01946	1.00309	1.83407	2.10912	2.16207
Sc				0.22	0.60	0.75	0.78			0.22	0.60	0.75	0.78