Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet

Table 1

Values of dimensionless film thickness 𝛽 and skin friction 𝑓^′′(0) when Pr=1, 𝑀=0, 𝑁_𝑅=0, ℏ_𝑓=−0.6, and ℏ_𝜃=−0.4 for different values of unsteadiness parameter 𝑆. The value of 𝑓^′′(0)/𝛽 in Wang [4] and the present work is the same as that of Abel et al. [14] despite different similarity transformations used.

	Wang [4]		Abel et al. [14]		Mahmoud [24]		Present work
𝑆	𝛽	𝑓^′′(0)/𝛽	𝛽	𝑓^′′(0)	𝛽	𝑓^′′(0)	𝛽	𝑓^′′(0)/𝛽
0.4	5.122490	−1.307785	4.981455	−1.134098	—	—	5.126821	−1.040765
0.6	3.131250	−1.195155	3.131710	−1.195128	—	—	3.131668	−1.193654
0.8	2.151990	−1.245795	2.151990	−1.245805	2.1519950	−1.245810	2.151994	−1.245793
1.0	1.543617	−1.277762	1.543617	−1.277769	—	—	1.543616	−1.277768
1.2	1.127780	−1.279177	1.127780	−1.279171	1.1277815	−1.279170	1.127780	−1.279172
1.4	0.821032	−1.233549	0.821033	−1.233545	—	—	0.821032	−1.233549
1.6	0.567173	−1.114937	0.576176	−1.114941	—	—	0.576173	−1.114937
1.8	0.356389	−0.867414	0.356390	−0.867416	—	—	0.356389	−0.867414