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Both bounds and are increasing functions of, and.
Since, for each and, for each, then and are increasing functions of.
It is easily proved that for a fixed, and are monotonically increasing functions of.
From the numerical computation, the mean, mode and standard deviation are increasing functions of q.
For fixed ( alpha ), the mean and skewness are increasing functions of β.
Temperature and wall heat flux are increasing functions of convective heating parameter (Biot number).
For α≤ 1, the skewness and kurtosis are decreasing functions of q but increasing functions of β.
It is evident from these figures that both θ and φ are increasing functions of N t.
From Table 1, the mean, mode and standard deviation are decreasing functions of β but increasing functions of α.
In fact, Theorem 2 implies that (r_{2}(n)) and (r_{3}(n)) are strictly increasing functions of n.
From Figure 4(b) we observe that the wall heat transfer rates for the nanofluids are increasing functions of ϕ.
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