$(1)$ \[ \begin{align} Re_d&=\frac{ud}{\nu}=\frac{0.15\times4\times10^{-3}}{0.544\times10^{-6}}\\ &=1.103\times10^3\ \Longrightarrow \ 1.10\times10^3\ (<2300) \end{align} \] $(2)$ \[ \begin{align} \frac{\alpha_m\cdot d}{k}&=Nu_m=3.66+\frac{0.0668}{0.04x^{1/3}+x}\\ x&=\frac{\left(x/d\right)}{\left(Re_d\cdot Pr\right)}\\&=\frac{\left(\frac{1.5}{4\times10^{-3}}\right)}{1.103\times10^3\times3.57}=9.523\times10^{-2}\\ \alpha_m&=\frac{k}{d}Nu_m\\&=\frac{0.640}{4\times10^{-3}}\left(3.66+\frac{0.0668}{0.04\times\left(9.523\times10^{-2}\right)^{1/3}+9.523\times10^{-2}}\right)\\ &=679.8\, \rm{w/m^2\cdot K} \end{align} \] $(3)$ \[ \begin{align} \frac{\pi}{4}\alpha^2\cdot \rho u_m\cdot C_p(Tb_2-20)&=nd\times l\times\alpha_m\frac{(100-20)-(100-Tb_2)}{\ln\left(\frac{100-20}{100-Tb_2}\right)}\\ \Longrightarrow \ln\left(\frac{80}{100-Tb_2}\right)&=\frac{\alpha_m\cdot l}{\frac{d}{4}\cdot\rho u_mC_p}\\ \ln(100-Tb_2)&=\ln(80)-\frac{4\alpha_m\cdot l}{d\cdot \rho u_mC_p}\\ 100-Tb_2&=80 \exp\left[-\frac{4\alpha_m\cdot l}{d\cdot\rho u_mC_p}\right]\\ \therefore Tb_2&=100-80 \exp[-1.646]\\ &=84.58\rm{^\circ C}\\ &=84.6\rm{^\circ C} \end{align} \]