A fluid \(\left(\rho=1000 \mathrm{~kg} / \mathrm{m}^{3}, \mu=1.4 \times 10^{-3} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\right.\), \(c_{p}=4.2 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\), and \(\left.k=0.58 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\right)\) flows with an average velocity of \(0.3 \mathrm{~m} / \mathrm{s}\) through a \(14-\mathrm{m}\) long tube with inside diameter of \(0.01 \mathrm{~m}\). Heat is uniformly added to the entire tube at the rate of \(1500 \mathrm{~W} / \mathrm{m}^{2}\). Determine \((a)\) the value of convection heat transfer coefficient at the exit, \((b)\) the value of \(T_{s}-T_{m}\), and (c) the value of \(T_{e}-T_{i}\).

Question: Calculate the convection heat transfer coefficient at the exit, the temperature difference between the tube surface and the fluid's mean temperature, and the temperature difference between the exit and the inlet of the tube. given the fluid's density is 1000 kg/m³, the average velocity is 0.3 m/s, the tube's inside diameter is 0.01 m, the dynamic viscosity is 1.4 x 10⁻³ kg/(m·s), the specific heat capacity is 4.2 x 10³ J/(kg·K), the thermal conductivity is 0.58 W/(m·K), and the heat flux is 1500 W/m². Answer: To calculate the convection heat transfer coefficient (h), the temperature difference between the tube surface and the fluid's mean temperature (Ts - Tm), and the temperature difference between the exit and the inlet (Te - Ti), follow the step-by-step solution provided. Use the given fluid properties, average velocity, tube inside diameter, and heat flux to find the final answer.