3 An experimental nuclear core simulation apparatusconsists of a long thin-walled metallic tube of diameterD and length L, which is electrically heated to producethe sinusoidal heat flux distribution q_{s}^{\prime \prime}(x)=q_{o}^{\prime

\prime} \sin \left(\frac{\pi x}{L}\right) where x is the distance measured from the tube inlet.Fluid at an inlet temperature T flows through the tube at a rate of m. Assuming the flow is turbulent and fully developed over the entire length of the tube, develop expressions for ession) the total rate of heat transfer, q, from the tube to thefluid; the fluid outlet temperature, Tmom,0> (c) the axial distribution of the wall temperature, T,(x);and (d) the magnitude and position of the highest wall temperature. (e) Consider a 40-mm-diameter tube of 4-m length with a sinusoidal heat flux distribution for which g =10,000 W/m?. Fluid passing through the tube has a flow rate of 0.025 kg/s, a specific heat of 4180 J/kg · K, an entrance temperature of 25°C, and a convection coefficient of 1000 W/m2 · K. Plot the mean fluid and surface temperatures as a function of distance along the tube. Identify important features of the distributions. Explore the effect of±25% changes in the convection coefficient and the heat flux on the distributions.