2) approximate nusselt number for pipe flow with surface heat flux condition while using approximate integral methods, we typically start with a guess for the temperature or the velocity profile. we can use a similar approach to study the case of fully developed flow in a pipe of radius , and with a constant surface heat flux, ′′. the fluid flow solution for the hagen-poiseuille flow is known to be =−)2) suppose we guess that the temperature profile in the fully developed region can be approximated by a 2nd order polynomial of the form =−−=+)+)2 where and are the surface and mean temperature, respectively, at location a. write down the three boundary conditions required to solve for , , and . solve for the coefficients and show that =′′−−)2). (hint: you can assert both a temperature and a heat flux boundary condition at =.) b. now using a process similar to that used by the book in equations 8.50 → 8.53, solve for i. the mean fluid temperature, =∫ ii. the convection coefficient, ℎ iii. the nusselt number, how does this compare with for the exact solution?