1. The problem statement, all variables and given/known data Perform a one-dimensional energy balance for the heating of a fluid through a hot pipe in order to develop a differential equation that governs the variation of the mean temperature of the fluid along the length pipe. The pipe has an inner diameter D and length L; its walls are kept at a constant temperature Tw. The fluid has a mean velocity v. The heat transfer coefficient h between the pipe wall and the fluid is constant, and the radial convective heat flux q is: q = hA(Tw − T ) where T is the mean temperature of the fluid. If the fluid has a mean inlet temperature To, solve the above differential equation to obtain an expression for the variation of the temperature with the distance x along the pipe. For this part of the problem, you can neglect the influence of conduction (i.e. assume k ≈ 0) and assume heat transfer along the pipe only occurs through convection. 2. Relevant equations Accumulation=in-out+generation Generation=0 3. The attempt at a solution 0=q(x)A(x)-q(x+deltax)A(x+deltax)+h(Tw-T)A+p(x)A(x)v1-p(x)A(x+deltax)v2 =>d/dx[rho*v*U(x)A(x)]+d/dx[p(x)A(x)v]=h(Tw-T)A/deltax Any help will be greatly appreciated. Thanks.