90 90 Heating element Heating element 1. A viscous fluid with temperature independent physical properties is in fully developed, frictionless, laminar flow between two flat surfaces placed at a distance 2B apart. For z = 0 heat is added at a constant, uniform flux, qo at both walls. This leads to forced convection in the channel as heat is carried by the flowing fluid. As v.(x) Direction of flow Fully developed slit flow at z = 0; inlet temperature is T X=-B X=+B a) Solve the momentum balance equation to get the velocity profile for the upward fluid flow inside the space between two plates assuming velocity is a function of x only. 6 Marks b) Use the answer of a) and obtain the governing equation for forced convection where temperature is a function of both x and z. Identify the terms based on their physical significance. Give reasoning of all assumptions including neglecting axial conduction and viscous dissipation through the equations. 5 Marks c) Convert the dimensioned equation from b) into dimensionless equation in terms of the following dimensionless temperature and dimensionless distances: 3 Marks T-T 0 = (40B/R) 7 0 = B kz y= PCpvz,maxB2 d) Solve the dimensionless energy balance equation to obtain the dimensionless temperature profile as a function of o and y for a significantly large value of y. Explain and use appropriate boundary conditions based on the problem definition. 9 Marks