Hot wastewater of a heat recovery system is flowing through a concrete conduct(k = 1.4 W/m-K) of square cross section. The flow section of the duct is 40 cm x 40%3Dcm, and the thickness of the wall is 10 cm as shown in figure (next page). Theaverage temperature of the hot water in the conduct is T, = 300°C. The conduct is%3Dlosing heat from its outer surface to the ambient air at T 12°C by convectionwith a heat transfer coefficient of h = 35 W/m2 K. Using the finite difference%3Dmethod with Ar Ay 5 cm and taking full advantage of symmetry:a) obtain the finite difference formulation of this problem for steady two-dimensional heat transfer.b) determine the temperatures at the nodal points of a cross section.c) evaluate the rate of heat loss for a 1-m-long section of the conduct.

Given Datak=1.4W/mKt=10cmh=35W/m2K△x=△y=5cm=0.05mT∞=12°CTi=300°C

Hot wastewater of a heat recovery system is flowing through a concrete conduct (k = 1.4 W/m-K) of square cross section. The flow section of the duct is 40 cm x 40 cm, and the thickness of the wall is 10 cm as shown in figure (next page). The average temperature of the hot water in the conduct is T, = 300°C. The conduct is %3D losing heat from its outer surface to the ambient air at T = 12°C by convection %3D with a heat transfer coefficient of h 35 W/m2 K. Using the finite difference %3D method with Ax = Ay = 5 cm and taking full advantage of symmetry: a) obtain the finite difference formulation of this problem for steady two- dimensional heat transfer. b) determine the temperatures at the nodal points of a cross section. c) evaluate the rate of heat loss for a 1-m-long section of the conduct.

Hot wastewater of a heat recovery system is flowing through a concrete conduct (k = 1.4 W/m-K) of square cross section. The flow section of the duct is 40 cm x 40 cm, and the thickness of the wall is 10 cm as shown in figure (next page). The average temperature of the hot water in the conduct is T, = 300°C. The conduct is %3D losing heat from its outer surface to the ambient air at T = 12°C by convection %3D with a heat transfer coefficient of h 35 W/m2 K. Using the finite difference %3D method with Ax = Ay = 5 cm and taking full advantage of symmetry: a) obtain the finite difference formulation of this problem for steady two- dimensional heat transfer. b) determine the temperatures at the nodal points of a cross section. c) evaluate the rate of heat loss for a 1-m-long section of the conduct.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter10: Heat Exchangers

Section: Chapter Questions

Problem 10.28P

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