A thin flat plate of length L, thickness t, and width W>>L is thermally joined to two large heat sinks that are maintainedat a temperature To. The bottom of the plate is well insulated, while the net heat flux to the top surface of the plate isknown to have a uniform value of q”o.(a) Derive the differential equation thatdetermines the steady-statetemperature distribution T(x) in theplate.(b) Solve the foregoing equation for thetemperature distribution, and obtainan expression for the rate of heattransfer from the plate to the heatsinksAnswer: (b) q=2(9 WL/2)=qő WL.xHeat9%HeatsinksinkToTo

Answered: A thin flat plate of length L,…

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.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.44P

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H.W.: Q1: Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The temperatures at the selected nodes and the thermal conditions at the boundaries are as shown. The thermal conductivity of the body is k = 45 W/m. °C, and heat is generated in the body uniformly at a rate of g = 6 x 106 W/m3. Using the finite difference method with a mesh size of Ax = Ay = 5.0 cm, determine (a) the temperatures at nodes 1, 2, and 3 and (b) the rate of heat loss from the bottom surface through a 1-m-long section of the body. . 200°C 5 cm 5 cm g=6x 10 W/m² 260 3 240 305 290 Insulation 1 Convection T₂= 20°C, h= 50 W/m² °C 350°C 325

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