7. Consider an element that conducts heat as shown below with length L, cross sectional area A, and heat conductance k. Nodes 1 and 2 have temperatures of T, and T2. The heat flux q due to conduction is given by: dT - ~ – k=- dx ΔΤ q = - k Ax This relationship is analogous to Hooke's Law from the prior problem. Heat transfer by conduction Qc is given by: Oc = qA Use equilibrium requirements to solve for the heat transfer by conduction Qci and Qcz at the nodes and use these equations to derive a "conductance matrix" (or the stiffness matrix due to conduction which is the analog of the stiffness matrix) for this heat conducting element. For the sign convention, consider heat flux positive when heat flows into the element and negative when it flows out of the element. Show your full matrix equation and the conductance matrix. Oci T T2 Oc2

7. Consider an element that conducts heat as shown below with length L, cross sectional area A, and heat conductance k. Nodes 1 and 2 have temperatures of T, and T2. The heat flux q due to conduction is given by: dT - ~ – k=- dx ΔΤ q = - k Ax This relationship is analogous to Hooke's Law from the prior problem. Heat transfer by conduction Qc is given by: Oc = qA Use equilibrium requirements to solve for the heat transfer by conduction Qci and Qcz at the nodes and use these equations to derive a "conductance matrix" (or the stiffness matrix due to conduction which is the analog of the stiffness matrix) for this heat conducting element. For the sign convention, consider heat flux positive when heat flows into the element and negative when it flows out of the element. Show your full matrix equation and the conductance matrix. Oci T T2 Oc2

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 4.52P

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