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# 5a-r - Transient Conduction The Lumped Capacitance Method...

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Transient Conduction: Transient Conduction: The Lumped Capacitance Method The Lumped Capacitance Method Chapter Five Chapter Five Sections 5.1 thru 5.3 Sections 5.1 thru 5.3

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Transient Conduction Transient Conduction Transient Conduction • A heat transfer process for which the temperature varies with time , as well as location within a solid. • It is initiated whenever a system experiences a change in operating conditions and proceeds until a new steady state ( thermal equilibrium ) is achieved. • It can be induced by changes in: – surface convection conditions ( ), , hT • Solution Techniques –T h e Lumped Capacitance Method Exact Solutions The Finite-Difference Method – surface radiation conditions ( ), , rs u r – a surface temperature or heat flux, and/or – internal energy generation.
Lumped Capacitance Method Lumped Capacitance Method The Lumped Capacitance Method • Based on the assumption of a spatially uniform temperature distribution throughout the transient process. • Why is the assumption never fully realized in practice? • General Lumped Capacitance Analysis: ¾ Consider a general case, which includes convection, radiation and/or an applied heat flux at specified surfaces as well as internal energy generation () ,,, ,, , s cs rs h AAA Hence, . , Tr t Tt ⎛⎞ ⎜⎟ ⎝⎠

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Lumped Capacitance Method (cont.) Lumped Capacitance Method (cont.) ¾ First Law: st in out g dE dT cE E E dt dt ρ =∀ = − + ± ±± Assuming energy outflow due to convection and radiation and with inflow due to an applied heat flux , s q ′′ ()() ,, , g ss h s c rs r s u r dT cq A h A T T h A T T E dt ∀= −+ ± • Is this expression applicable in situations for which convection and/or radiation provide for energy inflow? •M ay h and h r be assumed to be constant throughout the transient process?
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5a-r - Transient Conduction The Lumped Capacitance Method...

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