Fundamentals of Heat and Mass Transfer

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Three) CH003. qxd 2/24/11 114 12:25 PM web page 114 bankruptcy three ᭿ One-Dimensional, Steady-State Conduction From this outcome it really is obtrusive that, for one-dimensional, steady-state conduction in a aircraft wall without warmth new release and relentless thermal conductivity, the temperature varies linearly with x. Now that we've got the temperature distribution, we may possibly use Fourier’s legislation, Equation 2. 1, to figure out the conduction warmth move cost. that's, qx ϭ ϪkA dT ϭ kA (Ts,1 Ϫ Ts,2) dx L (3. four) word is the world of the wall common to the course of warmth move and, for the airplane wall, it's a consistent self sufficient of x. the warmth flux is then qЉx ϭ qx ok ϭ (T Ϫ Ts,2) A L s,1 (3. five) Equations three. four and three. five point out that either the warmth price qx and warmth flux qЉx are constants, self reliant of x. within the foregoing paragraphs now we have used the normal method of fixing conduction difficulties. that's, the overall answer for the temperature distribution is first acquired through fixing the correct kind of the warmth equation. The boundary stipulations are then utilized to acquire the actual resolution, that is used with Fourier’s legislation to figure out the warmth move cost. notice that we've got opted to prescribe floor temperatures at x ϭ zero and x ϭ L as boundary stipulations, although it is the fluid temperatures, now not the outside temperatures, which are in general identified. besides the fact that, given that adjacent fluid and floor temperatures are simply similar via a floor strength stability (see part 1. three. 1), it's a uncomplicated topic to specific Equations three. three via three. five when it comes to fluid, instead of floor, temperatures. however, an identical effects can be bought at once by utilizing the outside strength balances as boundary stipulations of the 3rd type in comparing the constants of Equation three. 2 (see challenge three. 1). three. 1. 2 Thermal Resistance At this element we observe that, for the exact case of one-dimensional warmth move with out inner power iteration and with consistent houses, a vital thought is advised via Equation three. four. specifically, an analogy exists among the diffusion of warmth and electric cost. simply as an electric resistance is linked to the conduction of electrical energy, a thermal resistance might be linked to the conduction of warmth. Defining resistance because the ratio of a riding capability to the corresponding move cost, it follows from Equation three. four that the thermal resistance for conduction in a airplane wall is Rt,cond ϵ Ts,1 Ϫ Ts,2 ϭ L qx kA (3. 6) equally, for electric conduction within the similar procedure, Ohm’s legislation offers an electric resistance of the shape Re ϭ Es,1 Ϫ Es,2 ϭ L I ␴A (3. 7) CH003. qxd 2/24/11 12:25 PM web page one hundred fifteen three. 1 ᭿ a hundred and fifteen The aircraft Wall The analogy among Equations three. 6 and three. 7 is apparent. A thermal resistance can also be linked to warmth move by way of convection at a floor. From Newton’s legislation of cooling, q ϭ hA(Ts Ϫ Tȍ) (3. eight) The thermal resistance for convection is then Rt,conv ϵ Ts Ϫ Tȍ ϭ 1 q hA (3. nine) Circuit representations supply a great tool for either conceptualizing and quantifying warmth move difficulties.

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