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Fig.7.5 Energy balance for an extended surface A general form of the energy equation for an extended surface is as follows: 2 d T 2 dx ⎛ 1 ⎜ ⎝ Ac dA dx ⎞dT ⎟ ⎠ dx ⎛ 1 − ⎜ ⎝ Ac h dA k dx ⎞ ⎟ ⎠ ( T −T ) = 0 c s + ∞ Its solution for appropriate boundary conditions provides the temperature distribution, which may be used with Fourier’s equation ( dT q x = −kA ) to calculate the conduction rate at any x. dx
LECTURE NO.8 EQUATION OF TEMPERATURE DISTRIBUTION WITH DIFFERENT BOUNDARY CONDITIONS, FIN PERFORMANCE AND OVERALL SURFACE EFFICIENCY OF FINS Fins of Uniform Cross-Sectional Area To solve general form of fin energy equation it is necessary to be more specific about the geometry. We begin with the simplest case of straight rectangular and pin fins of uniform cross section (Figure 8.1). Each fin is attached to a base surface of temperature T(O) = T b and extends into a fluid of temperature T ∞. Fig. 8.1 Straight fins of uniform cross section (a) Rectangular fin (b) Pin fin For the prescribed fins, A c is a constant and A s = P x , where A s is the surface area measured from the base to x and P is the fin perimeter. Accordingly, with dA c /dx = 0 and dA s /dx = P, general form of the energy equation for an extended surface reduces to 2 d T 2 dx hP − kA c ( T − T ) = 0 ∞ --------(1) To simplify the form of this equation, we transform the dependent variable by defining an excess temperature θ as where, since into ∞ Equation (3), we then obtain θ ( x ) = T ( x) −T -------------(2) ∞ T is a constant, d θ / dx = dT / dx . . Substituting Equation (2)
Page 1 and 2: For Class use only ACHARYA N.G. RAN
Page 3 and 4: Simplified Case For Systems With Ne
Page 5 and 6: LECTURE NO.1 INTRODUCTION TO HEAT T
Page 7 and 8: q A k = ( T ) 1 −T 2 -------- (4)
Page 9 and 10: LECTURE NO.2 THE BASIC EQUATION THA
Page 11 and 12: The general three-dimensional heat-
Page 13 and 14: LECTURE NO.3 ONE-DIMENSIONAL STEADY
Page 15 and 16: The cross-sectional area normal to
Page 17 and 18: Total temperature difference, ∆T
Page 19 and 20: LECTURE NO.5 THE OVERALL HEAT-TRANS
Page 21 and 22: Note that the area for convection i
Page 23 and 24: T 1 ,T 0 , K, L, r o , r i are cons
Page 25 and 26: 2 d T 2 dx . q + = 0 k 2 d T q =−
Page 27 and 28: LECTURE NO.7 STEADY STATE HEAT COND
Page 29: Different fin configurations Differ
Page 33 and 34: That is, the rate at which energy i
Page 35 and 36: eason, there is no assurance that t
Page 37 and 38: LECTURE NO.9 PRINCIPLES OF UNSTEADY
Page 39 and 40: where α is k / ρc p , thermal dif
Page 41 and 42: calculate the temperature of the ba
Page 43 and 44: dimensionless numbers can be used i
Page 45 and 46: Repeating this procedure for π 2 a
Page 47 and 48: q k ( Tw T* = ) L " − w The Nusse
Page 49 and 50: The mass transfer analog of the Pra
Page 51 and 52: The transition to turbulent flow oc
Page 53 and 54: long-wavelength thermal radiation.
Page 55 and 56: Figure 11.4 Method of constructing
Page 57 and 58: LECTURE NO.12 INTRODUCTION TO CONDE
Page 59 and 60: are plotted against temperature exc
Page 61 and 62: LECTURE NO.13 HEAT EXCHANGERS- GENE
Page 63 and 64: counterflow to the hot shell-side f
Page 65 and 66: to be calculated in the above equat
Page 67 and 68: divided by the natural logarithm of
Page 69 and 70: Figure 13.7 Correction-factor plot
Page 71 and 72: Then, Since q= UA ∆T m , 5 1.895
Page 73 and 74: 3.8 A = = 0.0104 (1000 )(0.366 ) m
Page 75 and 76: LECTURE NO.15 INTRODUCTION TO MASS
Page 77 and 78: concentration of water vapor at the
Page 79 and 80: T is temperature in K, R is 8314.3
Page 81 and 82:
Equating Eq. J J * Az = −D AB dc
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