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An expression for the midplane temperature T o may be obtained through an energy balance. At steady-state conditions the total heat generated must equal the heat lost at the faces. Thus ⎛ 2⎜− KA ⎝ dT dx ⎤ ⎥ ⎦ x= L ⎞ • ⎟= q. A.2L ⎠ where A is the cross-sectional area of the plate. The temperature gradient at the wall is obtained by differentiating Equation (4): T −T0 T −T w 0 ⎛ = ⎜ ⎝ x L 2 ⎞ ⎟ ⎠ T −T x ⎝L ⎛ ⎞ 0 = ( Tw −T0 ) ⎜ ⎟ ⎠ 2x dT = w 0 . 2 L ( T −T ) dx dT ⎤ ⎦ at x= L ( T T ) dx ⎥ = w− o . L x= L 2 2 Since, dT −K. dx = q • L dT dx • q L = − K • qL T w − 2 0 =− L K ( T ) • 2 qL T w −T 0 =− 2K • 2 qL T 0 = + T w 2K ----- (5)
LECTURE NO.7 STEADY STATE HEAT CONDUCTION WITH HEAT DISSIPATION TO ENVIRONMENT- INTRODUCTION TO EXTENDED SURFACES (FINS) OF UNIFORM AREA OF CROSS SECTION - DIFFERENT FIN CONFIGURATIONS - GENERAL CONDUCTION ANALYSIS EQUATION Steady State heat conduction with heat dissipation to environment: Introduction to extended surfaces (FINS) of Uniform area of cross section The term extended surface is commonly used to depict an important special case involving heat transfer by conduction within a solid and heat transfer by convection (and/or radiation) from the boundaries of the solid. Heat transfer from the boundaries of a solid to be in the same direction as heat transfer by conduction in the solid. In contrast, for an extended surface, the direction of heat transfer from the boundaries is perpendicular to the principal direction of heat transfer in the solid. Fig. 7.1 Combined conduction and convection in a structural element. Consider a strut that connects two walls at different temperatures and across which there is fluid flow (Figure 7.1). With T 1 >T 2 , temperature gradients in the x-direction sustain heat transfer by conduction in the strut. However, with T 1 >T 2 > T∞there is concurrent heat transfer by convection to the fluid, causing q x , and hence the magnitude of the temperature gradient, decrease with increasing x. dT / dx An extended surface is used specifically to enhance heat transfer between a solid and adjoining fluid. Such an extended surface is termed a fin. , to
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: 2 d T 2 dx . q + = 0 k 2 d T q =−
Page 29 and 30: Different fin configurations Differ
Page 31 and 32: LECTURE NO.8 EQUATION OF TEMPERATUR
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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