. The London, Edinburgh and Dublin philosophical magazine and journal of science. ous one. The surface of the solid being cooled by the current issupposed to be isothermal, and the liquid in immediatecontact with it at any instant is supposed to have the sametemperature as the solid. These two assumptions are quitelegitimate. 4. Flow in Two Dimensions. Making the above assumptions we shall now obtain thedifferential equation which determines the temperature atany point of the liquid, once the steady state has beenestablished. Let us suppose that the velocity of the liquid at a greatdistance fr
. The London, Edinburgh and Dublin philosophical magazine and journal of science. ous one. The surface of the solid being cooled by the current issupposed to be isothermal, and the liquid in immediatecontact with it at any instant is supposed to have the sametemperature as the solid. These two assumptions are quitelegitimate. 4. Flow in Two Dimensions. Making the above assumptions we shall now obtain thedifferential equation which determines the temperature atany point of the liquid, once the steady state has beenestablished. Let us suppose that the velocity of the liquid at a greatdistance from the solid being cooled is V. In our problem * Nuov. Cim. xxx. p. 33 (1891).t Phil. Trans, clxxxiii. part i. p. 371 (1892).% Nuov. Cim. iv. p. 81 (1890;. § L. c. ante. j| Jom-n. Inst. Elect, Engin. xxxv. p. 364 (1905).f Brit. AssocKeport,.1898. In this report Sir G. G. Stokes gives atheoretical proof of the method. , from a Body cooled by a Stream of Fluid. 595 it is convenient to denote the kydrodynamical stream-function by Va, and the velocity-potential by V/3. h\ fig. 1,. CL+OCL AA and BB denote adjacent stream-lines, and AB andAB denote adjacent equipotential curves. Let and let Then, by hydrodynamics, AA = d*2, AB = 0*i. oV£ 0*2 = ?> (3) where g is the velocity of the flow of the liquid at the point Consider the flow of heat in the time Dt into a prismhaving unit length, and having ABBA for its cross-section(fig. 1). We suppose that this prism is moving with theliquid, and its velocity is therefore q. Let 6 be the initialtemperature of the liquid inside this prism, and let 0 + 1)9 bethe temperature at the time J)t. The gain by the flow of heatfrom AA to BB/ during this interval is and the oain by the flow from AB to AB is o# 0*2 \ 0*2/ where k is the conductivity of the liquid. Hence, if c denotethe capacity for heat of the liquid per unit volume, the gainof heat by the element contained by the prism is cd*iO*2 D0. 2R2 596 Dr. A. Russell on the Convection of Heat We
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