. The London, Edinburgh and Dublin philosophical magazine and journal of science. «y« ag y/8 A similar equation holds for ^râ-â. 3*2Noticing that 3*^3/3 = 1 3^=__M = o3*i 3*2 V 3*2 3*i V2« = 0, and V2£ = 0> we get 3*0 , W_£/W^BV\ 3*i2 + 3*22 V2 \3*2 + 3/32/ We also have 30 _30 q3*2 - 3/3 V* from a Body cooled by a Stream of Fluid. 597 Hence, substituting these values in (5), we get ^cVW + W ⢠w which is a much simpler equation than (5) as the coefficientof the right-hand side is a constant quantity. Our assumptions allow us to simplify this equation stillfurther. Since the liquid is a
. The London, Edinburgh and Dublin philosophical magazine and journal of science. «y« ag y/8 A similar equation holds for ^râ-â. 3*2Noticing that 3*^3/3 = 1 3^=__M = o3*i 3*2 V 3*2 3*i V2« = 0, and V2£ = 0> we get 3*0 , W_£/W^BV\ 3*i2 + 3*22 V2 \3*2 + 3/32/ We also have 30 _30 q3*2 - 3/3 V* from a Body cooled by a Stream of Fluid. 597 Hence, substituting these values in (5), we get ^cVW + W ⢠w which is a much simpler equation than (5) as the coefficientof the right-hand side is a constant quantity. Our assumptions allow us to simplify this equation stillfurther. Since the liquid is a very bad conductor of heat,6 alters very rapidly with a but very slowly with /5. Theterm d20/B/32 is also negligibly small compared with B2#/c)« thus obtain the equation M -1 ?!? m d/3~cVB*2 K J the solution of: which has been put into various forms byFourier and others. 5. Circular shall now consider the problem of the cooling of acircular cylinder immersed in a stream of liquid with its axishorizontal and at right angles to the direction of flow. Fig. 2. * ^K n/ U5/\j o 45°\yA 5/. ream lin*& ctj Fluid (fowi/yg past ; & A °re ^e tWo aity&ular equipo/eKtfia/ curves. Let us take the origin of co-ordinates on the axis of thecylinder, and let us suppose that the liquid is flowing with 598 Dr. A. Russell on the Convection of Heat velocity V in the direction XO, and that its temperature iszero before it meets the this case we know * that ami
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