# Heat Transfer of Laminar Mixed Convection of Liquid (Heat by De-Yi Shang, Liang-Cai Zhong

By De-Yi Shang, Liang-Cai Zhong

This booklet provides a brand new set of rules to calculate fluid move and warmth move of laminar combined convection. It offers step by step educational support to benefit quick the way to arrange the theoretical and numerical types of laminar combined convection, to contemplate the variable actual homes of fluids, to acquire the method of numerical options, to create a sequence of formalization equations for the convection warmth move through the use of a curve-fitting  method mixed with theoretical research and derivation. It provides the governing usual differential equations of laminar combined convection, equivalently remodeled through an leading edge similarity transformation with the outline of the similar transformation procedure. A procedure of numerical calculations of the governing traditional differential equations is gifted for the water laminar combined convection. A polynomial version is brought about for handy and trustworthy therapy of variable actual houses of drinks. The built formalization equations of combined convection warmth move coefficient have robust theoretical and sensible price for warmth move functions simply because they're created in accordance with a greater attention of variable actual properties of fluids, actual numerical suggestions and rigorous formalization equations mixed with rigorous theoretical derivation. This e-book is acceptable for clinical researchers, engineers, professors, grasp and PhD scholars of fluid mechanics and convection warmth and mass transfer.

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Extra info for Heat Transfer of Laminar Mixed Convection of Liquid (Heat and Mass Transfer)

Sample text

Where U ¼ À 23 lðr Á W Þ2 þ 2l½e2 is viscous dissipation function, which is further described as @wx 2 @wy 2 @wz 2 @wx @wy 2 @wy @wz 2 Þ þ 2ð Þ þ 2ð Þ þð þ Þ þð þ Þ @x @y @z @y @x @z @y ! 6) can be rewritten as ! rÁW ¼À 1 Dq D 1 ¼q ð Þ q Ds Ds q With the above equation, Eq. 41) can be expressed as the following enthalpy form: DðqhÞ Dp ¼ þ U þ r Á ðkrtÞ Ds Ds ð2:43Þ Dðqcp tÞ Dp þ U þ r Á ðkrtÞ ¼ Ds Ds ð2:44Þ or where h ¼ cp t, while cp is speciﬁc heat. In Cartesian form, the energy Eq. 45) is changed into wx @ðqcp tÞ @ðqcp tÞ @ðqcp tÞ @ @t @ @t @ @t ðk Þ þ ðk Þ þ wy þ wz ¼ ðk Þ þ @x @x @y @y @z @z @x @y @z ð2:46Þ Above equation is usually approximately rewritten as q½wx @ðcp tÞ @ðcp tÞ @ðcp tÞ @ @t @ @t @ @t ðk Þ þ ðk Þ ð2:46aÞ þ wy þ wz  ¼ ðk Þ þ @x @x @y @y @z @z @x @y @z or qcp ½wx @t @t @t @ @t @ @t @ @t þ wy þ wz  ¼ ðk Þ þ ðk Þ þ ðk Þ @x @y @z @x @x @y @y @z @z ð2:46bÞ In fact, in Eq.

W dA þ A k A @t dA @n ð2:30Þ where D Ds Z ! sn ! Z Á W dA ¼ A Z qðe þ V ! W2 Þ dV ¼ 2 Z ! D W2 ½qðe þ Þ dV 2 V Ds ! n ½s Á W dA ¼ A Z ! Z k A ! n ð½s Á W Þ dA ¼ r Á ð½s Á W Þ dV ð2:32Þ A Z @t dA ¼ @n ð2:31Þ V Z r Á ðkrtÞ dV ð2:33Þ V With Eqs. 33), Eq. 30) is rewritten as Z D W2 ½qðe þ Þ dV ¼ 2 V Ds Z ! Z ! q F Á W dV þ V Z r Á ð½s Á W Þ dV þ v r Á ðkrtÞ dV: V ð2:34Þ Then, ! ! D W2 ½qðe þ Þ ¼ q F Á W þ r Á ð½s Á W Þ þ r Á ðkrtÞ Ds 2 where ½s denotes tensor of shear force. 35) is the energy equation.

In Cartesian form, the energy Eq. 45) is changed into wx @ðqcp tÞ @ðqcp tÞ @ðqcp tÞ @ @t @ @t @ @t ðk Þ þ ðk Þ þ wy þ wz ¼ ðk Þ þ @x @x @y @y @z @z @x @y @z ð2:46Þ Above equation is usually approximately rewritten as q½wx @ðcp tÞ @ðcp tÞ @ðcp tÞ @ @t @ @t @ @t ðk Þ þ ðk Þ ð2:46aÞ þ wy þ wz  ¼ ðk Þ þ @x @x @y @y @z @z @x @y @z or qcp ½wx @t @t @t @ @t @ @t @ @t þ wy þ wz  ¼ ðk Þ þ ðk Þ þ ðk Þ @x @y @z @x @x @y @y @z @z ð2:46bÞ In fact, in Eq. 46b) both the temperature-dependent density and speciﬁc heat are ignored.