{"id":490279,"date":"2024-07-06T22:18:00","date_gmt":"2024-07-06T21:18:00","guid":{"rendered":"https:\/\/www.thermal-engineering.org\/%e0%a4%ae%e0%a4%b9%e0%a4%be%e0%a4%b8%e0%a4%be%e0%a4%97%e0%a4%b0-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b0%e0%a4%a3-%e0%a4%ae%e0%a5%89%e0%a4%a1%e0%a4%b2%e0%a4%bf%e0%a4%82%e0%a4%97\/"},"modified":"2024-07-06T22:18:00","modified_gmt":"2024-07-06T21:18:00","slug":"%e0%a4%ae%e0%a4%b9%e0%a4%be%e0%a4%b8%e0%a4%be%e0%a4%97%e0%a4%b0-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b0%e0%a4%a3-%e0%a4%ae%e0%a5%89%e0%a4%a1%e0%a4%b2%e0%a4%bf%e0%a4%82%e0%a4%97","status":"publish","type":"post","link":"https:\/\/www.thermal-engineering.org\/hi\/%e0%a4%ae%e0%a4%b9%e0%a4%be%e0%a4%b8%e0%a4%be%e0%a4%97%e0%a4%b0-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b0%e0%a4%a3-%e0%a4%ae%e0%a5%89%e0%a4%a1%e0%a4%b2%e0%a4%bf%e0%a4%82%e0%a4%97\/","title":{"rendered":"\u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u092a\u0930\u093f\u0938\u0902\u091a\u0930\u0923 \u092e\u0949\u0921\u0932\u093f\u0902\u0917"},"content":{"rendered":"

\u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u092a\u0930\u093f\u0938\u0902\u091a\u0930\u0923 \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0907\u0938 \u0932\u0947\u0916 \u092e\u0947\u0902, \u092e\u0939\u093e\u0938\u093e\u0917\u0930\u094b\u0902 \u0915\u0940 \u090a\u0937\u094d\u092e\u0940\u092f \u0917\u0924\u093f\u0915\u0940 \u0914\u0930 \u091c\u0932\u0935\u093e\u092f\u0941 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935\u094b\u0902 \u092a\u0930 \u0938\u0930\u0932 \u0914\u0930 \u0938\u094d\u092a\u0937\u094d\u091f \u0935\u093f\u0935\u0947\u091a\u0928\u093e\u0964<\/p>\n

\"\u092e\u0939\u093e\u0938\u093e\u0917\u0930<\/p>\n

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\u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u092a\u0930\u093f\u0938\u0902\u091a\u0930\u0923 \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u090f\u0915 \u0905\u0924\u094d\u092f\u0927\u093f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0936\u093e\u0916\u093e \u0939\u0948 \u091c\u094b \u0909\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948 \u091c\u094b \u092e\u0939\u093e\u0938\u093e\u0917\u0930\u0940\u092f \u091c\u0932 \u0915\u0947 \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923 \u0914\u0930 \u0909\u0938\u0915\u0940 \u0935\u093f\u0935\u093f\u0927\u0924\u093e \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0938 \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u092e \u091c\u0932\u0935\u093e\u092f\u0941 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928, \u0938\u092e\u0941\u0926\u094d\u0930\u0940 \u092a\u093e\u0930\u093f\u0938\u094d\u0925\u093f\u0924\u093f\u0915\u0940 \u0924\u0902\u0924\u094d\u0930 \u0914\u0930 \u0935\u093f\u0926\u094d\u092f\u0941\u0924 \u0909\u0924\u094d\u092a\u093e\u0926\u0928 \u091c\u0948\u0938\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u0939\u0932\u0941\u0913\u0902 \u0915\u094b \u0938\u092e\u091d \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n

\u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u092a\u0930\u093f\u0938\u0902\u091a\u0930\u0923 \u0915\u0947 \u0924\u0924\u094d\u0935<\/h2>\n

<\/p>\n

  • \u0924\u093e\u092a\u0940\u092f \u0935\u093f\u0938\u094d\u0924\u093e\u0930<\/li>\n
  • \u0932\u0935\u0923\u0924\u093e<\/li>\n
  • \u092a\u0935\u0928 \u092c\u0932<\/li>\n
  • \u0938\u092e\u0941\u0926\u094d\u0930\u0940 \u0927\u093e\u0930\u093e\u090f\u0901<\/li>\n

    <\/u1><\/p>\n

    \u0924\u093e\u092a\u0940\u092f \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0914\u0930 \u0932\u0935\u0923\u0924\u093e<\/h2>\n

    \u092e\u0939\u093e\u0938\u093e\u0917\u0930\u094b\u0902 \u092e\u0947\u0902 \u091c\u0932 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 \u0914\u0930 \u0909\u0938\u092e\u0947\u0902 \u0918\u0941\u0932\u0947 \u0939\u0941\u090f \u0932\u0935\u0923 \u0915\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u092a\u094d\u0930\u092e\u0941\u0916 \u0915\u093e\u0930\u0915 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u091c\u0932 \u0915\u0940 \u0918\u0928\u0924\u094d\u0935 \u0935\u093f\u0935\u093f\u0927\u0924\u093e \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u093e\u092a\u0940\u092f \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \u091c\u092c \u091c\u0932 \u0917\u0930\u094d\u092e \u0939\u094b\u0924\u093e \u0939\u0948 \u0924\u094b \u0909\u0938\u0915\u093e \u0918\u0928\u0924\u094d\u0935 \u0915\u092e \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u092f\u0939 \u090a\u092a\u0930\u0940 \u0938\u0924\u0939 \u092a\u0930 \u0906 \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u0940 \u0913\u0930, \u0920\u0902\u0921\u093e \u091c\u0932 \u0905\u0927\u093f\u0915 \u0918\u0928\u0924\u094d\u0935 \u0935\u093e\u0932\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 \u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u0915\u0940 \u0917\u0939\u0930\u093e\u0908 \u092e\u0947\u0902 \u091a\u0932\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n

    \u092a\u0935\u0928 \u092c\u0932<\/h2>\n

    \u092a\u0935\u0928 \u092c\u0932 \u092e\u0939\u093e\u0938\u093e\u0917\u0930\u094b\u0902 \u0915\u0947 \u091c\u0932 \u0915\u094b \u0938\u0924\u0939 \u092a\u0930 \u091a\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u091c\u092c\u0942\u0930 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0924\u0939\u0940 \u0927\u093e\u0930\u093e\u0913\u0902 \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f \u0917\u0932\u094d\u092b \u0938\u094d\u091f\u094d\u0930\u0940\u092e \u0914\u0930 \u092d\u093e\u0930\u0924-\u0911\u0938\u094d\u091f\u094d\u0930\u0947\u0932\u093f\u092f\u093e \u092e\u093e\u0928\u0938\u0942\u0928 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e\u0964 \u092a\u0935\u0928 \u0914\u0930 \u0917\u0930\u094d\u092e\u0940 \u0926\u094b\u0928\u094b\u0902 \u0939\u0940 \u092e\u093f\u0932\u0915\u0930 \u0907\u0928 \u0927\u093e\u0930\u093e\u0913\u0902 \u0915\u094b \u0938\u0902\u091a\u093e\u0932\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n

    \u0938\u092e\u0941\u0926\u094d\u0930\u0940 \u0927\u093e\u0930\u093e\u090f\u0902<\/h2>\n

    \u092e\u0939\u093e\u0938\u093e\u0917\u0930\u0940\u092f \u0927\u093e\u0930\u093e\u090f\u0902 \u092c\u0921\u093c\u0947 \u091c\u0932 \u0928\u093f\u0915\u093e\u092f\u094b\u0902 \u092e\u0947\u0902 \u091c\u0932 \u0915\u094b \u090f\u0915 \u0938\u094d\u0925\u093e\u0928 \u0938\u0947 \u0926\u0942\u0938\u0930\u0947 \u0938\u094d\u0925\u093e\u0928 \u0924\u0915 \u0932\u0947 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0928 \u0927\u093e\u0930\u093e\u0913\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0915\u0947 \u091c\u0932\u0935\u093e\u092f\u0941 \u0935\u093f\u091c\u094d\u091e\u093e\u0928\u093f\u092f\u094b\u0902 \u0915\u094b \u092e\u094c\u0938\u092e \u0915\u0940 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u093e\u0923\u0940 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964 \u0927\u093e\u0930\u093e\u090f\u0902 \u0926\u094b \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902:<\/p>\n

    <\/p>\n

  • \u0938\u0924\u0939\u0940 \u0927\u093e\u0930\u093e\u090f\u0902<\/li>\n
  • \u0917\u0939\u0930\u0947 \u091c\u0932 \u0927\u093e\u0930\u093e\u090f\u0902<\/li>\n

    <\/o1><\/p>\n

    \u0938\u0924\u0939\u0940 \u0927\u093e\u0930\u093e\u0913\u0902 \u0915\u094b \u092e\u0941\u0916\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u092a\u0935\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u0902\u091a\u093e\u0932\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u092c\u0915\u093f \u0917\u0939\u0930\u0947 \u091c\u0932 \u0927\u093e\u0930\u093e\u0913\u0902 \u0915\u094b \u0924\u093e\u092a\u0940\u092f \u0914\u0930 \u0932\u0935\u0923\u0924\u093e \u092c\u0926\u0932\u093e\u0935\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u0902\u091a\u093e\u0932\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n

    \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u0924\u0915\u0928\u0940\u0915<\/h2>\n

    \u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u092a\u0930\u093f\u0938\u0902\u091a\u0930\u0923 \u092e\u0949\u0921\u0932\u093f\u0902\u0917 \u0915\u0947 \u0932\u093f\u090f \u0917\u0923\u093f\u0924\u0940\u092f \u092e\u0949\u0921\u0932 \u0914\u0930 \u0938\u093f\u092e\u0941\u0932\u0947\u0936\u0928\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u0941\u091b \u092a\u094d\u0930\u092e\u0941\u0916 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u092e\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902:<\/p>\n

    <\/p>\n

  • \u0905\u0928\u0941\u0917\u093e\u092e\u0940 \u092e\u0949\u0921\u0932 (Numerical Models)<\/li>\n
  • \u0928\u0935\u0940\u0928\u0924\u092e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e<\/li>\n
  • \u0921\u0947\u091f\u093e \u0905\u0938\u093f\u092e\u093f\u0932\u0947\u0936\u0928 \u0924\u0915\u0928\u0940\u0915<\/li>\n

    <\/u1><\/p>\n

    \u0905\u0928\u0941\u0917\u093e\u092e\u0940 \u092e\u0949\u0921\u0932 \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092e\u0939\u093e\u0938\u093e\u0917\u0930\u094b\u0902 \u0915\u0947 \u091c\u0932 \u0915\u0940 \u0917\u0924\u093f \u0914\u0930 \u0924\u093e\u092a\u092e\u093e\u0928 \u0915\u093e \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u093e\u0923\u0940 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0928\u0935\u0940\u0928\u0924\u092e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0907\u0928 \u092e\u0949\u0921\u0932\u094b\u0902 \u0915\u094b \u0914\u0930 \u092d\u0940 \u092a\u0930\u093f\u0937\u094d\u0915\u0943\u0924 \u0914\u0930 \u0938\u091f\u0940\u0915 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0914\u0930 \u092d\u0940 \u092a\u094d\u0930\u093e\u092e\u093e\u0923\u093f\u0915 \u092a\u0930\u093f\u0923\u093e\u092e \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n

    \u0905\u0928\u0941\u0917\u093e\u092e\u0940 \u092e\u0949\u0921\u0932 \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923<\/h2>\n

    \u0938\u093f\u0902\u092a\u0932 \u0905\u0928\u0941\u0917\u093e\u092e\u0940 \u092e\u0949\u0921\u0932 \u091c\u094b \u0935\u0947\u0932\u093f\u0915\u0932\u0941 (Velocity) \u0914\u0930 \u092b\u0949\u0930\u094d\u0938\u093f\u0902\u0917 (Forcing) \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u092e\u0947\u0902 \u0930\u0916\u0915\u0930 \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n

    \\[
    \n\\frac{du}{dt} + u \\cdot \\nabla u = – \\frac{1}{\\rho} \\nabla p + \\nu \\Delta u + f
    \n\\]\n

    \u092f\u0939\u093e\u0901 \u092a\u0930:<\/p>\n

    <\/p>\n

  • \u0926\u094b \/ dt = \u0924\u094d\u0935\u0930\u0923<\/li>\n
  • u = \u0935\u0947\u0932\u093f\u0915\u0932\u0941 \u092b\u0940\u0932\u094d\u0921<\/li>\n
  • \\rho = \u0918\u0928\u0924\u094d\u0935<\/li>\n
  • p = \u0926\u092c\u093e\u0935<\/li>\n
  • \\nu = \u0935\u0947\u0917 \u0935\u093f\u0938\u094d\u0915\u094b\u0938\u093f\u091f\u0940<\/li>\n
  • f = \u092c\u093e\u0939\u0930\u0940 \u092b\u094b\u0930\u094d\u0938\u093f\u0902\u0917<\/li>\n

    <\/u1><\/p>\n

    \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092e\u0949\u0921\u0932 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0921\u0947\u091f\u093e \u0905\u0938\u093f\u092e\u093f\u0932\u0947\u0936\u0928 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947 \u092c\u0947\u0939\u0924\u0930 \u092c\u0928\u093e\u090f \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u092e\u0939\u093e\u0938\u093e\u0917\u0930 \u092a\u0930\u093f\u0938\u0902\u091a\u0930\u0923 \u0915\u0947 \u0914\u0930 \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u092e\u093f\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n

    \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n

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