Updated formulation for Biot number calculation

.github/workflows/ci.yml

@@ -181,7 +181,7 @@ jobs:
           python-version: ${{ env.MAIN_PYTHON_VERSION }}
 
       - name: Download package
-        uses: actions/download-artifact@018cc2cf5baa6db3ef3c5f8a56943fffe632ef53 # v6.0.0
+        uses: actions/download-artifact@37930b1c2abaa49bbe596cd826c3c89aef350131 # v7.0.0
         with:
           name: ${{ env.PACKAGE_NAME }}-artifacts
           path: dist
@@ -264,7 +264,7 @@ jobs:
           python-version: ${{ env.MAIN_PYTHON_VERSION }}
 
       - name: Download package
-        uses: actions/download-artifact@018cc2cf5baa6db3ef3c5f8a56943fffe632ef53 # v6.0.0
+        uses: actions/download-artifact@37930b1c2abaa49bbe596cd826c3c89aef350131 # v7.0.0
         with:
           name: ${{ env.PACKAGE_NAME }}-artifacts
           path: dist
@@ -326,7 +326,7 @@ jobs:
       #    extra_mem_top: 30000000
 
       - name: Upload HTML Documentation
-        uses: actions/upload-artifact@330a01c490aca151604b8cf639adc76d48f6c5d4 # v5.0.0
+        uses: actions/upload-artifact@b7c566a772e6b6bfb58ed0dc250532a479d7789f # v6.0.0
         with:
           name: documentation-html
           path: doc/_build/html
@@ -369,7 +369,7 @@ jobs:
     steps:
 
       - name: "Download the library artifacts from build-library step"
-        uses: actions/download-artifact@018cc2cf5baa6db3ef3c5f8a56943fffe632ef53 # v6.0.0
+        uses: actions/download-artifact@37930b1c2abaa49bbe596cd826c3c89aef350131 # v7.0.0
         with:
           name: ${{ env.PACKAGE_NAME }}-artifacts
           path: ${{ env.PACKAGE_NAME }}-artifacts

examples/00-systemcoupling/cht_pipe.py

@@ -251,41 +251,74 @@
 mu_fluid = 0.001  # Dynamic viscosity of fluid
 cp_fluid = 4182  # Specific heat capacity of fluid
 k_fluid = 0.6  # Thermal conductivity of fluid
-k_solid = 1.2  # Thermal conductivity of solid
-
-
-def compute_thermo_numbers(rho, mu, cp, k_fluid, k_solid, velocity, L_c, n=0.4):
+k_solid = 237  # Thermal conductivity of solid
+
+
+def compute_thermo_numbers(
+    rho,
+    mu,
+    cp,
+    k_fluid,
+    k_solid,
+    velocity,
+    L_c,
+):
     """Compute Reynolds, Nusselt, h, and Biot numbers."""
 
     def reynolds_number(rho, mu, velocity, D_h):
-        """Reynolds number."""
         return (rho * velocity * D_h) / mu
 
-    def nusselt_number(Re, Pr, n):
-        """Dittus–Boelter Nusselt number."""
-        return 0.023 * (Re**0.8) * (Pr**n)
+    def nusselt_dittus_boelter(
+        Re,
+        Pr,
+    ):
+        # Formulation from: # Bergman, T. L., Lavine, A. S.,
+        # Incropera, F. P., & DeWitt, D. P. (2017).
+        # Fundamentals of heat and mass transfer (8th ed.). Wiley.
+        return 0.023 * Re**0.8 * Pr ** (1 / 3)
+
+    def hausen(Re, Pr):
+        return 3.66 + (0.068 * (Re * Pr * d_in / l)) / (
+            1 + 0.04 * (Re * Pr * d_in / l) ** (2 / 3)
+        )
 
     def biot_number(h, L_c, k_solid):
-        """Biot number."""
         return h * L_c / k_solid
 
+    # --- Dimensionless numbers ---
     Pr = (cp * mu) / k_fluid
     Re = reynolds_number(rho, mu, velocity, L_c)
-    Nu = nusselt_number(Re, Pr, n)
+
+    # --- Correlation selection ---
+    if Re < 6000:
+        Nu = hausen(Re, Pr)
+        correlation = "Hausen"
+    else:
+        Nu = nusselt_dittus_boelter(Re, Pr)
+        correlation = "Dittus–Boelter"
+
+    # --- Heat transfer coefficient ---
     h = Nu * k_fluid / L_c
     Bi = biot_number(h, L_c, k_solid)
 
-    return Re, Nu, h, Bi
+    return Re, Nu, h, Bi, correlation
 
 
-Re, Nu, h, Bi = compute_thermo_numbers(
-    fluid_rho, mu_fluid, cp_fluid, k_fluid, k_solid, U, L_c
+Re, Nu, h, Bi, corr = compute_thermo_numbers(
+    fluid_rho,
+    mu_fluid,
+    cp_fluid,
+    k_fluid,
+    k_solid,
+    U,
+    L_c,
 )
 
-print("Reynolds Number =", Re)
-print("Nusselt Number =", Nu)
-print("Heat Transfer Coefficient =", h)
-print("Biot Number =", Bi)
+print(f"Reynolds Number ={Re}")
+print(f"Nusselt Number ={Nu}")
+print(f"Heat Transfer Coefficient={h}")
+print(f"Biot number= {Bi}")
+print(f"Nusselt number correlation used= {corr}")
 
 # %%
 # Apply stabilization if Biot number exceeds 10.

pyproject.toml

@@ -71,10 +71,12 @@ doc = [
 	"sphinx-gallery==0.20.0",
 	"sphinx-notfound-page==1.1.0",
 	"sphinxcontrib-websupport==2.0.0",
-	"sphinxemoji==0.3.1",
+	"sphinxemoji==0.3.2",
 
 	# pyansys dependencies for sphinx gallery examples
 	"ansys-fluent-core==0.35.0",
+	# ... temporary to fix fluent runtime error: 
+	"ansys-units==0.9.1", 
 	"ansys-mapdl-core==0.71.3",
 ]
 style = [