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

@@ -251,42 +251,49 @@
 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
+k_solid = 237  # Thermal conductivity of solid
 
 
-def compute_thermo_numbers(rho, mu, cp, k_fluid, k_solid, velocity, L_c, n=0.4):
-    """Compute Reynolds, Nusselt, h, and Biot numbers."""
+def nusselt_number(Re, Pr, d_in, L):
+    # From: Bergman, T. L., Lavine, A. S., Incropera, F. P., & DeWitt, D. P. (2017).
+    # Fundamentals of Heat and Mass transfer (8th ed.). Wiley.
+    if Re >= 6000:
+        Nu = 0.023 * Re**0.8 * Pr ** (1 / 3)
+        method = "Colburn"
+    else:
+        Nu = 3.66 + (0.068 * (Re * Pr * d_in / L)) / (
+            1 + 0.04 * (Re * Pr * d_in / L) ** (2 / 3)
+        )
+        method = "Hausen"
 
-    def reynolds_number(rho, mu, velocity, D_h):
-        """Reynolds number."""
-        return (rho * velocity * D_h) / mu
+    return Nu, method
 
-    def nusselt_number(Re, Pr, n):
-        """Dittus–Boelter Nusselt number."""
-        return 0.023 * (Re**0.8) * (Pr**n)
 
-    def biot_number(h, L_c, k_solid):
-        """Biot number."""
-        return h * L_c / k_solid
+def compute_thermo_numbers(rho, mu, cp, k_fluid, k_solid, velocity, d_in, L, L_c):
+    Pr = cp * mu / k_fluid
+    Re = rho * velocity * d_in / mu
 
-    Pr = (cp * mu) / k_fluid
-    Re = reynolds_number(rho, mu, velocity, L_c)
-    Nu = nusselt_number(Re, Pr, n)
-    h = Nu * k_fluid / L_c
-    Bi = biot_number(h, L_c, k_solid)
+    # Nusselt number
+    Nu, correlation = nusselt_number(Re, Pr, d_in, L)
 
-    return Re, Nu, h, Bi
+    # Convective heat transfer coefficient
+    h = Nu * k_fluid / d_in
 
+    # Biot number
+    Bi = h * L_c / k_solid
+
+    return Re, Pr, h, Bi, correlation
 
-Re, Nu, h, Bi = 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)
+Re, Nu, h, Bi, corr = compute_thermo_numbers(
+    fluid_rho, mu_fluid, cp_fluid, k_fluid, k_solid, U, d_in, l, L_c
+)
 
+print(f"Reynolds number = {Re}")
+print(f"Nusselt number = {Nu}")
+print(f"Heat transfer coefficient h = {h} W/(m^2·K)")
+print(f"Biot number = {Bi}")
+print(f"Nusselt correlation used = {corr}")
 # %%
 # Apply stabilization if Biot number exceeds 10.
 if Bi > 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 = [