solver: heat flow through each heat load, and the imbalance (#362)

solve.heat's reply and the results report give heat_flows: each convection,
flux and source load's heat into the body, the prescribed temperatures'
total and their sum; the results panel lists them for a heat step.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/ui-egui/src/results_panel.rs

@@ -212,6 +212,9 @@ pub fn controls(app: &mut ModelApp, plot: &Plot, ui: &mut egui::Ui, t: &Tokens)
                 }
             }
         });
+    } else if let Kind::Heat(h) = plot.result.kind() {
+        ui.separator();
+        heat_flows(ui, &fieldcraft_engine::results::heat_flows(h), t);
     } else {
         ui.separator();
         if ui.button("Reaction sums").on_hover_text("Reaction force and moment per boundary-condition set (results.reactions)").clicked() {
@@ -287,6 +290,24 @@ fn explicit(ui: &mut egui::Ui, e: &ExplicitResult, plot: &Plot, t: &Tokens, run:
     });
 }
 
+/// A heat step's balance: the heat each heat load carries in (negative: out), the prescribed
+/// temperatures' total, and what is left over (about 0 when steady).
+fn heat_flows(ui: &mut egui::Ui, flows: &Value, t: &Tokens) {
+    ui.label(RichText::new("Heat flow into the body").color(t.text_dim));
+    egui::Grid::new("fc_results_heat").num_columns(2).spacing(vec2(8.0, 2.0)).show(ui, |ui| {
+        let row = |ui: &mut egui::Ui, name: &str, v: Option<f64>| {
+            ui.label(name);
+            ui.label(v.map_or("—".into(), number));
+            ui.end_row();
+        };
+        for l in flows["loads"].as_array().into_iter().flatten() {
+            row(ui, &format!("{} ({})", l["name"].as_str().unwrap_or("?"), l["type"].as_str().unwrap_or("").replace('_', " ")), l["heat"].as_f64());
+        }
+        row(ui, "Prescribed temperatures", flows["reactions"].as_f64());
+        row(ui, "Imbalance", flows["imbalance"].as_f64());
+    });
+}
+
 fn reactions_table(ui: &mut egui::Ui, r: &Value, t: &Tokens) {
     let row = |ui: &mut egui::Ui, name: &str, v: &Value| {
         let f = |k: usize| v.pointer(&format!("/force/{k}")).and_then(Value::as_f64).map_or("—".into(), number);